List Colouring When The Chromatic Number Is Close To the Order Of The Graph

Ohba has conjectured [7] that if G has 2 (G)+1 or fewer vertices then the list chromatic number and chromatic number of G are equal. In this short note we prove the weaker version of the conjecture obtained by replacing 2 (G)+1 by * This research was partially supported by DIMACS and by CNRS/NSF collaboration grant. Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey.     

Packing triangles in a graph and its complement

How few edge‐disjoint triangles can there be in a graph G on n vertices and in its complement ? This question was posed by P. Erd?s, who noticed that if G is a disjoint union of two complete graphs of order n/2 then this number is n²/12 + o(n²). Erd?s conjectured that any other graph with n vertices together with its complement should also contain at least that many edge‐disjoint triangles. In this paper, we show how to use a fractional relaxation of the above problem to prove that for every graph G of order n, the total number of edge‐disjoint triangles contained in G and is at least n²/13 for all sufficiently large n. This bound improves some earlier results. We discuss a few related questions as well. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 203–216, 2004     

Photodissociation of HCl and small (HCl)m complexes in and on large Ar n clusters

Photodissociation experiments were carried out at 193 nm for single HCl molecules which are adsorbed on the surface of large Ar n clusters and small (HCl)m complexes which are embedded in the interior of these clusters. For the surface case the size dependence is measured for the average sizes n=140-1000. No cage exit events are observed in agreement with the substitutional position of the molecule deeply buried in the outermost shell. This result is confirmed by a molecular dynamics simulation of the pickup process under realistic conditions concerning the experiment and the interaction potentials. The calculations of the dissociation process employ the surface hopping model. For the embedded case the average sizes covered are m=3 and 6 and n=8-248. The kinetic energy of the H atom fragments is measured exhibiting peaks at zero and around 2.0 eV which mark completely caged and unperturbed fragments, respectively. The ratio of theses peaks strongly depends on the cluster size and agrees well with theoretical predictions for one and two closed icosahedral shells, in which the nonadiabatic coupling of all states was accounted for.     

Spreading of viscous fluid drops on a solid substrate assisted by thermal fluctuations

We study the spreading of viscous drops on a solid substrate, taking into account the effects of thermal fluctuations in the fluid momentum. A nonlinear stochastic lubrication equation is derived and studied using numerical simulations and scaling analysis. We show that asymptotically spreading drops admit self-similar shapes, whose average radii can increase at rates much faster than these predicted by Tanner's law. We discuss the physical realizability of our results for thin molecular and complex fluid films, and predict that such phenomenon can in principal be observed in various flow geometries.     

Diffusion of Active Ingredients in Textiles

Most practical textile models are based on a two scale approach: a one-dimensional fiber model and a fabric model, see Fan et al. (Commun Comput Phys 4(4):929–948, 2008). No meso-level is used in between, i.e. the yarn scale is neglected in this setup. For dense textile substrates this seems appropriate as the yarns connect everywhere, but for loose fabrics or scrims this approach cannot be kept. Specifically when one is interested in tracking an active component released by the fibers, the yarn level plays an important role. This is because the saturation vapor pressure will influence the release rate from the fibers, and its value will vary over the yarn cross-section. Therefore, in this work we present a three step multiscale model: the active component is tracked in the fiber, the yarn, and finally at the fabric level. At the fiber level a one-dimensional reduction to a non-linear diffusion equation is performed, and solved on an as needed basis. At the yarn level both a two-dimensional or a one-dimensional model can be applied, and finally the yarn result is upscaled to the fabric level.     

Mature or emerging markets: Competitive duopoly investment decisions

We develop a competitive investment model wherein two competing firms consider investing into two projects targeting, separately, a mature and an emerging market. The returns firms obtain from investments into these markets are assumed to follow an S-shaped curve and depend on both firms’ actions. Considering symmetric environments (in terms of investment opportunities), we find that different forms of interactions may arise (e.g., Prisoner’s Dilemma and Game of Chicken) and outline corresponding strategies that offer higher returns by exploiting first-mover advantages, cooperation opportunities and aggressive choices. We also discuss the market conditions that can lead to these outcomes. Finally, considering non-symmetric environments, we show that a firm may be better off when its competitor’s budget increases.     

Vibrational spectroscopy of (SO4(2-)).(H2O)n clusters, n=1-5: harmonic and anharmonic calculations and experiment

The vibrational spectroscopy of (SO4(2-)).(H2O)n is studied by theoretical calculations for n=1-5, and the results are compared with experiments for n=3-5. The calculations use both ab initio MP2 and DFT/B3LYP potential energy surfaces. Both harmonic and anharmonic calculations are reported, the latter with the CC-VSCF method. The main findings are the following: (1) With one exception (H2O bending mode), the anharmonicity of the observed transitions, all in the experimental window of 540-1850 cm(-1), is negligible. The computed anharmonic coupling suggests that intramolecular vibrational redistribution does not play any role for the observed linewidths. (2) Comparison with experiment at the harmonic level of computed fundamental frequencies indicates that MP2 is significantly more accurate than DFT/B3LYP for these systems. (3) Strong anharmonic effects are, however, calculated for numerous transitions of these systems, which are outside the present observation window. These include fundamentals as well as combination modes. (4) Combination modes for the n=1 and n=2 clusters are computed. Several relatively strong combination transitions are predicted. These show strong anharmonic effects. (5) An interesting effect of the zero point energy (ZPE) on structure is found for (SO4(2-)).(H2O)(5): The global minimum of the potential energy corresponds to a C(s) structure, but with incorporation of ZPE the lowest energy structure is C2v, in accordance with experiment. (6) No stable structures were found for (OH-).(HSO4-).(H2O)n, for n相似文献   

Predicted stability and structure of (HXeCCH)n (n=2 or 4) clusters and of crystalline HXeCCH

Ab initio calculations predict the existence of the dimer and tetramer of HXeCCH. The interaction energies are -6.66 and -19.40 kcal mol-1 for the dimer and tetramer, respectively. For both complexes, larger blue shifts of the Xe-H stretching mode are found, while the Xe-C stretching modes are slightly redshifted. The stability and structure of HXeCCH crystals is predicted by density functional theory calculations with periodic boundary conditions. Strong electrostatic interactions are found between the monomers in the crystal. The results are first evidence for the existence of crystalline materials made of a novel class of noble gas molecules.     

Embedding nearly-spanning bounded degree trees

We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − ε)n vertices, in terms of the expansion properties of G. As a result we show that for fixed d ≥ 2 and 0 < ε < 1, there exists a constant c = c(d, ε) such that a random graph G(n, c/n) contains almost surely a copy of every tree T on (1 − ε)n vertices with maximum degree at most d. We also prove that if an (n, D, λ)-graph G (i.e., a D-regular graph on n vertices all of whose eigenvalues, except the first one, are at most λ in their absolute values) has large enough spectral gap D/λ as a function of d and ε, then G has a copy of every tree T as above. Research supported in part by a USA-Israeli BSF grant, by NSF grant CCR-0324906, by a Wolfensohn fund and by the State of New Jersey. Research supported in part by USA-Israel BSF Grant 2002-133, and by grants 64/01 and 526/05 from the Israel Science Foundation. Research supported in part by NSF CAREER award DMS-0546523, NSF grant DMS-0355497, USA-Israeli BSF grant, and by an Alfred P. Sloan fellowship.