On two problems in graph Ramsey theory

We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of H. A famous result of Chv\'atal, R\"{o}dl, Szemer\'edi and Trotter states that there exists a constant c(\Delta) such that r(H) \leq c(\Delta) n for every graph H with n vertices and maximum degree \Delta. The important open question is to determine the constant c(\Delta). The best results, both due to Graham, R\"{o}dl and Ruci\'nski, state that there are constants c and c' such that 2^{c' \Delta} \leq c(\Delta) \leq 2^{c \Delta \log^2 \Delta}. We improve this upper bound, showing that there is a constant c for which c(\Delta) \leq 2^{c \Delta \log \Delta}. The induced Ramsey number r_{ind}(H) of a graph H is the least positive integer N for which there exists a graph G on N vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of H. Erd\H{o}s conjectured the existence of a constant c such that, for any graph H on n vertices, r_{ind}(H) \leq 2^{c n}. We move a step closer to proving this conjecture, showing that r_{ind} (H) \leq 2^{c n \log n}. This improves upon an earlier result of Kohayakawa, Pr\"{o}mel and R\"{o}dl by a factor of \log n in the exponent.Comment: 18 page

Blobs in Wolf-Rayet Winds: Random Photometric and Polarimetric Variability

Some isolated Wolf-Rayet stars present random variability in their optical flux and polarization. We make the assumption that such variability is caused by the presence of regions of enhanced density, i.e. blobs, in their envelopes. In order to find the physical characteristics of such regions we have modeled the stellar emission using a Monte Carlo code to treat the radiative transfer in an inhomogeneous electron scattering envelope. We are able to treat multiple scattering in the regions of enhanced density as well as in the envelope itself. The finite sizes of the source and structures in the wind are also taken into account. Most of the results presented here are based on a parameter study of models with a single blob. The effects due to multiple blobs in the envelope are considered to a more limited extent. Our simulations indicate that the density enhancements must have a large geometric cross section in order to produce the observed photopolarimetric variability. The sizes must be of the order of one stellar radius and the blobs must be located near the base of the envelope. These sizes are the same inferred from the widths of the sub-peaks in optical emission lines of Wolf-Rayet stars. Other early-type stars show random polarimetric fluctuations with characteristics similar to those observed in Wolf-Rayet stars, which may also be interpreted in terms of a clumpy wind. Although the origin of such structures is still unclear, the same mechanism may be working in different types of hot stars envelopes to produce such inhomogeneities.Comment: Accepted to ApJ. 17 pages + 6 figure

Preliminary results from the STEPHI2009 campaign on the open cluster NGC 1817

We present preliminary observational results of the multi-site STEPHI campaign on the cluster NGC 1817. The three observatories involved are San Pedro Martir (Mexico), Xing Long (China) and the Observatorio del Teide (Spain) - giving an ideal combination to maximise the duty cycle. The cluster has 12 known delta Scuti stars and at least two detached eclipsing binary systems. This combination of characteristics is ideal for extracting information about global parameters of the targets, which will in turn impose strict constraints on the stellar models. From an initial comparison with stellar models using the known fundamental parameters, and just the observed pulsation frequencies and measured effective temperatures, it appears that a lower value of initial helium mass fraction will most likely explain the observations of these stars.Comment: 4 pages, proceedings from HELAS IV meeting 2010, Lanzarot

Pulsational frequencies of the eclipsing delta-Scuti star HD 172189

The eclipsing delta-Scuti star HD 172189 is a probable member of the open cluster IC 4756 and a promising candidate target for the CoRoT mission. The detection of pulsation modes is the first step in the asteroseismological study of the star. Further, the calculation of the orbital parameters of the binary system allows us to make a dynamical determination of the mass of the star, which works as an important constraint to test and calibrate the asteroseismological models. From a detailed frequency analysis of 210 hours of photometric data of HD 172189 obtained from the STEPHI XIII campaign we have identified six pulsation frequencies with a confidence level of 99% and a seventh with a 65% confidence level in the range between 100-300 uHz. In addiction, three eclipses were observed during the campaign, allowing us to improve the determination of the orbital period of the system.Comment: 6 pages, 7 figure

A revised CNCPS feed carbohydrate fractionation scheme for formulating rations for ruminants

Balancing ruminant diets for appropriate levels and types of dietary carbohydrates (CHO) is necessary to maximize production while assuring the health of the animals. Several feed fractions (i.e., volatile fatty acids (VFA), lactate, sugars, starch) are now being measured in some commercial feed laboratories and this information may assist in better formulating diets. A CHO fractionation scheme based on ruminal degradation characteristics needed for nutritional models is described and its impact on predictions with the Cornell Net Carbohydrate and Protein System (CNCPS) is assessed. Dietary CHO are divided into eight fractions: the CA1 is volatile fatty acids (VFA), CA2 is lactic acid, CA3 is other organic acids, CA4 is sugars, CB1 is starch, CB2 is soluble fiber, CB3 is available neutral detergent fiber (NDF), and CC is unavailable NDF. A Monte Carlo analysis was conducted with an example lactating dairy cow ration to compare the original CNCPS CHO scheme (CA=sugars and organic acids, CB1=starch and soluble fiber, CB2=available NDF, CC=unavailable NDF) with the developed CHO scheme. A database was used to obtain distributions and correlations of the feed inputs used in the schemes for the ingredients of the ration (corn and grass silages, high moisture corn, soybean meal, and distillers\u27 grains). The CHO fractions varied in a decreasing order as VFAs, soluble fiber, lactic acid, sugar, NDF, starch, and total non-fiber carbohydrates (NFC). Use of the expanded scheme in the CNCPS decreased the microbial CP production, which was sensitive (standard regression coefficient in parenthesis) to corn silage starch (0.55), grass silage NDF rate (0.46), high moisture corn grain starch rate (0.44), and corn silage NDF rate (0.33). Predicted ruminal NFC digestibility remained similar. The expanded CHO scheme provides a more appropriate feed description to account for variation in changes in silage quality and diet NFC composition. However, to fully account for differences in feed CHO utilization, further improvements in the methodology used to estimate the fractions and their corresponding degradation rates, inclusion of dietary factors in dry matter intake predictions, and prediction of ruminal VFA production and pH are necessary

Fluctuation-Response Relations for Multi-Time Correlations

We show that time-correlation functions of arbitrary order for any random variable in a statistical dynamical system can be calculated as higher-order response functions of the mean history of the variable. The response is to a ``control term'' added as a modification to the master equation for statistical distributions. The proof of the relations is based upon a variational characterization of the generating functional of the time-correlations. The same fluctuation-response relations are preserved within moment-closures for the statistical dynamical system, when these are constructed via the variational Rayleigh-Ritz procedure. For the 2-time correlations of the moment-variables themselves, the fluctuation-response relation is equivalent to an ``Onsager regression hypothesis'' for the small fluctuations. For correlations of higher-order, there is a new effect in addition to such linear propagation of fluctuations present instantaneously: the dynamical generation of correlations by nonlinear interaction of fluctuations. In general, we discuss some physical and mathematical aspects of the {\it Ans\"{a}tze} required for an accurate calculation of the time correlations. We also comment briefly upon the computational use of these relations, which is well-suited for automatic differentiation tools. An example will be given of a simple closure for turbulent energy decay, which illustrates the numerical application of the relations.Comment: 28 pages, 1 figure, submitted to Phys. Rev.

Mars atmospheric loss and isotopic fractionation by solar-wind-induced sputtering and photochemical escape

We examine the effects of loss of Mars atmospheric constituents by solar-wind-induced sputtering and by photochemical escape during the last 3.8 b.y. Sputtering is capable of efficiently removing all species from the upper atmosphere including the light noble gases; N is removed by photochemical processes as well. Due to diffusive separation (by mass) above the homopause, removal from the top of the atmosphere will fractionate the isotopes of each species with the lighter mass being preferentially lost. For C and O, this allows us to determine the size of nonatmospheric reservoirs that mix with the atmosphere; these reservoirs can be CO2 adsorbed in the regolith or H2O in the polar ice caps. We have constructed both simple analytical models and time-dependent models of the loss from and supply of volatiles to the Martian atmosphere

Quantifying Self-Organization with Optimal Predictors

Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we propose a new criterion, namely an internally-generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. We precisely define this complexity for spatially-extended dynamical systems, using the probabilistic ideas of mutual information and minimal sufficient statistics. This leads to a general method for predicting such systems, and a simple algorithm for estimating statistical complexity. The results of applying this algorithm to a class of models of excitable media (cyclic cellular automata) strongly support our proposal.Comment: Four pages, two color figure

Development of high-order realizable finite-volume schemes for quadrature-based moment method

Kinetic equations containing terms for spatial transport, gravity, fluid drag and particle-particle collisions can be used to model dilute gas-particle flows. However, the enormity of independent variables makes direct numerical simulation of these equations almost impossible for practical problems. A viable alternative is to reformulate the problem in terms of moments of velocity distribution. Recently, a quadrature-based moment method was derived by Fox for approximating solutions to kinetic equation for arbitrary Knudsen number. Fox also described 1st- and 2nd-order finite-volume schemes for solving the equations. The success of the new method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from moments. The moment-inversion algorithm does not work if the moments are non-realizable, meaning they do not correspond to a distribution function. Not all the finite-volume schemes lead to realizable moments. Desjardins et al. showed that realizability is guaranteed with the 1 st-order finite-volume scheme, but at the expense of excess numerical diffusion. In the present work, the nonrealizability of the standard 2 nd-order finite-volume scheme is demonstrated and a generalized idea for the development of high-order realizable finite-volume schemes for quadrature-based moment methods is presented. This marks a significant improvement in the accuracy of solutions using the quadrature-based moment method as the use of 1st-order scheme to guarantee realizability is no longer a limitation

Quasi Harmonic Lattice Dynamics and Molecular Dynamics calculations for the Lennard-Jones solids

We present Molecular Dynamics (MD), Quasi Harmonic Lattice Dynamics (QHLD) and Energy Minimization (EM) calculations for the crystal structure of Ne, Ar, Kr and Xe as a function of pressure and temperature. New Lennard-Jones (LJ) parameters are obtained for Ne, Kr and Xe to reproduce the experimental pressure dependence of the density. We employ a simple method which combines results of QHLD and MD calculations to achieve densities in good agreement with experiment from 0 K to melting. Melting is discussed in connection with intrinsic instability of the solid as given by the QHLD approximation. (See http://www.fci.unibo.it/~valle for related papers)Comment: 7 pages, 5 figures, REVte