Theoretical and software considerations for nonlinear dynamic analysis

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented

The power of monitoring stellar orbits

The center of the Milky Way hosts a massive black hole. The observational evidence for its existence is overwhelming. The compact radio source Sgr A* has been associated with a black hole since its discovery. In the last decade, high-resolution, near-infrared measurements of individual stellar orbits in the innermost region of the Galactic Center have shown that at the position of Sgr A* a highly concentrated mass of 4 x 10^6 M_sun is located. Assuming that general relativity is correct, the conclusion that Sgr A* is a massive black hole is inevitable. Without doubt this is the most important application of stellar orbits in the Galactic Center. Here, we discuss the possibilities going beyond the mass measurement offered by monitoring these orbits. They are an extremely useful tool for many scientific questions, such as a geometric distance estimate to the Galactic Center or the puzzle, how these stars reached their current orbits. Future improvements in the instrumentation will open up the route to testing relativistic effects in the gravitational potential of the black hole, allowing to take full advantage of this unique laboratory for celestial mechanics.Comment: Proceedings of the Galactic Center Workshop 2009, Shangha

Happiness is assortative in online social networks

Social networks tend to disproportionally favor connections between individuals with either similar or dissimilar characteristics. This propensity, referred to as assortative mixing or homophily, is expressed as the correlation between attribute values of nearest neighbour vertices in a graph. Recent results indicate that beyond demographic features such as age, sex and race, even psychological states such as "loneliness" can be assortative in a social network. In spite of the increasing societal importance of online social networks it is unknown whether assortative mixing of psychological states takes place in situations where social ties are mediated solely by online networking services in the absence of physical contact. Here, we show that general happiness or Subjective Well-Being (SWB) of Twitter users, as measured from a 6 month record of their individual tweets, is indeed assortative across the Twitter social network. To our knowledge this is the first result that shows assortative mixing in online networks at the level of SWB. Our results imply that online social networks may be equally subject to the social mechanisms that cause assortative mixing in real social networks and that such assortative mixing takes place at the level of SWB. Given the increasing prevalence of online social networks, their propensity to connect users with similar levels of SWB may be an important instrument in better understanding how both positive and negative sentiments spread through online social ties. Future research may focus on how event-specific mood states can propagate and influence user behavior in "real life".Comment: 17 pages, 9 figure

An Inverse Compton Scattering Origin of X-ray Flares from Sgr A*

The X-ray and near-IR emission from Sgr A* is dominated by flaring, while a quiescent component dominates the emission at radio and sub-mm wavelengths. The spectral energy distribution of the quiescent emission from Sgr A* peaks at sub-mm wavelengths and is modeled as synchrotron radiation from a thermal population of electrons in the accretion flow, with electron temperatures ranging up to $\sim 5-20$\,MeV. Here we investigate the mechanism by which X-ray flare emission is produced through the interaction of the quiescent and flaring components of Sgr A*. The X-ray flare emission has been interpreted as inverse Compton, self-synchrotron-Compton, or synchrotron emission. We present results of simultaneous X-ray and near-IR observations and show evidence that X-ray peak flare emission lags behind near-IR flare emission with a time delay ranging from a few to tens of minutes. Our Inverse Compton scattering modeling places constraints on the electron density and temperature distributions of the accretion flow and on the locations where flares are produced. In the context of this model, the strong X-ray counterparts to near-IR flares arising from the inner disk should show no significant time delay, whereas near-IR flares in the outer disk should show a broadened and delayed X-ray flare.Comment: 22 pages, 6 figures, 2 tables, AJ (in press

Geometry of River Networks I: Scaling, Fluctuations, and Deviations

This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, we report here a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of sub-basin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density and show that fluctuations about scaling are substantial. We find strong deviations from scaling at small scales which can be explained by the existence of linear network structure. At intermediate scales, we find slow drifts in exponent values indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations and will not be improved by increases in network resolution.Comment: 16 pages, 13 figures, Revtex4, submitted to PR

High-speed Civil Transport Aircraft Emissions

Estimates are given for the emissions from a proposed high speed civil transport (HSCT). This advanced technology supersonic aircraft would fly in the lower stratosphere at a speed of roughly Mach 1.6 to 3.2 (470 to 950 m/sec or 920 to 1850 knots). Because it would fly in the stratosphere at an altitude in the range of 15 to 23 km commensurate with its design speed, its exhaust effluents could perturb the chemical balance in the upper atmosphere. The first step in determining the nature and magnitude of any chemical changes in the atmosphere resulting from these proposed aircraft is to identify and quantify the chemically important species they emit. Relevant earlier work is summarized, dating back to the Climatic Impact Assessment Program of the early 1970s and current propulsion research efforts. Estimates are provided of the chemical composition of an HSCT's exhaust, and these emission indices are presented. Other aircraft emissions that are not due to combustion processes are also summarized; these emissions are found to be much smaller than the exhaust emissions. Future advances in propulsion technology, in experimental measurement techniques, and in understanding upper atmospheric chemistry may affect these estimates of the amounts of trace exhaust species or their relative importance

Nonequilibrium phase transitions in models of adsorption and desorption

The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of particles is finite to one in which it grows linearly in time. The exponents characterizing the mass distribution near the critical point are calculated in all dimensions.Comment: 10 pages, 2 figures (To appear in Phys. Rev. E

Stochastic analysis of surface roughness

For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method was applied to different road surface profiles which were measured with high resolution. Evidence of Markov properties is shown. Estimations for the parameters of the Fokker-Planck equation are based on pure, parameter free data analysis

Residual Strength Predictions with Crack Buckling

Fracture tests were conducted on middle crack tension, M(T), and compact tension, C(T), specimens of varying widths, constructed from 0.063 inch thick sheets of 2024-T3 aluminum alloy. Guide plates were used to restrict out-of-plane displacements in about half of the tests. Analyses using the three-dimensional, elastic-plastic finite element code WARP3D simulated the tests with and without guide plates using a critical CTOA fracture criterion. The experimental results indicate that crack buckling reduced the failure loads by up to 40%. Using a critical CTOA value of 5.5 deg., the WARP3D analyses predicted the failure loads for the tests with guide plates within +/- 10% of the experimentally measured values. For the M(T) tests without guide plates, the WARP3D analyses predicted the failure loads for the 12 and 24 inch tests within 10%, while over predicting the failure loads for the 40 inch wide tests by about 20%

The two states of Sgr A* in the near-infrared: bright episodic flares on top of low-level continuous variability

In this paper we examine properties of the variable source Sgr A* in the near-infrared (NIR) using a very extensive Ks-band data set from NACO/VLT observations taken 2004 to 2009. We investigate the variability of Sgr A* with two different photometric methods and analyze its flux distribution. We find Sgr A* is continuously emitting and continuously variable in the near-infrared, with some variability occurring on timescales as long as weeks. The flux distribution can be described by a lognormal distribution at low intrinsic fluxes (<~5 mJy, dereddened with A_{Ks}=2.5). The lognormal distribution has a median flux of approximately 1.1 mJy, but above 5 mJy the flux distribution is significantly flatter (high flux events are more common) than expected for the extrapolation of the lognormal distribution to high fluxes. We make a general identification of the low level emission above 5 mJy as flaring emission and of the low level emission as the quiescent state. We also report here the brightest Ks-band flare ever observed (from August 5th, 2008) which reached an intrinsic Ks-band flux of 27.5 mJy (m_{Ks}=13.5). This flare was a factor 27 increase over the median flux of Sgr A*, close to double the brightness of the star S2, and 40% brighter than the next brightest flare ever observed from Sgr~A*.Comment: 14 pages, 6 figures, accepted for publication in Ap