The Principal Stresses and Planes in a Masonry Dam.

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Stresses in isostatic granular systems and emergence of force chains

Progress is reported on several questions that bedevil understanding of granular systems: (i) are the stress equations elliptic, parabolic or hyperbolic? (ii) how can the often-observed force chains be predicted from a first-principles continuous theory? (iii) How to relate insight from isostatic systems to general packings? Explicit equations are derived for the stress components in two dimensions including the dependence on the local structure. The equations are shown to be hyperbolic and their general solutions, as well as the Green function, are found. It is shown that the solutions give rise to force chains and the explicit dependence of the force chains trajectories and magnitudes on the local geometry is predicted. Direct experimental tests of the predictions are proposed. Finally, a framework is proposed to relate the analysis to non-isostatic and more realistic granular assemblies.Comment: 4 pages, 2 figures, Corrected typos and clkearer text, submitted to Phys. Rev. Let

Chandra Observations of NGC 4438: An Environmentally Damaged Galaxy in the Virgo Cluster

We present results from a 25 ksec CHANDRA ACIS-S observation of galaxies NGC4438 and NGC4435 in the Virgo Cluster. X-ray emission in NGC4438 is observed in a ~700 pc nuclear region, a 2.3 kpc spherical bulge, and a network of filaments extending 4-10 kpc to the W and SW of the galaxy. The X-ray emission in all 3 regions is highly correlated to similar features observed in Halpha. Spectra of the filaments and bulge are well represented by a 0.4 keV MEKAL model with combined 0.3-2 keV intrinsic luminosity of 1.24x10^{40}erg/s, electron densities ~ 0.02-0.04 cm^{-3}, cooling times of 400-700 Myr and X-ray gas mass <~ 3.7x10^8 Msolar. In the nuclear region of NGC4438 X-ray emission is seen from the nucleus and from two outflow bubbles extending 360(730) pc to the NW(SE) of the nucleus. The spectrum of the NW outflow bubble plus nucleus is well fitted by an absorbed (n_H=1.9x10^{21} cm^{-2}) 0.58 keV MEKAL plasma model plus a heavily absorbed (n_H = 2.9 x10^{22} cm^{-2}) Gamma = 2, power law component. The electron density, cooling time, and X-ray gas mass in the NW outflow are ~0.5 cm^{-3}, 30 Myr and 3.5x10^6 Msolar. Weak X-ray emission is observed in the central region of NGC4435 with the peak of the hard emission coincident with the galaxy's optical center; while the peak of the soft X-ray emission is displaced 316 pc to the NE. The spectrum of NGC 4435 is well fitted by a non-thermal power law plus a thermal component from 0.2-0.3 keV diffuse ISM gas. We argue that the X-ray properties of gas outside the nuclear region in NGC4438 and in NGC4435 favor a high velocity, off-center collision between these galaxies ~ 100 Myr ago; while the nuclear X-ray emitting outflow gas in NGC4438 has been heated only recently (within ~ 1-2 Myr) by shocks (v_s ~ 600 kms^{-1}) possibly powered by a central AGN.Comment: 40 pages, 7 figures; minor changes to conform to published version, improved spectral fits to NGC 4435, improved figures 3,5; new figures 6b,

Development of Stresses in Cohesionless Poured Sand

The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum below the apex (`the dip'). Recent work of the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for which the equations are elliptic within any elastic zones present .... This displacement field appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps. Philosophical Transactions A, Royal Society, submitted 02/9

A Connection between Star Formation in Nuclear Rings and their Host Galaxies

We present results from a photometric H-alpha survey of 22 nuclear rings, aiming to provide insight into their star formation properties, including age distribution, dynamical timescales, star formation rates, and galactic bar influence. We find a clear relationship between the position angles and ellipticities of the rings and those of their host galaxies, which indicates the rings are in the same plane as the disk and circular. We use population synthesis models to estimate ages of each H-alpha emitting HII region, which range from 1 Myr to 10 Myrs throughout the rings. We find that approximately half of the rings contain azimuthal age gradients that encompass at least 25% of the ring, although there is no apparent relationship between the presence or absence of age gradients and the morphology of the rings or their host galaxies. NGC1343, NGC1530, and NGC4321 show clear bipolar age gradients, where the youngest HII regions are located near the two contact points of the bar and ring. We speculate in these cases that the gradients are related to an increased mass inflow rate and/or an overall higher gas density in the ring, which would allow for massive star formation to occur on short timescales, after which the galactic rotation would transport the HII regions around the ring as they age. Two-thirds of the barred galaxies show correlation between the locations of the youngest HII region(s) in the ring and the location of the contact points, which is consistent with predictions from numerical modeling.Comment: 23 pages, 10 figures (7 color), 23 tables, accepted for publication in ApJS (Feb 08); NASA-GSFC, IAC, University of Maryland, STSc

Line Forces in Keplerian Circumstellar Disks and Precession of Nearly Circular Orbits

We examine the effects of optically thick line forces on orbiting circumstellar disks, such as occur around Be stars. For radially streaming radiation, line forces are only effective if there is a strong radial velocity gradient, as occurs, for example, in a line-driven stellar wind. However, within an orbiting disk, the radial shear of the azimuthal velocity leads to strong line-of-sight velocity velocity gradients along nonradial directions. As such, in the proximity of a stellar surface extending over a substantial cone angle, the nonradial stellar radiation can impart a significant line force, even in the case of purely circular orbits. Given the highly supersonic nature of orbital velocity variations, we use the Sobolev approximation, thereby extending to the disk case the standard CAK formalism developed for line-driven winds. We delineate the parameter regimes for which radiative forces might alter disk properties; but even when radiative forces are small, we analytically quantify higher-order effects in the linear limit, including the precession of weakly elliptical orbits. We find that optically thick line forces can have observable implications for the dynamics of disks around Be stars, including the generation of either prograde or retrograde precession in slightly eccentric orbits. However, our analysis suggests a net retrograde effect, in apparent contradiction with observed long-term variations of violet/red line profile asymmetries from Be stars, which are generally thought to result from prograde propagation of a so-called ``one arm mode''. We also conclude that radiative forces may alter the dynamical properties at the surface of the disk where disk winds originate, and may even make low-density disks vulnerable to being blown away.Comment: 31 pages, Latex, aaspp4 macro, 4 figure

A Close Look at Star Formation around Active Galactic Nuclei

We analyse star formation in the nuclei of 9 Seyfert galaxies at spatial resolutions down to 0.085arcsec, corresponding to length scales of less than 10pc in some objects. Our data were taken mostly with the near infrared adaptive optics integral field spectrograph SINFONI. The stellar light profiles typically have size scales of a few tens of parsecs. In two cases there is unambiguous kinematic evidence for stellar disks on these scales. In the nuclear regions there appear to have been recent - but no longer active - starbursts in the last 10-300Myr. The stellar luminosity is less than a few percent of the AGN in the central 10pc, whereas on kiloparsec scales the luminosities are comparable. The surface stellar luminosity density follows a similar trend in all the objects, increasing steadily at smaller radii up to 10^{13}L_sun/kpc^2 in the central few parsecs, where the mass surface density exceeds 10^4M_sun/pc^2. The intense starbursts were probably Eddington limited and hence inevitably short-lived, implying that the starbursts occur in multiple short bursts. The data hint at a delay of 50--100Myr between the onset of star formation and subsequent fuelling of the black hole. We discuss whether this may be a consequence of the role that stellar ejecta could play in fuelling the black hole. While a significant mass is ejected by OB winds and supernovae, their high velocity means that very little of it can be accreted. On the other hand winds from AGB stars ultimately dominate the total mass loss, and they can also be accreted very efficiently because of their slow speeds.Comment: 51 pages, including 27 figures; accepted by ApJ (paper reorganised, but results & conclusions the same

Chandra Observations of the Interacting NGC 4410 Galaxy Group

We present high resolution X-ray imaging data from the ACIS-S instrument on the Chandra telescope of the nearby interacting galaxy group NGC 4410. Four galaxies in the inner portion of this group are clearly detected by Chandra, including the peculiar low luminosity radio galaxy NGC 4410A. In addition to a nuclear point source, NGC 4410A contains diffuse X-ray emission, including an X-ray ridge extending out to about 12" (6 kpc) to the northwest of the nucleus. This ridge is coincident with an arc of optical emission-line gas, which has previously been shown to have optical line ratios consistent with shock ionization. This structure may be due to an expanding superbubble of hot gas caused by supernovae and stellar winds or by the active nucleus. The Chandra observations also show four or five possible compact ultra-luminous X-ray (ULX) sources (L(x) >= 10^39 erg/s) associated with NGC 4410A. At least one of these candidate ULXs appears to have a radio counterpart, suggesting that it may be due to an X-ray binary with a stellar-mass black hole, rather than an intermediate mass black hole. In addition, a faint diffuse intragroup X-ray component has been detected between the galaxies (L(x) ~ 10^41 erg/s). This supports the hypothesis that the NGC 4410 group is in the process of evolving via mergers from a spiral-dominated group (which typically have no X-ray-emitting intragroup gas) to an elliptical-dominated group (which often have a substantial intragroup medium).Comment: 27 pages, 14 figures; Accepted by Astronomical Journal; color images at http://www.etsu.edu/physics/bsmith/research/n4410.htm

Revealing the Nature of Algol Disks through Optical and UV Spectroscopy, Synthetic Spectra, and Tomography of TT Hydrae

We have developed a systematic procedure to study the disks in Algol-type binaries using spectroscopic analysis, synthetic spectra, and tomography. We analyzed 119 H-alpha spectra of TT Hya, an Algol-type eclipsing interacting binary, collected from 1985-2001. The new radial velocities enabled us to derive reliable orbital elements, including a small non-zero eccentricity, and to improve the accuracy of the absolute dimensions of the system. High resolution IUE spectra were also analyzed to study the formation of the ultraviolet lines and continuum. Synthetic spectra of the iron curtain using our new shellspec program enabled us to derive a characteristic disk temperature of 7000K. We have demonstrated that the UV emission lines seen during total primary eclipse cannot originate from the accretion disk, but most likely arise from a hotter disk-stream interaction region. The synthetic spectra of the stars, disk, and stream allowed us to derive a lower limit to the mass transfer rate of 2e-10 solar masses per year. Doppler tomography of the observed H-alpha profiles revealed a distinct accretion disk. The difference spectra produced by subtracting the synthetic spectra of the stars resulted in an image of the disk, which virtually disappeared once the composite synthetic spectra of the stars and disk were used to calculate the difference spectra. An intensity enhancement of the resulting tomogram revealed images of the gas stream and an emission arc. We successfully modeled the gas stream using shellspec and associated the emission arc with an asymmetry in the accretion disk.Comment: 46 pages, 15 figures, 6 tables, accepted by Ap

A survey of extended radio jets with Chandra and HST

We present the results from an X-ray and optical survey of a sample of 17 radio jets in AGN performed with Chandra and HST. The sample was selected from the radio and is unbiased toward detection at shorter wavelengths, but preferentially it includes beamed sources. We find that X-ray emission is common on kpc-scales, with over half radio jets exhibiting at least one X-ray knot on the Chandra images. The distributions of the radio-to-X-ray and radio-to-optical spectral indices for the detected jets are similar to the limits for the non-detections,suggesting all bright radio jets have X-ray counterparts which will be visible in longer observations. Comparing the radio and X-ray morphologies shows that the majority of the X-ray jets have structures that closely map the radio. Analysis of the SED of the jet knots suggest the knots in which the X-ray and radio morphologies track each other produce X-rays by IC scattering of the Cosmic Microwave Background. The remaining knots produce X-rays by the synchrotron process. Spectral changes are detected along the jets, with the ratio of the X-ray-to-radio and optical-to-radio flux densities decreasing from the inner to the outer regions. This suggests the presence of an additional contribution to the X-ray flux in the jet's inner part, either from synchrotron or IC of the stellar light. Alternatively, in a pure IC/CMB scenario, the plasma decelerates as it flows from the inner to the outer regions. Finally, the X-ray spectral indices for the brightest knots are flat, indicating that the bulk of the luminosity of the jets is emitted at GeV energies, and raising the interesting possibility of future detections with GLAST.Comment: 26 pages, 6 ps figures, 6 jpeg figures (1 replaced); accepted for publication in Ap