Energy-based comparison between the Fourier--Galerkin method and the finite element method

The Fourier-Galerkin method (in short FFTH) has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom. Because the method incorporates the fast Fourier transform (FFT) in the linear solver, it is believed to provide an improvement in computational and memory requirements compared to the conventional finite element method (FEM). Here, we systematically compare these two methods using the energetic norm of local fields, which has the clear physical interpretation as being the error in the homogenised properties. This enables the comparison of memory and computational requirements at the same level of approximation accuracy. We show that the methods' effectiveness relies on the smoothness (regularity) of the solution and thus on the material coefficients. Thanks to its approximation properties, FEM outperforms FFTH for problems with jumps in material coefficients, while ambivalent results are observed for the case that the material coefficients vary continuously in space. FFTH profits from a good conditioning of the linear system, independent of the number of degrees of freedom, but generally needs more degrees of freedom to reach the same approximation accuracy. More studies are needed for other FFT-based schemes, non-linear problems, and dual problems (which require special treatment in FEM but not in FFTH).Comment: 24 pages, 10 figures, 2 table

The Formation of Population III Binaries from Cosmological Initial Conditions

Previous high resolution cosmological simulations predict the first stars to appear in the early universe to be very massive and to form in isolation. Here we discuss a cosmological simulation in which the central 50 solar mass clump breaks up into two cores, having a mass ratio of two to one, with one fragment collapsing to densities of 10^{-8} g/cc. The second fragment, at a distance of 800 astronomical units, is also optically thick to its own cooling radiation from molecular hydrogen lines, but is still able to cool via collision-induced emission. The two dense peaks will continue to accrete from the surrounding cold gas reservoir over a period of 10^5 years and will likely form a binary star system.Comment: Accepted by Science, first published online on July 9, 2009 in Science Express. 16 pages, 4 figures, includes supporting online materia

Testing Observational Techniques with 3D MHD Jets in Clusters

Observations of X-ray cavities formed by powerful jets from AGN in galaxy cluster cores are commonly used to estimate the mechanical luminosity of these sources. We test the reliability of observationally measuring this power with synthetic X-ray observations of 3-D MHD simulations of jets in a galaxy cluster environment. We address the role that factors such as jet intermittency and orientation of the jets on the sky have on the reliability of observational measurements of cavity enthalpy and age. An estimate of the errors in these quantities can be made by directly comparing ``observationally'' derived values with values from the simulations. In our tests, cavity enthalpy, age and mechanical luminosity derived from observations are within a factor of two of the simulation values.Comment: 4 pages, 3 figures; to appear in proceedings of The Monster's Fiery Breath: Feedback in Galaxies, Groups, and Clusters (AIP conference series

Spatial land-use inventory, modeling, and projection/Denver metropolitan area, with inputs from existing maps, airphotos, and LANDSAT imagery

A landscape model was constructed with 34 land-use, physiographic, socioeconomic, and transportation maps. A simple Markov land-use trend model was constructed from observed rates of change and nonchange from photointerpreted 1963 and 1970 airphotos. Seven multivariate land-use projection models predicting 1970 spatial land-use changes achieved accuracies from 42 to 57 percent. A final modeling strategy was designed, which combines both Markov trend and multivariate spatial projection processes. Landsat-1 image preprocessing included geometric rectification/resampling, spectral-band, and band/insolation ratioing operations. A new, systematic grid-sampled point training-set approach proved to be useful when tested on the four orginal MSS bands, ten image bands and ratios, and all 48 image and map variables (less land use). Ten variable accuracy was raised over 15 percentage points from 38.4 to 53.9 percent, with the use of the 31 ancillary variables. A land-use classification map was produced with an optimal ten-channel subset of four image bands and six ancillary map variables. Point-by-point verification of 331,776 points against a 1972/1973 U.S. Geological Survey (UGSG) land-use map prepared with airphotos and the same classification scheme showed average first-, second-, and third-order accuracies of 76.3, 58.4, and 33.0 percent, respectively

Employing pre-stress to generate finite cloaks for antiplane elastic waves

It is shown that nonlinear elastic pre-stress of neo-Hookean hyperelastic materials can be used as a mechanism to generate finite cloaks and thus render objects near-invisible to incoming antiplane elastic waves. This approach appears to negate the requirement for special cloaking metamaterials with inhomogeneous and anisotropic material properties in this case. These properties are induced naturally by virtue of the pre-stress. This appears to provide a mechanism for broadband cloaking since dispersive effects due to metamaterial microstructure will not arise.Comment: 4 pages, 2 figure

Cost-efficient manufacturing of composite structures

The Advanced Composites Technology (ACT) program is seeking research breakthroughs that will allow structures made of graphite epoxy materials to replace metals in the wings and fuselages of future aircrafts. NASA's goals are to reduce acquisition cost by 20 to 25 percent, structural weight for a resized aircraft by 40 to 50 percent, and the number of parts by half compared to current production aluminum aircraft. The innovative structural concepts, materials, and fabrication techniques emerging from the ACT program are described, and the relationship between aerospace developments and industrial, commercial, and sporting goods applications are discussed

How collective asperity detachments nucleate slip at frictional interfaces

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius $A_c$ governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding $x_\sigma$ presents a pseudo-gap $P(x_\sigma) \sim (x_\sigma)^\theta$, where $\theta$ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius $A_c$ diverges as a $\theta$-dependent power law of the system size. We discuss how these predictions can be tested experimentally

Theory for the density of interacting quasi-localised modes in amorphous solids

Quasi-localised modes appear in the vibrational spectrum of amorphous solids at low-frequency. Though never formalised, these modes are believed to have a close relationship with other important local excitations, including shear transformations and two-level systems. We provide a theory for their frequency density, $D_{L}(\omega)\sim\omega^{\alpha}$, that establishes this link for systems at zero temperature under quasi-static loading. It predicts two regimes depending on the density of shear transformations $P(x)\sim x^{\theta}$ (with $x$ the additional stress needed to trigger a shear transformation). If $\theta>1/4$, $\alpha=4$ and a finite fraction of quasi-localised modes form shear transformations, whose amplitudes vanish at low frequencies. If $\theta<1/4$, $\alpha=3+ 4 \theta$ and all quasi-localised modes form shear transformations with a finite amplitude at vanishing frequencies. We confirm our predictions numerically