Matchings from a set below to a set above

AbstractOne way to represent a matching in a graph of a set A with a set B is with a one-to-one function m : A → B for which each pair {a, m(a)} is an edge of the graph. If the underlying set of vertices of the graph is linearly ordered and every element of A is less than every element of B, then such a matching is a down-up matching. In this paper we investigate graphs on well-ordered sets of type α and in many circumtances find either large independent sets of type β or down-up matchings with the initial set of some prescribed size γ. In this case we write α → (β, γ-matching)

Three-dimensional imaging and detection efficiency performance of orthogonal coplanar CZT strip detectors

We report on recent three-dimensional imaging performance and detection efficiency measurements obtained with 5 mm thick prototype CdZnTe detectors fabricated with orthogonal coplanar anode strips. In previous work, we have shown that detectors fabricated using this design achieve both very good energy resolution and sub-millimeter spatial resolution with fewer electronic channels than are required for pixel detectors. As electron-only devices, like pixel detectors, coplanar anode strip detectors can be fabricated in the thickness required to be effective imagers for photons with energies in excess of 500 keV. Unlike conventional double-sided strip detectors, the coplanar anode strip detectors require segmented contacts and signal processing electronics on only one surface. The signals can be processed to measure the total energy deposit and the photon interaction location in three dimensions. The measurements reported here provide a quantitative assessment of the detection capabilities of orthogonal coplanar anode strip detectors

The Role of Solid Friction in the Sedimentation of Strongly Attractive Colloidal Gels

We study experimentally and theoretically the sedimentation of gels made of strongly aggregated colloidal particles, focussing on the long time behavior, when mechanical equilibrium is asymptotically reached. The asymptotic gel height is found to vary linearly with the initial height, a finding in stark contrast with a recent study on similar gels [Manley \textit{et al.} 2005 \textit{Phys. Rev. Lett.} \textbf{94} 218302]. We show that the asymptotic compaction results from the balance between gravity pull, network elasticity, and solid friction between the gel and the container walls. Based on these ingredients, we propose a simple model to account for the dependence of the height loss on the initial height and volume fraction. As a result of our analysis, we show that the static friction coefficient between the gel and the container walls strongly depends on volume fraction: the higher the volume fraction, the weaker the solid friction. This nonintuitive behavior is explained using simple scaling arguments.Comment: 13 pages, 5 figures. Submitted to JSTA

Shearing a Glassy Material: Numerical Tests of Nonequilibrium Mode-Coupling Approaches and Experimental Proposals

The predictions of a nonequilibrium schematic mode-coupling theory developed to describe the nonlinear rheology of soft glassy materials have been numerically challenged in a sheared binary Lennard-Jones mixture. The theory gives an excellent description of the stress/temperature `jamming phase diagram' of the system. In the present paper, we focus on the issue of an effective temperature Teff for the slow modes of the fluid, as defined from a generalized fluctuation-dissipation theorem. As predicted theoretically, many different observables are found to lead to the same value of Teff, suggesting several experimental procedures to measure Teff. New, simple experimental protocols to access Teff from a generalized equipartition theorem are also proposed, and one such experiment is numerically performed. These results give strong support to the thermodynamic interpretation of Teff and make it experimentally accessible in a very direct way.Comment: Version accepted for publication - Physical Review Letter

Statistics of counter-streaming solar wind suprathermal electrons at solar minimum : STEREO observations

Previous work has shown that solar wind suprathermal electrons can display a number of features in terms of their anisotropy. Of importance is the occurrence of counter-streaming electron patterns, i.e., with "beams" both parallel and anti-parallel to the local magnetic field, which is believed to shed light on the heliospheric magnetic field topology. In the present study, we use STEREO data to obtain the statistical properties of counter-streaming suprathermal electrons (CSEs) in the vicinity of corotating interaction regions (CIRs) during the period March–December 2007. Because this period corresponds to a minimum of solar activity, the results are unrelated to the sampling of large-scale coronal mass ejections, which can lead to CSE owing to their closed magnetic field topology. The present study statistically confirms that CSEs are primarily the result of suprathermal electron leakage from the compressed CIR into the upstream regions with the combined occurrence of halo depletion at 90° pitch angle. The occurrence rate of CSE is found to be about 15–20% on average during the period analyzed (depending on the criteria used), but superposed epoch analysis demonstrates that CSEs are preferentially observed both before and after the passage of the stream interface (with peak occurrence rate >35% in the trailing high speed stream), as well as both inside and outside CIRs. The results quantitatively show that CSEs are common in the solar wind during solar minimum, but yet they suggest that such distributions would be much more common if pitch angle scattering were absent. We further argue that (1) the formation of shocks contributes to the occurrence of enhanced counter-streaming sunward-directed fluxes, but does not appear to be a necessary condition, and (2) that the presence of small-scale transients with closed-field topologies likely also contributes to the occurrence of counter-streaming patterns, but only in the slow solar wind prior to CIRs