510 research outputs found

    Equilateral convex pentagons which tile the plane

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    AbstractIt is shown that an equilateral convex pentagon tiles the plane if and only if it has two angles adding to 180° or it is the unique equilateral convex pentagonwith angles A, B, C, D, E satisfying A + 2B = 360°, C + 2E = 360°, A + C +2D = 360° (A ≊ 70.88°, B ≊ 144.56, C ≊ 89.26°, D ≊ 99.93°, E ≊ 135.37°)

    Coarsening of Surface Structures in Unstable Epitaxial Growth

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    We study unstable epitaxy on singular surfaces using continuum equations with a prescribed slope-dependent surface current. We derive scaling relations for the late stage of growth, where power law coarsening of the mound morphology is observed. For the lateral size of mounds we obtain ξ∼t1/z\xi \sim t^{1/z} with z≥4z \geq 4. An analytic treatment within a self-consistent mean-field approximation predicts multiscaling of the height-height correlation function, while the direct numerical solution of the continuum equation shows conventional scaling with z=4, independent of the shape of the surface current.Comment: 15 pages, Latex. Submitted to PR

    Macrosegregation During Dendritic Arrayed Growth of Hypoeutectic Pb-Sn Alloys: Influence of Primary Arm Spacing and Mushy Zone Length

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    Thermosolutal convection in the dendritic mushy zone occurs during directional solidification of hypoeutectic lead tin alloys in a positive thermal gradient, with the melt on the top and the solid below. This results in macrosegregation along the length of the solidified samples. The extent of macrosegregation increases with increasing primary dendrite spacings for constant mushy zone length. For constant primary spacings, the macrosegregation increases with decreasing mushy zone length. Presence of convection reduces the primary dendrite spacings. However, convection in the interdendritic melt has significantly more influence on the spacings as compared with that in the overlying melt, which is caused by the solutal buildup at the dendrite tips

    Mushy-Zone Rayleigh Number to Describe Macrosegregation and Channel Segregate Formation During Directional Solidification of Metallic Alloys

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    A recently defined mushy-zone Rayleigh number (R-aM) that includes side-branching contributions to the mushy-zone permeability has been examined for its correlation with the longitudinal macrosegregation and channel segregate formation. The Rayleigh number shows (1) a strong correlation between the extent of longitudinal macrosegregation and increase in the mushy-zone convection and (2) a good ability to predict the formation of channel segregates during directional solidification

    Mushy Zone Morphology During Directional Solidification of Pb-5.8 Wt Pct Sb Alloy

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    The Pb-5.8 wt pet Sb alloy was directionally solidified with a positive thermal gradient of 140 K cm(-1) at a growth speed ranging from 0.8 to 30 mu m s(-1), and then it was quenched to retain the mushy zone morphology. The morphology of the mushy zone along its entire length has been characterized by using a serial sectioning and three-dimensional image reconstruction technique. Variation in the cellular/dendritic shape factor, hydraulic radius of the interdendritic region, and fraction solid along the mushy zone length has been studied. A comparison with predictions from theoretical models indicates that convection remarkably reduces the primary dendrite spacing while its influence on the dendrite tip radius is not as significant

    Eutectic colony formation: A phase field study

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    Eutectic two-phase cells, also known as eutectic colonies, are commonly observed during the solidification of ternary alloys when the composition is close to a binary eutectic valley. In analogy with the solidification cells formed in dilute binary alloys, colony formation is triggered by a morphological instability of a macroscopically planar eutectic solidification front due to the rejection by both solid phases of a ternary impurity that diffuses in the liquid. Here we develop a phase-field model of a binary eutectic with a dilute ternary impurity and we investigate by dynamical simulations both the initial linear regime of this instability, and the subsequent highly nonlinear evolution of the interface that leads to fully developed two-phase cells with a spacing much larger than the lamellar spacing. We find a good overall agreement with our recent linear stability analysis [M. Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a destabilization of the front by long-wavelength modes that may be stationary or oscillatory. A fine comparison, however, reveals that the assumption commonly attributed to Cahn that lamella grow perpendicular to the envelope of the solidification front is weakly violated in the phase-field simulations. We show that, even though weak, this violation has an important quantitative effect on the stability properties of the eutectic front. We also investigate the dynamics of fully developed colonies and find that the large-scale envelope of the composite eutectic front does not converge to a steady state, but exhibits cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.

    Cmr is a redox-responsive regulator of DosR that contributes to M. tuberculosis virulence.

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    Mycobacterium tuberculosis (MTb) is the causative agent of pulmonary tuberculosis (TB). MTb colonizes the human lung, often entering a non-replicating state before progressing to life-threatening active infections. Transcriptional reprogramming is essential for TB pathogenesis. In vitro, Cmr (a member of the CRP/FNR super-family of transcription regulators) bound at a single DNA site to act as a dual regulator of cmr transcription and an activator of the divergent rv1676 gene. Transcriptional profiling and DNA-binding assays suggested that Cmr directly represses dosR expression. The DosR regulon is thought to be involved in establishing latent tuberculosis infections in response to hypoxia and nitric oxide. Accordingly, DNA-binding by Cmr was severely impaired by nitrosation. A cmr mutant was better able to survive a nitrosative stress challenge but was attenuated in a mouse aerosol infection model. The complemented mutant exhibited a ∼2-fold increase in cmr expression, which led to increased sensitivity to nitrosative stress. This, and the inability to restore wild-type behaviour in the infection model, suggests that precise regulation of the cmr locus, which is associated with Region of Difference 150 in hypervirulent Beijing strains of Mtb, is important for TB pathogenesis

    Primary Dendrite Distribution and Disorder During Directional Solidification of Pb-Sb Alloys

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    Pb-2.2 wt pct Sb and Pb-5.8 wt pet Sb alloys have been directionally solidified from a single-crystal seed with its [100] orientation parallel to the growth direction, to examine the primary dendrite distribution and disorder of the dendrite arrays. The dendrite distribution and ordering have been investigated using analysis techniques such as the Gauss-amplitude fit to the frequency distribution of nearest and higher-order spacings, minimum spanning tree (MST), Voronoi polygon, and Fourier transform (FT) of the dendrite centers. Since the arrangement of dendrites is driven by the requirement to accommodate side-branch growth along the (100) directions, the FT images of the fully developed dendrite centers contain spots which indicate this preferred alignment. A directional solidification distance of about three mushy-zone lengths is sufficient to ensure a steady-state dendritic array, in terms of reaching a constant mean primary spacing. However, local dendrite ordering continues throughout the directional solidification process. The interdendritic convection not only decreases the mean primary spacing, it also makes the dendrite array more disordered and reduces the ratio of the upper and lower spacing limits, as defined by the largest 5 pct and the smallest 5 pct of the population

    The Fueling and Evolution of AGN: Internal and External Triggers

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    In this chapter, I review the fueling and evolution of active galactic nuclei (AGN) under the influence of internal and external triggers, namely intrinsic properties of host galaxies (morphological or Hubble type, color, presence of bars and other non-axisymmetric features, etc) and external factors such as environment and interactions. The most daunting challenge in fueling AGN is arguably the angular momentum problem as even matter located at a radius of a few hundred pc must lose more than 99.99 % of its specific angular momentum before it is fit for consumption by a BH. I review mass accretion rates, angular momentum requirements, the effectiveness of different fueling mechanisms, and the growth and mass density of black BHs at different epochs. I discuss connections between the nuclear and larger-scale properties of AGN, both locally and at intermediate redshifts, outlining some recent results from the GEMS and GOODS HST surveys.Comment: Invited Review Chapter to appear in LNP Volume on "AGN Physics on All Scales", Chapter 6, in press. 40 pages, 12 figures. Typo in Eq 5 correcte
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