2,423 research outputs found
Inducing Effect on the Percolation Transition in Complex Networks
Percolation theory concerns the emergence of connected clusters that
percolate through a networked system. Previous studies ignored the effect that
a node outside the percolating cluster may actively induce its inside
neighbours to exit the percolating cluster. Here we study this inducing effect
on the classical site percolation and K-core percolation, showing that the
inducing effect always causes a discontinuous percolation transition. We
precisely predict the percolation threshold and core size for uncorrelated
random networks with arbitrary degree distributions. For low-dimensional
lattices the percolation threshold fluctuates considerably over realizations,
yet we can still predict the core size once the percolation occurs. The core
sizes of real-world networks can also be well predicted using degree
distribution as the only input. Our work therefore provides a theoretical
framework for quantitatively understanding discontinuous breakdown phenomena in
various complex systems.Comment: Main text and appendices. Title has been change
The Age-Redshift Relationship of Old Passive Galaxies
We use 32 age measurements of passively evolving galaxies as a function of
redshift to test and compare the standard model (CDM) with the Universe. We show that the latter fits the data with a reduced
for a Hubble constant km
. By comparison, the optimal flat CDM
model, with two free parameters (including and km ), fits the age-\emph{z} data with a reduced .
Based solely on their values, both models appear to account
for the data very well, though the optimized CDM parameters are only
marginally consistent with those of the concordance model ( and km ). Fitting the age-
data with the latter results in a reduced . However,
because of the different number of free parameters in these models, selection
tools, such as the Akaike, Kullback and Bayes Information Criteria, favour
over CDM with a likelihood of
versus . These results are suggestive, though not yet
compelling, given the current limited galaxy age- sample. We carry out Monte
Carlo simulations based on these current age measurements to estimate how large
the sample would have to be in order to rule out either model at a confidence level. We find that if the real cosmology is CDM, a
sample of galaxy ages would be sufficient to rule out
at this level of accuracy, while galaxy ages would be required to
rule out CDM if the real Universe were instead .Comment: 36 pages, 13 figures, 1 table; accepted for publication in The
Astronomical Journal. arXiv admin note: text overlap with arXiv:1405.238
Discrete element modelling of material non-coaxiality in simple shear flows
We investigate the quasi-static simple shear flow of a two-dimensional assembly of cohesionless particles using discrete element method (DEM) simulations. We focus on the unsteady flow regime where the solid would experience significant evolution of stresses, mobilised shear strength and dilation. We construct the DEM model using a discretised-wall confined granular cell where the apparent boundary is allowed to dilate or contract synchronously with the confined solid. A rather uniform simple shear field is achieved across the whole assembly, which benefits rheological studies in generalising constitutive laws for continuum methods. We examine two aspects of the simple shear behaviour: macroscopic stress and strain rate evolution, particularly the non-coaxiality between the principal directions of the two; and micromechanics such as evolution of fabric. For an initially anisotropic specimen sheared under constant normal pressure, the direction of principal stress rotates towards that of the principal strain rate, gradually reducing the degree of non-coaxiality from about 45° to fluctuating around 0°. The rate in approaching coaxiality is slower in samples with larger initial porosity, stress ratio and mean stress. Generally, a faster rate in approaching coaxiality in simple shear is observed in a more dilatant sample, which often shows a larger degree of mobilised fabric anisotropy, suggesting the possible important role of instantaneous internal friction angle. The evolution of principal fabric direction resembles that of the principal stress direction
1,3-Dimethyl-5-(3-methylphenoxy)-1H-pyrazole-4-carbaldehyde
There are two independent molecules in the asymmetric unit of the title compound, C13H14N2O2, in which the dihedral angles between the substituted phenyl ring and the pyrazole ring are 86.5 (2) and 82.3 (3)°. The crystal packing features weak intermolecular C—H⋯O interactions
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