1,189 research outputs found
Mutual selection in time-varying networks
Copyright @ 2013 American Physical SocietyTime-varying networks play an important role in the investigation of the stochastic processes that occur on complex networks. The ability to formulate the development of the network topology on the same time scale as the evolution of the random process is important for a variety of applications, including the spreading of diseases. Past contributions have investigated random processes on time-varying networks with a purely random attachment mechanism. The possibility of extending these findings towards a time-varying network that is driven by mutual attractiveness is explored in this paper. Mutual attractiveness models are characterized by a linking function that describes the probability of the existence of an edge, which depends mutually on the attractiveness of the nodes on both ends of that edge. This class of attachment mechanisms has been considered before in the fitness-based complex networks literature but not on time-varying networks. Also, the impact of mutual selection is investigated alongside opinion formation and epidemic outbreaks. We find closed-form solutions for the quantities of interest using a factorizable linking function. The voter model exhibits an unanticipated behavior as the network never reaches consensus in the case of mutual selection but stays forever in its initial macroscopic configuration, which is a further piece of evidence that time-varying networks differ markedly from their static counterpart with respect to random processes that take place on them. We also find that epidemic outbreaks are accelerated by uncorrelated mutual selection compared to previously considered random attachment
Modeling temporal networks using random itineraries
We propose a procedure to generate dynamical networks with bursty, possibly
repetitive and correlated temporal behaviors. Regarding any weighted directed
graph as being composed of the accumulation of paths between its nodes, our
construction uses random walks of variable length to produce time-extended
structures with adjustable features. The procedure is first described in a
general framework. It is then illustrated in a case study inspired by a
transportation system for which the resulting synthetic network is shown to
accurately mimic the empirical phenomenology
The origin of aubrites: Evidence from lithophile trace element abundances and oxygen isotope compositions
We report the abundances of a selected set of “lithophile” trace elements (including lanthanides, actinides and high field strength elements) and high-precision oxygen isotope analyses of a comprehensive suite of aubrites. Two distinct groups of aubrites can be distinguished: (a) the main-group aubrites display flat or light-REE depleted REE patterns with variable Eu and Y anomalies; their pyroxenes are light-REE depleted and show marked negative Eu anomalies; (b) the Mount Egerton enstatites and the silicate fraction from Larned display distinctive light-REE enrichments, and high Th/Sm ratios; Mount Egerton pyroxenes have much less pronounced negative Eu anomalies than pyroxenes from the main-group aubrites.
Leaching experiments were undertaken to investigate the contribution of sulfides to the whole rock budget of the main-group aubrites. Sulfides contain in most cases at least 50% of the REEs and of the actinides. Among the elements we have analyzed, those displaying the strongest lithophile behaviors are Rb, Ba, Sr and Sc.
The homogeneity of the Δ17O values obtained for main-group aubrite falls [Δ17O = +0.009 ± 0.010‰ (2σ)] suggests that they originated from a single parent body whose differentiation involved an early phase of large-scale melting that may have led to the development of a magma ocean. This interpretation is at first glance in agreement with the limited variability of the shapes of the REE patterns of these aubrites. However, the trace element concentrations of their phases cannot be used to discuss this hypothesis, because their igneous trace-element signatures have been modified by subsolidus exchange. Finally, despite similar O isotopic compositions, the marked light-REE enrichments displayed by Mount Egerton and Larned suggest that they are unrelated to the main-group aubrites and probably originated from a distinct parent body
Thermalization of an anisotropic granular particle
We investigate the dynamics of a needle in a two-dimensional bath composed of
thermalized point particles. Collisions between the needle and points are
inelastic and characterized by a normal restitution coefficient . By
using the Enskog-Boltzmann equation, we obtain analytical expressions for the
translational and rotational granular temperatures of the needle and show that
these are, in general, different from the bath temperature. The translational
temperature always exceeds the rotational one, though the difference decreases
with increasing moment of inertia. The predictions of the theory are in very
good agreement with numerical simulations of the model.Comment: 7 pages, 6 Figures, submitted to PRE. Revised version (Fig1, Fig5 and
Fig6 corrected + minor typos
Crystal nucleation and cluster-growth kinetics in a model glass under shear
Crystal nucleation and growth processes induced by an externally applied
shear strain in a model metallic glass are studied by means of nonequilibrium
molecular dynamics simulations, in a range of temperatures. We observe that the
nucleation-growth process takes place after a transient, induction regime. The
critical cluster size and the lag-time associated with this induction period
are determined from a mean first-passage time analysis. The laws that describe
the cluster growth process are studied as a function of temperature and strain
rate. A theoretical model for crystallization kinetics that includes the time
dependence for nucleation and cluster growth is developed within the framework
of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the
molecular dynamics data. Scalings for the cluster growth laws and for the
crystallization kinetics are also proposed and tested. The observed nucleation
rates are found to display a nonmonotonic strain rate dependency
Local structure of liquid carbon controls diamond nucleation
Diamonds melt at temperatures above 4000 K. There are no measurements of the
steady-state rate of the reverse process: diamond nucleation from the melt,
because experiments are difficult at these extreme temperatures and pressures.
Using numerical simulations, we estimate the diamond nucleation rate and find
that it increases by many orders of magnitude when the pressure is increased at
constant supersaturation. The reason is that an increase in pressure changes
the local coordination of carbon atoms from three-fold to four-fold. It turns
out to be much easier to nucleate diamond in a four-fold coordinated liquid
than in a liquid with three-fold coordination, because in the latter case the
free-energy cost to create a diamond-liquid interface is higher. We speculate
that this mechanism for nucleation control is relevant for crystallization in
many network-forming liquids. On the basis of our calculations, we conclude
that homogeneous diamond nucleation is likely in carbon-rich stars and unlikely
in gaseous planets
On the singular homology of one class of simply-connected cell-like spaces
In our earlier papers we constructed examples of 2-dimensional nonaspherical
simply-connected cell-like Peano continua, called {\sl Snake space}. In the
sequel we introduced the functor defined on the category of all
spaces with base points and continuous mappings. For the circle , the
space is a Snake space. In the present paper we study the
higher-dimensional homology and homotopy properties of the spaces
for any path-connected compact spaces
Tetratic Order in the Phase Behavior of a Hard-Rectangle System
Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have found
two unusual phases in two-dimensional systems of anisotropic hard particles: a
tetratic phase of four-fold symmetry for hard squares [Comp. Methods in Science
and Tech., 10: 235-255, 2004], and a nonperiodic degenerate solid phase for
hard-disk dimers [Phys. Rev. Lett., 66: 3168-3171, 1991]. In this work, we
study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers
(or dominos), and demonstrate that it exhibits a solid phase with both of these
unusual properties. The solid shows tetratic, but not nematic, order, and it is
nonperiodic having the structure of a random tiling of the square lattice with
dominos. We obtain similar results with both a classical Monte Carlo method
using true rectangles and a novel molecular dynamics algorithm employing
rectangles with rounded corners. It is remarkable that such simple convex
two-dimensional shapes can produce such rich phase behavior. Although we have
not performed exact free-energy calculations, we expect that the random domino
tiling is thermodynamically stabilized by its degeneracy entropy, well-known to
be per particle from previous studies of the dimer problem on the
square lattice. Our observations are consistent with a KTHNY two-stage phase
transition scenario with two continuous phase transitions, the first from
isotropic to tetratic liquid, and the second from tetratic liquid to solid.Comment: Submitted for publicatio
Heterogeneous aging in spin glasses
We introduce a set of theoretical ideas that form the basis for an analytical
framework capable of describing nonequilibrium dynamics in glassy systems. We
test the resulting scenario by comparing its predictions with numerical
simulations of short-range spin glasses. Local fluctuations and responses are
shown to be connected by a generalized local out-of-equilibrium
fluctuation-dissipation relation. Scaling relationships are uncovered for the
slow evolution of heterogeneities at all time scales.Comment: Substantially reorganized to improve clarity of exposition. Accepted
for publication in Physical Review Letters. 5 pages, 4 figure
Low Friction Flows of Liquids at Nanopatterned Interfaces
With the recent important development of microfluidic systems,
miniaturization of flow devices has become a real challenge. Microchannels,
however, are characterized by a large surface to volume ratio, so that surface
properties strongly affect flow resistance in submicrometric devices. We
present here results showing that the concerted effect of wetting . properties
and surface roughness may considerably reduce friction of the fluid past the
boundaries. The slippage of the fluid at the channel boundaries is shown to be
drastically increased by using surfaces that are patterned at the nanometer
scale. This effect occurs in the regime where the surface pattern is partially
dewetted, in the spirit of the 'superhydrophobic' effects that have been
recently discovered at the macroscopic scales. Our results show for the first
time that, in contrast to the common belief, surface friction may be reduced by
surface roughness. They also open the possibility of a controlled realization
of the 'nanobubbles' that have long been suspected to play a role in
interfacial slippag
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