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 $\alpha<1$. 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 $SC(-,-)$ defined on the category of all spaces with base points and continuous mappings. For the circle $S^1$, the space $SC(S^1, \ast)$ is a Snake space. In the present paper we study the higher-dimensional homology and homotopy properties of the spaces $SC(Z, \ast)$ for any path-connected compact spaces $Z$

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 $1.79k_{B}$ 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