Two-temperature Ising model at an exact limit

Ankara : The Department of Physics and the Institute of Engineering and Sciences of Bilkent University, 2008.Thesis (Master's) -- Bilkent University, 2008.Includes bibliographical references leaves 37-39.We analyze the order-disorder transition for a two dimensional Ising model. We consider a ferromagnetic exchange interaction between the nearest neighbor Ising spins. The spin exchanges are introduced in two different temperatures, at infinite and finite temperatures. The model is first proposed by Præstgaard, Schmittmann, and Zia [1]. In this thesis, we look at a limit of the system where the spin exchange at infinite temperature proceeds at a very fast rate in one of the lattice direction (the “y−direction”). In the other direction (the “x−direction”), the spin exchange at a finite temperature is driven by one of several possible exchange dynamics such as Metropolis, Glauber, and exponential rates. We investigate an exact nonequilibrium stationary state solution of the model far from equilibrium. We apply basic stochastic formalisms such as the Master equation and the Fokker-Planck equation. Our main interest is to analyze the possibility of various types of phase transitions. Using the magnetization as a phase order parameter, we observe two kinds of phase transitions: transverse segregation and longitudinal segregation with respect to the direction x. We find analytically the transition temperature and the nonequilibrium stationary state for small magnetizations at an exact limit. We show that depending on the type of microscopic interaction (such as Metropolis, Glauber, exponential spin exchange rates) the transition temperature and the phase boundary vary. For some exchange rates, we observe no transverse segregation.Sanlı, CeydaM.S

Collective motion of macroscopic spheres floating on capillary ripples: Dynamic heterogeneity and dynamic criticality

When a dense monolayer of macroscopic slightly polydisperse spheres floats on chaotic capillary Faraday waves, a coexistence of large scale convective motion and caging dynamics typical for jammed systems is observed. We subtract the convective mean flow using a coarse graining and reveal subdiffusion for the caging time scales followed by a diffusive regime at later times. To test the system in the light of dynamic criticality, we apply the methods of dynamic heterogeneity to obtain the power-law divergent time and length scales as the floater concentration approaches the jamming point. We find that these are independent of the application of the coarse graining procedure. The critical exponents are consistent with those found in dense suspensions of colloids indicating universal stochastic dynamics.Comment: submitted, 6 pages, 3 figure

From antinode clusters to node clusters: The concentration dependent transition of floaters on a standing Faraday wave

A hydrophilic floating sphere that is denser than water drifts to an amplitude maximum (antinode) of a surface standing wave. A few identical floaters therefore organize into antinode clusters. However, beyond a transitional value of the floater concentration $\phi$, we observe that the same spheres spontaneously accumulate at the nodal lines, completely inverting the self-organized particle pattern on the wave. From a potential energy estimate we show (i) that at low $\phi$ antinode clusters are energetically favorable over nodal ones and (ii) how this situation reverses at high $\phi$, in agreement with the experiment.Comment: [accepted PRE 2014] 9 pages, 9 figure

Local variation of hashtag spike trains and popularity in Twitter

We draw a parallel between hashtag time series and neuron spike trains. In each case, the process presents complex dynamic patterns including temporal correlations, burstiness, and all other types of nonstationarity. We propose the adoption of the so-called local variation in order to uncover salient dynamics, while properly detrending for the time-dependent features of a signal. The methodology is tested on both real and randomized hashtag spike trains, and identifies that popular hashtags present regular and so less bursty behavior, suggesting its potential use for predicting online popularity in social media.Comment: 7 pages, 7 figure

The cumulative (a), <i>CDF</i>(Δ<i>τ</i>), and probability (b), <i>P</i>(Δ<i>τ</i>), distributions of the inter-hashtag spike intervals.

<p>We observe that <i>P</i>(Δ<i>τ</i>), for different classes of hashtags distinguished by their popularity, exhibits non-exponential features. The different colors correspond to those in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131704#pone.0131704.g002" target="_blank">Fig 2</a>. The legend provides the average popularity ⟨<i>p</i>⟩ in each hashtag class. The dash lines indicate the positions of 1 day, 2 days, and 3 days, where <i>P</i>(Δ<i>τ</i>) gives peaks for low <i>p</i> (pink symbols). The binning is varied from 8 minutes to 2 hours depending on <i>p</i>, e.g. 8 min. for high <i>p</i> (red-orange), 1.5 hour for moderate <i>p</i> (yellow-green-blue-purple), and 2 hours for low <i>p</i> (pink). All <i>P</i>(Δ<i>τ</i>) present maxima at 1 second, which is not shown to describe tails in a larger window.</p

Linear correlation of <i>L</i>_<i>V</i> through real hashtag spike trains.

<p>(a) The linear relations of the first and the second halves of the empirical spike trains, <i>L</i>_<i>V</i>(<i>t</i>₁) and <i>L</i>_<i>V</i>(<i>t</i>₂), respectively, are investigated. The legend ranks ⟨<i>p</i>⟩ in different colors and symbols. (b) The Pearson correlation coefficient <i>r</i>(<i>L</i>_<i>V</i>(<i>t</i>₁), <i>L</i>_<i>V</i>(<i>t</i>₂)) between these quantities shows that while the linear correlations through moderately popular spike trains give maximum values, <i>r</i> reaches the minimum values for both bursty (high <i>L</i>_<i>V</i> and low <i>p</i>) and regular (low <i>L</i>_<i>V</i> and high <i>p</i>) spike trains.</p

Ranking of popular hashtags.

<p>The first 40 most used hashtags are listed with the corresponding popularity <i>p</i>. The hashtags related to the debate and the presidential election such as ledebat, hollande, sarkozy, votehollande, france2012, and présidentielle are recognized.</p

Heterogeneity in the hashtag popularity <i>p</i> is shown in (a) Zipf-plot and (b) probability density function (PDF), <i>P</i>(<i>p</i>).

<p>(a) Diversity in <i>p</i> (frequency) is visible in a power-law scaling in the log-log plot. We rank hashtags from high <i>p</i> (left) to low <i>p</i> (right). Different colored shaded rectangles highlight the value of <i>p</i> from red and orange (high <i>p</i>) to purple and pink (low <i>p</i>). The percentages describe the overall contributions of the corresponding rectangles. (b) Similarly, <i>P</i>(<i>p</i>) obeys a slowly decaying function and presents a power-law distribution with a fat tail. The same colored schema in (a) is applied to visualize the contributions of different values of <i>p</i>.</p

Statistical inference of <i>L</i>_<i>V</i> and comparison between the real and the random hashtag spike trains.

<p>(a) Mean <i>μ</i> of the local variation <i>L</i>_<i>V</i> of single hashtag time series versus the logarithmic average popularity log₁₀⟨<i>p</i>⟩. The real hashtag propagation is described in blue circles, whereas red squares represent randomly selected hashtag activity from the real data set. The arrow indicates the decay of <i>μ</i>(<i>L</i>_<i>V</i>) when ⟨<i>p</i>⟩ increases, which shows that popular hashtags propagate regularly on the contrary to moderately popular hashtags presenting bursty time sequences. The bars indicate the corresponding standard deviations <i>σ</i>(<i>L</i>_<i>V</i>). (b) A standard <i>z</i>−values versus log₁₀⟨<i>p</i>⟩. While the random trains (red squares) with <i>z</i> ≈ 0 show the evidence of Poisson signals with mean <i>μ</i>₀(<i>L</i>_<i>V</i>) = 1, large and non-zero values of <i>z</i> for the real trains (blue circles) suggest the presence of temporal correlations.</p