In the last 30 days

• Open/close Mode-coupling theory

  David R Reichman and Patrick Charbonneau J. Stat. Mech. (2005) P05013 Tag this article

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  In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the use the Mori–Zwanzig projection operator technique. We also derive schematic mode-coupling equations of a similar form from a field-theoretic perspective. We review the successes and failures of mode-coupling theory, and discuss recent advances in the applications of the theory.

• Open/close Crowding at the front of marathon packs

  Sanjib Sabhapandit et al J. Stat. Mech. (2008) L03001 Tag this article

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  We study the crowding of near-extreme events in the time gaps between successive finishers in major international marathons. Naively, one might expect these gaps to become progressively larger for better-placing finishers. While such an increase does indeed occur from the middle of the finishing pack down to approximately 20th place, the gaps saturate for the first 10–20 finishers. We give a probabilistic account of this feature. However, the data suggest that the gaps have a weak maximum around the 10th place, a feature that seems to have a sociological origin.

• Open/close Fast unfolding of communities in large networks

  Vincent D Blondel et al J. Stat. Mech. (2008) P10008 Tag this article

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  We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks.

• Open/close Phase-plane analysis of driven multi-lane exclusion models

  Vandana Yadav et al J. Stat. Mech. (2012) P04004 Tag this article

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  We show how a fixed-point-based boundary layer analysis technique can be used to obtain the steady-state particle density profiles of driven exclusion processes on two-lane systems with open boundaries. We have considered two distinct two-lane systems. In the first, particles hop on the lanes in one direction obeying the exclusion principle and there is no exchange of particles between the lanes. The hopping on one lane is affected by the particle occupancies on the other, which thereby introduces an indirect interaction among the lanes. Through a phase-plane analysis of the boundary layer equation, we show why the bulk density undergoes a sharp change as the interaction between the lanes is increased. The second system involves one lane with a driven exclusion process and the other with biased diffusion of particles. In contrast to the previous model, here there is a direct interaction between the lanes due to particle exchange between them. In this model, we have looked at two possible scenarios with constant (flat) and non-constant bulk profiles. The fixed-point-based boundary layer method provides a new perspective on several aspects including those related to maximal/minimal current phases, the possibilities of shocks under very restricted boundary conditions for the flat profile but over a wide range of boundary conditions for the non-constant profile.

• Open/close Spin-glass theory for pedestrians

  Tommaso Castellani and Andrea Cavagna J. Stat. Mech. (2005) P05012 Tag this article

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  In these notes the main theoretical concepts and techniques in the field of mean-field spin glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is analysed (the p-spin spherical model) by using three different approaches: thermodynamics, covering pure states, overlaps, overlap distribution, replica symmetry breaking, and the static transition; dynamics, covering the generating functional method, generalized Langevin equation, equations for the correlation and the response, the mode coupling approximation, and the dynamical transition; and finally complexity, covering the mean-field (Thouless–Anderson–Palmer) free energy, metastable states, entropy crisis, threshold energy, and saddles. Particular attention has been paid to the mutual consistency of the results obtained from the different methods.

• Open/close Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states

  R K P Zia and B Schmittmann J. Stat. Mech. (2007) P07012 Tag this article

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  One of the key features of non-equilibrium steady states (NESS) is the presence of non-trivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we specify the transformations of the dynamic transition rates which leave a given NESS invariant. The formalism is most transparent within a continuous-time master equation framework since it allows for a general graph-theoretical representation of the NESS. We discuss the consequences of these transformations for entropy production, present several simple examples, and explore some generalizations, to discrete time and continuous variables.

• Open/close Comparing community structure identification

  Leon Danon et al J. Stat. Mech. (2005) P09008 Tag this article

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  We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.

• Open/close How a finite potential barrier decreases the mean first-passage time

  Vladimir V Palyulin and Ralf Metzler J. Stat. Mech. (2012) L03001 Tag this article

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  We consider the mean first-passage time of a random walker moving in a potential landscape on a finite interval, the starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first-passage time for a piecewise linear curve between these two points is minimized by the introduction of a potential barrier. Due to thermal fluctuations, this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first-passage time is shorter than for a linear potential drop between the two points.

• Open/close Implementing the lattice Boltzmann model on commodity graphics hardware

  Arie Kaufman et al J. Stat. Mech. (2009) P06016 Tag this article

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  Modern graphics processing units (GPUs) can perform general-purpose computations in addition to the native specialized graphics operations. Due to the highly parallel nature of graphics processing, the GPU has evolved into a many-core coprocessor that supports high data parallelism. Its performance has been growing at a rate of squared Moore's law, and its peak floating point performance exceeds that of the CPU by an order of magnitude. Therefore, it is a viable platform for time-sensitive and computationally intensive applications.

  The lattice Boltzmann model (LBM) computations are carried out via linear operations at discrete lattice sites, which can be implemented efficiently using a GPU-based architecture. Our simulations produce results comparable to the CPU version while improving performance by an order of magnitude. We have demonstrated that the GPU is well suited for interactive simulations in many applications, including simulating fire, smoke, lightweight objects in wind, jellyfish swimming in water, and heat shimmering and mirage (using the hybrid thermal LBM).

  We further advocate the use of a GPU cluster for large scale LBM simulations and for high performance computing. The Stony Brook Visual Computing Cluster has been the platform for several applications, including simulations of real-time plume dispersion in complex urban environments and thermal fluid dynamics in a pressurized water reactor.

  Major GPU vendors have been targeting the high performance computing market with GPU hardware implementations. Software toolkits such as NVIDIA CUDA provide a convenient development platform that abstracts the GPU and allows access to its underlying stream computing architecture. However, software programming for a GPU cluster remains a challenging task. We have therefore developed the Zippy framework to simplify GPU cluster programming. Zippy is based on global arrays combined with the stream programming model and it hides the low-level details of the underlying cluster architecture.

• Open/close Continuous particle size separation and size sorting using ultrasound in a microchannel

  Sergey Kapishnikov et al J. Stat. Mech. (2006) P01012 Tag this article

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  Continuous separation and size sorting of particles and blood cells suspended in a microchannel flow due to an acoustic force are investigated both numerically and experimentally. Good agreement in the measured particle trajectories in a microchannel flow subjected to the acoustic force with those obtained by the numerical simulations up to the fitting parameter is found. High separation efficiency, particularly in a three-stage microdevice (up to 99.975%), for particles and blood cells leads us to believe that the device can be developed into commercially useful set-up. The novel particle size sorting microdevice provides an opportunity to replace rather expensive existing devices based on specific chemical bonding with an ultrasound cell size sorter that can be considerably improved by adding many stages for multistage size sorting.