In the last 30 days

• Open/close Criticality and condensation in a non-conserving zero-range process

  A G Angel et al  J. Stat. Mech. (2007) P08017 Tag this article

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  The zero-range process, in which particles hop between sites on a lattice under conserving dynamics, is a prototypical model for studying real-space condensation. Within this model the system is critical only at the transition point. Here we consider a non-conserving zero-range process which is shown to exhibit generic critical phases which exist in a range of creation and annihilation parameters. The model also exhibits phases characterized by mesocondensates, each of which contains a subextensive number of particles. A detailed phase diagram, delineating the various phases, is derived.

• Open/close A dynamically extending exclusion process

  K E P Sugden and M R Evans  J. Stat. Mech. (2007) P11013 Tag this article

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  An extension of the totally asymmetric exclusion process, which incorporates a dynamically extending lattice, is explored. Although originally inspired as a model for filamentous fungal growth, here the dynamically extending exclusion process (DEEP) is studied in its own right as a nontrivial addition to the class of nonequilibrium exclusion process models. Here we discuss various mean-field approximation schemes and elucidate the steady state behaviour of the model and its associated phase diagram. Of particular note is that the dynamics of the extending lattice leads to a new region in the phase diagram in which a shock discontinuity in the density travels forward with a velocity that is lower than the velocity of the tip of the lattice. Thus in this region the shock recedes from both boundaries.

• Open/close Self-organization without conservation: are neuronal avalanches generically critical?

  Juan A Bonachela et al  J. Stat. Mech. (2010) P02015 Tag this article

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  Recent experiments on cortical neural networks have revealed the existence of well-defined avalanches of electrical activity. Such avalanches have been claimed to be generically scale invariant—i.e. power law distributed—with many exciting implications in neuroscience. Recently, a self-organized model has been proposed by Levina, Herrmann and Geisel to explain this empirical finding. Given that (i) neural dynamics is dissipative and (ii) there is a loading mechanism progressively 'charging' the background synaptic strength, this model/dynamics is very similar in spirit to forest-fire and earthquake models, archetypical examples of non-conserving self-organization, which have recently been shown to lack true criticality. Here we show that cortical neural networks obeying (i) and (ii) are not generically critical; unless parameters are fine-tuned, their dynamics is either subcritical or supercritical, even if the pseudo-critical region is relatively broad. This conclusion seems to be in agreement with the most recent experimental observations. The main implication of our work is that, if future experimental research on cortical networks were to support the observation that truly critical avalanches are the norm and not the exception, then one should look for more elaborate (adaptive/evolutionary) explanations, beyond simple self-organization, to account for this.

• Open/close Evolving networks and the development of neural systems

  Samuel Johnson et al  J. Stat. Mech. (2010) P03003 Tag this article

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  It is now generally assumed that the heterogeneity of most networks in nature probably arises via preferential attachment of some sort. However, the origin of various other topological features, such as degree–degree correlations and related characteristics, is often not clear, and they may arise from specific functional conditions. We show how it is possible to analyse a very general scenario in which nodes can gain or lose edges according to any (e.g., nonlinear) function of local and/or global degree information. Applying our method to two rather different examples of brain development—synaptic pruning in humans and the neural network of the worm C. Elegans—we find that simple biologically motivated assumptions lead to very good agreement with experimental data. In particular, many nontrivial topological features of the worm's brain arise naturally at a critical point.

• Open/close Statistics of acoustic emission in paper fracture: precursors and criticality

  J Rosti et al  J. Stat. Mech. (2010) P02016 Tag this article

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  We present statistical analysis of acoustic emission (AE) data from tensile experiments on paper sheets, for loading mode I, with samples broken under strain control. The results are based on 100 experiments on unnotched samples and 70 samples with a long initial edge notch. First, AE energy release and AE event rates are considered for both cases, to test for the presence of 'critical points' in fracture. For AE energy, no clear signatures are found, whereas the main finding is that the event rate diverges when a sample-dependent 'critical time' of the maximum event rate is approached. This takes place after the maximum stress is reached. The results are compared with statistical fracture models of heterogeneous materials. We also discuss the dependence of the AE energy and event interval distributions on average event rates.

• 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 Condensation transitions in a one-dimensional zero-range process with a single defect site

  A G Angel et al  J. Stat. Mech. (2004) P04001 Tag this article

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  Condensation occurs in nonequilibrium steady states when a finite fraction of the particles in the system occupies a single lattice site. We study condensation transitions in a one-dimensional zero-range process with a single defect site. The system is analysed in the grand canonical and canonical ensembles and the two are contrasted. Two distinct condensation mechanisms are found in the grand canonical ensemble. Discrepancies between the infinite and large but finite systems' particle current versus particle density diagrams are investigated and an explanation for how the finite current goes above a maximum value predicted for infinite systems is found in the canonical ensemble.

• Open/close Minimal vertex covers of random trees

  Stéphane Coulomb  J. Stat. Mech. (2005) P06007 Tag this article

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  We study minimal vertex covers of trees. In contrast to the number N _vc( A) of minimal vertex covers of the tree A, log N _vc( A) is a self-averaging quantity. We show that, for large sizes n, . The basic idea is, given a tree, to concentrate on its degenerate vertices, that is those vertices which belong to some minimal vertex cover but not to all of them. Deletion of the other vertices induces a forest of totally degenerate trees. We show that the problem reduces to the computation of the size distribution of this forest, which we perform analytically, and of the average over totally degenerate trees of given size, which we perform numerically.

• 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 Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann simulations

  Martin Hecht and Jens Harting  J. Stat. Mech. (2010) P01018 Tag this article

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  On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as those of porous media or microfluidic devices. The possibility of specifying the exact position of the boundary, independently of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow one to freely specify the direction of the flux, and it should be straightforward to implement in three dimensions. Furthermore, especially for parallelized solvers, it is of great advantage if the boundary condition can be applied locally, involving only information available on the current lattice site. We meet this need by describing in detail how to transfer the approach suggested by Zou and He to a D3Q19 lattice. The boundary condition acts locally, is independent of the details of the relaxation process during collision and contains no artificial slip. In particular, the case of an on-site no-slip boundary condition is naturally included. We test the boundary condition in several setups and confirm that it can be used to accurately model the velocity field up to second order and does not contain any numerical slip.