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 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 Exact enumeration of self-avoiding walks

  R D Schram et al J. Stat. Mech. (2011) P06019 Tag this article

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  A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks. Here, we show an advance in the methodology of enumeration, making the process thousands or millions of times faster. This allowed us to enumerate self-avoiding walks on the simple cubic lattice up to a length of 36 steps.

• Open/close Leaping shampoo and the stable Kaye effect

  Michel Versluis et al J. Stat. Mech. (2006) P07007 Tag this article

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  Shear-thinning fluids exhibit surprisingly rich behaviour. One example is the Kaye effect which occurs when a thin stream of a solution of polyisobutylene in decalin is poured into a dish of the fluid. As pouring proceeds, a small stream of liquid occasionally leaps upward from the heap. This surprising effect, which lasts only a second or so, is named after its first observer, Kaye, who could offer no explanation for this behaviour. Later, Collyer and Fischer suggested from 250 frames s ⁻¹ cine recordings that the fluid must be highly shear thinning as well as elastic and 'pituitous' (slimy or sticky). In addition, their results suggested that a rigid surface is required to back the reflected liquid stream. While the words bouncing and reflection are associated with elastic effects, we will show here that the Kaye effect is in fact a continuous flow phenomenon. We show that the Kaye effect works for many common fluids, including shampoos and liquid soaps. We reveal its physical mechanism (formation, stability and disruption) through high-speed imaging. The measurements are interpreted with a simple theoretical model including only the shear thinning behaviour of the liquid; elastic properties of the liquid play no role. We show that the Kaye effect can be stable and that it can be directed. We even demonstrate a stable Kaye effect on a thin soap film excluding the necessity of a rigid backing surface.

• Open/close Double transitions, non-Ising criticality and the critical absorbing phase in an interacting monomer–dimer model on a square lattice

  Keekwon Nam et al J. Stat. Mech. (2011) L06001 Tag this article

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  We present a numerical study on an interacting monomer–dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is observed to exhibit two nearby continuous transitions: the Z ₂ symmetry-breaking order–disorder transition and the absorbing transition with directed percolation criticality. We find that the symmetry-breaking transition shows a non-Ising critical behavior, and that the absorbing phase becomes critical, in the sense that the critical decay of the dimer density observed at the absorbing transition persists even within the absorbing phase. Our findings call for further studies on microscopic models and the corresponding continuum description belonging to the generalized voter university class.

• Open/close Self-organization of social hierarchy on interaction networks

  Ryo Fujie and Takashi Odagaki J. Stat. Mech. (2011) P06011 Tag this article

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  In order to examine the effects of interaction network structures on the self-organization of social hierarchy, we introduce the agent-based model: each individual as on a node of a network has its own power and its internal state changes by fighting with its neighbors and relaxation. We adopt three different networks: regular lattice, small-world network and scale-free network. For the regular lattice, we find the emergence of classes distinguished by the internal state. The transition points where each class emerges are determined analytically, and we show that each class is characterized by the local ranking relative to their neighbors. We also find that the antiferromagnetic-like configuration emerges just above the critical point. For the heterogeneous networks, individuals become winners (or losers) in descending order of the number of their links. By using mean-field analysis, we reveal that the transition point is determined by the maximum degree and the degree distribution in its neighbors.

• Open/close Stochastic models of evolution in genetics, ecology and linguistics

  R A Blythe and A J McKane J. Stat. Mech. (2007) P07018 Tag this article

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  We give an overview of stochastic models of evolution that have found applications in genetics, ecology and linguistics for an audience of non-specialists, especially statistical physicists. In particular, we focus mostly on neutral models in which no intrinsic advantage is ascribed to a particular type of the variable unit, for example a gene, appearing in the theory. In many cases these models are exactly solvable and furthermore go some way to describing observed features of genetic, ecological and linguistic systems.

• Open/close Exploration of order in chaos using the replica exchange Monte Carlo method

  Tatsuo Yanagita and Yukito Iba J. Stat. Mech. (2009) P02043 Tag this article

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  A method for exploring unstable structures generated by non-linear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters using the replica exchange Monte Carlo method, and it is efficient in searching for rare initial conditions and in the combined search for rare initial conditions and parameters. Examples discussed here include the sampling of unstable periodic orbits in chaos and searching for the stable manifold of unstable fixed points, as well as construction of the global bifurcation diagram of a map.

• Open/close Enhancement of diffusive transport by non-equilibrium thermal fluctuations

  Aleksandar Donev et al J. Stat. Mech. (2011) P06014 Tag this article

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  We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is enhanced because of long-range correlations between concentration fluctuations and fluctuations of the velocity parallel to the concentration gradient. The enhancement of the diffusive transport depends on the system size L and grows as ln( L/ L ₀) in quasi-two-dimensional systems, while in three dimensions it grows as L ₀ ^{− 1} − L ^{− 1}, where L ₀ is a reference length. The predictions of a simple fluctuating hydrodynamics theory, closely related to second-order mode–mode coupling analysis, are compared to results from particle simulations and a finite-volume solver and excellent agreement is observed. We elucidate the direct connection to the long-time tail of the velocity autocorrelation function in finite systems, as well as finite-size corrections employed in molecular dynamics calculations. Our results conclusively demonstrate that the nonlinear advective terms need to be retained in the equations of fluctuating hydrodynamics when modeling transport in small-scale finite systems.

• Open/close Metastable wetting

  Joël De Coninck et al J. Stat. Mech. (2011) P06013 Tag this article

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  Consider a droplet of liquid on top of a grooved substrate. The wetting or not of a groove implies the crossing of a potential barrier as the interface has to distort to hit the bottom of the groove. We start with computing the free energies of the dry and wet states in the context of a simple thermodynamical model before switching to a random microscopic version pertaining to the solid-on-solid (SOS) model. For some range in parameter space (Young angle, pressure difference, aspect ratio), the dry and wet states both share the same free energy, which means coexistence. We compute these coexistence lines together with the metastable regions. In the SOS case, we describe the dynamic transition between coexisting states in wetting. We show that the expected time to switch from one state to the other grows exponentially with the free energy barrier between the stable states and the saddle state, proportional to the groove's width. This random time appears to have an exponential-like distribution.