Statistical Physics Of Complex Systems

A two-species model of a two-dimensional sandpile surface: a case of asymptotic roughening

by Anita Mehta

Published in Granular Matter online , DOI 10.1007/s10035-012-0350-3 (2012).

Landscape encodings enhance optimisation

by Anita Mehta

PLoS ONE 7(4): e34780. doi:10.1371/journal.pone.0034780

Effect of the nature of randomness on quenching dynamics of Ising model on complex networks

by Soham Biswas

Phys. Rev. E 84, 066107 (2011)

Randomness is known to affect the dynamical behavior of many systems to a large extent. In this paper we investigate... more Randomness is known to affect the dynamical behavior of many systems to a large extent. In this paper we investigate how the nature of randomness affects the dynamics in a zero-temperature quench of the Ising model on two types of random networks. In both networks, which are embedded in a one-dimensional space, the first-neighbor connections exist and the average degree is 4 per node. In random model A the second-neighbor connections are rewired with a probability p, while in random model B additional connections between neighbors at a Euclidean distance l (l>1) are introduced with a probability P(l)∝l−α. We find that for both models, the dynamics leads to freezing such that the system gets locked in a disordered state. The point at which the disorder of the nonequilibrium steady state is maximum is located. The behavior of dynamical quantities such as residual energy, order parameter, and persistence are discussed and compared. Overall, the behavior of physical quantities are similar, although subtle differences are observed due to the difference in the nature of randomness.

Oscillatory settling in wormlike-micelle solutions: bursts and a long time scale

by Nitin Kumar

Nitin Kumar, Sayantan Majumdar, Aditya Sood, Rama Govindarajan, Sriram Ramaswamy and A.K. Sood

Soft Matter, 2012, 8, 4310-4313
DOI: 10.1039/C2SM25077B

Preprint available here:
http://arxiv.org/pdf/1203.2130.pdf

We study the dynamics of a spherical steel ball falling freely through a solution of entangled wormlike-micelles. If... more We study the dynamics of a spherical steel ball falling freely through a solution of entangled wormlike-micelles. If the sphere diameter is larger than a threshold value, the settling velocity shows repeated short oscillatory bursts separated by long periods of relative quiescence. We propose a model incorporating the interplay of settling-induced flow, viscoelastic stress and, as in M. E. Cates, D. A. Head and A. Ajdari, Phys. Rev. E, 2002, 66, 025202(R) and A. Aradian and M. E. Cates, Phys. Rev. E, 2006, 73, 041508, a slow structural variable for which our experiments offer independent evidence.

Synchronization of coupled oscillators

by Paulo Maurício

MsC Thesis

In this work we begin by introducing the Kuramoto model, constructing its solutions in the thermodynamic limit and... more In this work we begin by introducing the Kuramoto model, constructing its solutions in the thermodynamic limit and showing the close connection between statistical physics and
dynamical systems that lead to the main theoretical insights. The systematic study of a finite population of self sustained oscillators began in the first decade of this century.
Unlike most of the papers we have found, we are not interested in the synchronization transition in itself but rather in phase locked patterns and their relation with frequency distribution among oscillators.
The problem of stability, as we have already mentioned, experienced great advances in recent years. In a brief discussion we only address the problem of stability of the simplest solution allowed by the Kuramoto model: the incoherent solution. After that we introduce Chimera states, First noticed by Kuramoto and his colleagues in which the introduction of a non local coupling gives origin to a split in a region with synchronised oscillators and other with asynchronous one.
Then we proceed by exploring the literature and the results with a fnite number of oscillators, model explored with persistence only since mainly 2004. But here we are yet in Kuramoto framework which is abandoned, in a rigorous terminology, when we pursuit structured and not all-to-all coupling. Although we could introduce the same mean models quantities if well defined in each situation, this did not help us in making sense of the
results and is not an help in any analytical work.
In our analysis of a ring of coupled oscillators we construct a space that allows us to relate the stable solutions with the eigenvectors of the laplacian of the graph in which we work.
work.

Spectral properties of zero temperature dynamics in a model of a compacting granular column

by Anita Mehta

Published in the Journal of Statistical Physics, Volume 146, Number 5, 924-954, DOI 10.1007/s10955-012-0429-6 (2012)

The dynamics of competitive learning: the role of updates and memory

by Anita Mehta

Phys. Rev. E 85, 011134 (2012).

Dynamics of discrete opinions without compromise

by Kaan Öztürk

A new agent-based, bounded-confidence model for discrete one-dimensional opinion dynamics is presented. The agents... more A new agent-based, bounded-confidence model for discrete one-dimensional opinion dynamics is presented. The agents interact if their opinions do not differ more than a tolerance parameter. In pairwise interactions, one of the pair, randomly selected, converts to the opinion of the other. The model can be used to simulate cases where no compromise is possible, such as exclusive choices or competing brands. The fully-mixed case with maximum tolerance is equivalent to the Gambler's Ruin problem. A fully-mixed system always ends up in an absorbing state, which can have one or more surviving opinions. An upper bound for the final number of opinions is given. The distribution of absorption times fits the generalized extreme value distribution. The diffusion coefficient of an opinion increases linearly with the number of opinions within the tolerance parameter. A general master equation and specific Markov matrices are given. The software code developed for this study is provided as a supplement.

In search of smooth sandpiles: The Edwards-Wilkinson equation with flow

by Anita Mehta

Avalanches and ripples in sandpiles

by Anita Mehta

Statistical mechanics of powder mixtures

by Anita Mehta

Vibrated powders: A microscopic approach

by Anita Mehta

Vibrated powders: structure, correlations, and dynamics

by Anita Mehta

Novel temporal behavior of a nonlinear dynamical system: The completely inelastic bouncing ball

by Anita Mehta

Bouncing ball with a finite restitution: Chattering, locking, and chaos

by Anita Mehta

Transient phenomena, self-diffusion, and orientational effects in vibrated powders

by Anita Mehta

The dynamics of sand

by Anita Mehta

The Langevin dynamics of vibrated powders

by Anita Mehta

Dynamics of sandpiles: Physical mechanisms, coupled stochastic equations, and alternative universality classes

by Anita Mehta

Disorder, memory and avalanches in sandpiles

by Anita Mehta