Related papers: Statistical Mechanics of Avalanches
The response of a complex system to a slow varying external force often displays a jump discontinuity in the order parameter near the critical point. However, this discontinuity is not usually a single jump but rather breaks into smaller…
Slowly driven dissipative systems may evolve to a critical state where long periods of apparent equilibrium are punctuated by intermittent avalanches of activity. We present a self-organized critical model of punctuated equilibrium behavior…
Using the Bethe ansatz we obtain the exact solution for the one-dimensional asymmetric avalanche process. We evaluate the velocity of dispersive flow as a function of driving force and the density of particles. The obtained solution shows a…
We investigate thermal avalanche dynamics in amorphous solids using elastoplastic models with local activation rules and no external driving. Dynamical heterogeneities, quantified through persistence measurements and the associated…
The zero-temperature Glauber dynamics of the random-field Ising model describes various ubiquitous phenomena such as avalanches, hysteresis, and related critical phenomena. Here, for a model on a random graph with a special initial…
We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by…
A dissipative stochastic sandpile model is constructed and studied on small world networks in one and two dimensions with different shortcut densities $\phi$, where $\phi=0$ represents regular lattice and $\phi=1$ represents random network.…
The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different…
Avalanches are rapid cascades of rearrangements driven by cooperative flipping of hysteretic local elements. Here we show that flipping dynamics and race conditions -- where multiple elements become unstable simultaneously -- give rise to…
Self-organizing system is studied whose behavior is governed by field of an order parameter, a fluctuation amplitude of conjugate field and a couple of Grassmannian conjugated fields that define the entropy as a control parameter. Within…
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
Hysteresis, the lag between the force and the response, is often associated with noisy, jerky motion which have recently been called ``avalanches''. The interesting question is why the avalanches come in such a variety of sizes: naively one…
A century ago, the foundations of equilibrium statistical mechanics were laid. For a system in equilibrium with a thermal bath, much is understood through the Boltzmann factor, exp{-H[C]/kT}, for the probability of finding the system in any…
We introduce a simple lattice model of superconducting vortices driven by repulsive interactions through a random pinning potential. The model describes the behavior at the scale of the London length lambda or larger. It self-organizes to a…
This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…
We study numerically the avalanches in a two--dimensional critical height sandpile model with sand grains added at the center of the system. Smaller avalanches near the center of the system are isotropic. Larger avalanches are, however,…
In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the inter-avalanche periods, and thus…
We find that some equilibrium systems and their non-equilibrium counterparts actually show the same jerky response or avalanche behavior on many scales in response to slowly changing external conditions. In other words, their static and…
We study the influence of vacancy concentration on the behaviour of the three dimensional Random Field Ising model with metastable dynamics. We focus our analysis on the number of spanning avalanches which allows for a clean determination…
We study avalanche dynamics and local activity of forced-flow imbibition fronts in disordered media. We focus on the front dynamics as the mean velocity $\bar{v}$ of the interface is decreased and the pinning state is approached. Scaling…