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Rayleigh-L\'evy flights are simplified cosmological tools which capture certain essential statistical properties of the cosmic density field, including hierarchical structures in higher-order correlations, making them a valuable reference…
In a recent computer study, we have shown that the combination of spatially heterogeneous dynamics and kinetic facilitation provides a microscopic explanation for the emergence of excess wings in deeply supercooled liquids. Motivated by…
We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
We use a discrete-time formulation to study the asymmetric avalanche process [Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact expression for the average avalanche size of particles as a function of toppling…
We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and…
Three-dimensional discrete dislocation dynamics simulations are used to study strain-controlled plastic deformation of face-centered cubic aluminium single crystals. After describing the rate and size dependence of the average stress-strain…
Ultrametric structure of the energy cascade process in a dynamical model of turbulence is studied. The tree model we use can be viewed as an approximated one-dimensional truncation of the wavelets resolved Navier-Stokes dynamics. Varying…
Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are…
We present a new model for extinction in which species evolve in bursts or `avalanches', during which they become on average more susceptible to environmental stresses such as harsh climates and so are more easily rendered extinct. Results…
From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between…
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…
Fiber bundles with statistically distributed thresholds for breakdown of individual fibers are interesting models of the static and dynamics of failures in materials under stress. They can be analyzed to an extent that is not possible for…
A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…
Wood is a multi-scale material exhibiting a complex viscoplastic response. We study avalanches in small wood samples in compression. "Woodquakes" measured by acoustic emission are surprisingly similar to earthquakes and crackling noise in…
Recent experiments show that an avalanche initiated from a point source propagates downwards by invading a triangular shaped region. The opening angle of this triangle appears to reach 180$^o$ for a critical inclination of the pile, beyond…
Based on a theoretical model for opinion spreading on a network, through avalanches, the effect of external field is now considered, by using methods from non-equilibrium statistical mechanics. The original part contains the implementation…
Exact results for the first passage time and leapover statistics of symmetric and one-sided Levy flights (LFs) are derived. LFs with stable index alpha are shown to have leapover lengths, that are asymptotically power-law distributed with…
Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents…
The onsets of toppling and dissipation in the BTW model are studied by computer simulation. The distributions of these two onset times and their dependences on the system size are also studied. Simple power law dependences of these two…