Related papers: The Abelian distribution
We present generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states. Using these scaling laws we present a collection of the…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
Memcomputing is a novel computing paradigm that employs time non-locality (memory) to solve combinatorial optimization problems. It can be realized in practice by means of non-linear dynamical systems whose point attractors represent the…
We provide a comprehensive view on the role of Abelian symmetry and stochasticity in the universality class of directed sandpile models, in context of the underlying spatial correlations of metastable patterns and scars. It is argued that…
Recent observation for scale invariant neural avalanches in the brain have been discussed in details in the scientific literature. We point out, that these results do not necessarily imply that the properties of the underlying neural…
Various features of the mass yields in heavy ion collisions are studied. The mass yields are discussed in terms of iterative one dimensional discrete maps. These maps are shown to produce orbits for a monomer or for a nucleus which generate…
The Airy distribution (AD) describes the probability distribution of the area under a Brownian excursion. The AD is prominent in several areas of physics, mathematics and computer science. Here we use a dilute colloidal system to directly…
The role of correlations in self-organised critical (SOC) phenomena is investigated by studying the Abelian Manna Model (AMM) in two dimensions. Local correlations of the debris left behind after avalanches are destroyed by re-arranging…
The depinning transition critical point is manifested as power-law distributed avalanches exhibited by slowly driven elastic interfaces in quenched random media. Here we show that since avalanches with different starting heights relative to…
We investigate a non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For specific values of adsorption ($u_a$) and desorption($u_d$) rates…
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary…
We study several probability distributions relevant to the avalanche dynamics of elastic interfaces driven on a random substrate: The distribution of size, duration, lateral extension or area, as well as velocities. Results from the…
A theory is developed which relates the observed b-parameter of a Lyman-alpha absorption line to the velocity-curvature of the corresponding peak in the optical depth fluctuation. Its relation to the traditional interpretation of b as the…
We study the phenomenon of internal avalanching within the context of recently introduced lattice models of granular media. The avalanche is produced by pulling out a grain at the base of the packing and studying how many grains have to…
Mean field slider block models have provided an important entry point for understanding the behavior of discrete driven threshold systems. We present a method of constructing these models with an arbitrary frictional weakening function.…
The one-dimensional Dickman distribution arises in various stochastic models across number theory, combinatorics, physics, and biology. Recently, a definition of the multidimensional Dickman distribution has appeared in the literature,…
We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the…
Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A…
Topological defects dominate the deformation response of materials in processes ranging from quantum turbulence to crystal plasticity. We calculate the probability distribution function for the fluctuations in velocity $v$, using scaling…
Epidemic disease spreading is conventionally often modelled and analyzed by means of rate and diffusion equations, following the paradigms of well-controlled chemical reactions and diffusive dynamics in a test tube. Yet, serious worries…