Related papers: Avalanche and spreading exponents in systems with …
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
Complex systems, when poised near a critical point of a phase transition between order and disorder, exhibit a dynamics comprising a scale-free mixture of order and disorder which is universal, i.e. system-independent (1-5). It allows…
In these lectures, a variety of non-equilibrium transport phenomena are introduced that all involve, in some way, elastic manifolds being driven through random media. A simple class of models is studied focussing on the behavior near to the…
A minimal model for self-organized critical percolation on directed graphs with activating and de-activating links is studied. Unlike classical self-organized criticality, the variables that determine criticality are separated from the…
Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…
In a model of self-organized criticality unstable sites discharge to just one of their neighbors. For constant discharge ratio $\alpha$ and for a certain range of values of the input energy, avalanches are simple branchless P\'olya random…
We consider an interacting particle system $(\eta_t)_{t\geq 0}$ with values in $\{0,1\}^{\mathbb{Z}}$, in which each vacant site becomes occupied with rate 1, while each connected component of occupied sites become vacant with rate equal to…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…
Based on quasi-stationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as,…
Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…
We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group…
In the prototype sandpile model of self-organized criticality time series obtained by decomposing avalanches into waves of toppling show intermittent fluctuations. The q-th moments of wave size differences possess local multiscaling and…
We present an experimental study of the influence of quenched disorder on the distribution of flux avalanches in type-II superconductors. In the presence of much quenched disorder, the avalanche sizes are power-law distributed and show…
We solve a long-standing puzzle in Statistical Mechanics of disordered systems. By performing a high-statistics simulation of the D=3 random-field Ising model at zero temperature for different shapes of the random-field distribution, we…
Iterative construction of a Sierpinski carpet or sponge is shown to be a critical phenomenon analogous to uncorrelated percolation. Critical exponents are derived or calculated (by random walks over the carpet or sponge at infinite…
Scaling of the Reynolds stresses has been sought by many researchers, since it provides a template of universal dynamical patterns across a range of Reynolds numbers. Various statistical and normalization schemes have been attempted, but…
We introduce a nonequilibrium percolation model which shows a self-organized critical (SOC) state and several periodic states. In the SOC state, the correlation length diverges slower than the system size, and the corresponding exponent…
Survival and percolation probabilities are most important quantities in the theory and in the application of growth models with spreading. We construct field theoretical expressions for these probabilities which are feasible for…
Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a pre-critical to the…
Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand - where the concept of linear…