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We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states. After reviewing the bulk scaling behavior of…

We derive a generic expression for the generating function (GF) of the particle-number probability distribution (PNPD) for a simple reaction diffusion model that belongs to the directed percolation universality class. Starting with a single…

The values obtained experimentally for the conductivity critical exponent in numerous percolation systems, in which the interparticle conduction is by tunnelling, were found to be in the range of $t_0$ and about $t_0+10$, where $t_0$ is the…

In this paper we study the strict majority bootstrap percolation process on graphs. Vertices may be active or passive. Initially, active vertices are chosen independently with probability p. Each passive vertex becomes active if at least…

We present a general scaling theory for the surface critical behavior of non-equilibrium systems with phase transitions into absorbing states. The theory allows for two independent surface exponents which satisfy generalized hyperscaling…

The $n$-species particle-exchange process (PEP($n$)) is an exclusion process in which particles of $n$ different species exchange positions on neighbouring sites with rates chosen such that the invariant measure on the discrete torus is a…

The pair contact process with diffusion is studied by means of multispin Monte Carlo simulations and density matrix renormalization group calculations. Effective critical exponents are found to behave nonmonotonically as functions of time…

Random organizing hyperuniform fluid induced by reciprocal activation is a non-equilibrium fluid with vanishing density fluctuations at large length scales like crystals. Here we extend this new state of matter to a closed manifold, namely…

Defective spectral degeneracy, known as exceptional point (EP), lies at the heart of various intriguing phenomena in optics, acoustics, and other nonconservative systems. Despite extensive studies in the past two decades, the…

Hopf bifurcations are a universal route to self-sustained oscillations in driven systems. Despite the absence of any singular stationary state, we show that time-averaged observables generically exhibit singularities at the onset of…

In this paper we propose a computational framework for the investigation of the correlated motion between positive and negative ions exposed to the attraction of a bubble surface that mimics the (oscillating) cell membrane. The correlated…

We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…

A theoretical and numerically study of dynamical properties in the sol-gel transition is presented. In particular, the complex phenomenology observed experimentally and numerically in gelling systems is reproduced in the framework of…

A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and possess a variational structure. Thus, the mass, the momentum and the energy are…

The vacant set of random interlacements at level $u>0$, introduced in arXiv:0704.2560, is a percolation model on $\mathbb{Z}^d$, $d \geq 3$ which arises as the set of sites avoided by a Poissonian cloud of doubly infinite trajectories,…

The exotic physics emerging at singularities has long attracted intense theoretical and experimental attention. In non-Hermitian systems, exceptional points (EPs), unique spectral singularities, have given rise to a host of intriguing wave…

We study asymptotic percolation as $N\to \infty$ in an infinite random graph ${\cal G}_N$ embedded in the hierarchical group of order $N$, with connection probabilities depending on an ultrametric distance between vertices. ${\cal G}_N$ is…

We study the critical properties of the monopole-percolation transition in U(1) lattice gauge theory coupled to scalars at infinite ($\beta=0$) gauge coupling. We find strong scaling corrections in the critical exponents that must be…

Considering supercritical Bernoulli percolation on $\mathbb{Z}^d$, Garet and Marchand [GM09] proved a diffusive concentration for the graph distance. In this paper, we sharpen this result by establishing the subdiffusive concentration…

We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…