Related papers: Dynamical Persistency in River Flows
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
The Levy diffusion processes are a form of non ordinary statistical mechanics resting, however, on the conventional Markov property. As a consequence of this, their dynamic derivation is possible provided that (i) a source of randomness is…
A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and…
Flow instabilities play important roles in a wide range of engineering, geophysical, and astrophysical flows, ranging from supernova explosion in crab nebula, formation of clouds in sky, waves on ocean, to inertial confinement fusion…
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…
A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory…
We investigate the evolutionary dynamics in directed and/or weighted networks. We study the fixation probability of a mutant in finite populations in stochastic voter-type dynamics for several update rules. The fixation probability is…
We analyze circumstances under which the microscopic dynamics of particles which are driven by a forced, gradient-type flow can be consistently interpreted as a Markovian diffusion process. Special attention is paid to discriminating…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Connectivity is a fundamental structural feature of a network that determines the outcome of any dynamics that happens on top of it. However, an analytical approach to obtain connection probabilities between nodes associated to paths of…
In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
Power lines, roadways, pipelines and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
The coupling of sediment transport with the flow that drives it allows rivers to shape their own bed. Cross-stream fluxes of sediment play a crucial, yet poorly understood, role in this process. Here, we track particles in a laboratory…
Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a…
The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…
A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…