Related papers: Neither pulled nor pushed: Genetic drift and front…
Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…
Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling…
We investigate the inside structure of one-dimensional reaction-diffusion traveling fronts. The reaction terms are of the monostable, bistable or ignition types. Assuming that the fronts are made of several components with identical…
Front propagation into unstable states is often determined by the linearization, that is, propagation speeds agree with predictions from the linearized equation at the unstable state. The leading edge behavior is then a Gaussian tail…
We study the propagation of a ``pulled'' front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a separation of time scales for sufficiently…
The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous…
We show that in order to guide waves, it is sufficient to periodically truncate their edges. The modes supported by this type of wave guide propagate freely between the slits, and the propagation pattern repeats itself. We experimentally…
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…
In many pattern forming systems that exhibit traveling waves, sources and sinks occur which separate patches of oppositely traveling waves. We show that simple qualitative features of their dynamics can be compared to predictions from…
We analyze the spread of a localized peak of energy into vacuum for nonlinear diffusive processes. In contrast with standard diffusion, the nonlinearity results in a compact wave with a sharp front separating the perturbed region from…
We demonstrate a new class of elastic waves in the bulk: When longitudinal and transverse components propagate at the same speed, rolling waves with a spin that is not parallel to the wave vector can emerge. First, we give a general…
Languages and genes are both transmitted from generation to generation, with opportunity for differential reproduction and survivorship of forms. Here we apply a rigorous inference framework, drawn from population genetics, to distinguish…
We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges.…
It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. \textbf{88}, 138301 (2002)]. As a further investigation, here we observe different types of traveling…
The paper defines and discusses the concept of hidden drifts in two-dimensional turbulence. These are ordered components of the trajectories that average to zero and do not produce direct transport. Their effects appear in the evolution of…
Different evolutionary models are known to make disparate predictions for the success of an invading mutant in some situations. For example, some evolutionary mechanics lead to amplification of selection in structured populations, while…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic…
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical…