Related papers: Spiral Waves in Media with Complex Excitable Dynam…
A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical…
Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in…
Circumstellar asymmetries such as central warps have recently been shown to cast shadows on outer disks. We investigate the hydrodynamical consequences of such variable illumination on the outer regions of a transition disk, and the…
Most prior works studying tidal interactions in tight star/planet or star/star binary systems have employed linear theory of a viscous fluid in a uniformly-rotating two-dimensional spherical shell. However, compact systems may have…
Worm-like filaments that are propelled homogeneously along their tangent vector are studied by Brownian dynamics simulations. Systems in two dimensions are investigated, corresponding to filaments adsorbed to interfaces or surfaces. A large…
We review our recent theoretical results on multiple scattering of waves in nonlinear disordered media. In particular, we discuss angular correlations of scattered waves, coherent backscattering cone, and the new phenomenon of temporal…
Patterns of convection in internally heated, self-gravitating rotating spherical fluid shells are investigated through numerical simulations. While turbulent states are of primary interest in planetary and stellar applications the present…
A scroll wave in a very thin layer of excitable medium is similar to a spiral wave, but its behaviour is affected by the layer geometry. We identify the effect of sharp variations of the layer thickness, which is separate from filament…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
Spatially extended versions of the cyclic-dominance Rock-Paper-Scissors model have traveling wave (in one dimension) and spiral (in two dimensions) behavior. The far field of the spirals behave like traveling waves, which themselves have…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
Recent observational constraints restrict the strict applicability of stellar dynamics in spirals to a few rotation periods. However, stellar dynamics concepts such as periodic orbits are invaluable for understanding the various dynamical…
Steady linear gravity waves of small amplitude travelling on a current of constant vorticity are found. For negative vorticity we show the appearance of internal waves and vortices, wherein the particle trajectories are not any more closed…
We propose a travelling-wave perturbation method to control the spatiotemporal dynamics in a cardiac model. It is numerically demonstrated that the method can successfully suppress the wave instability (alternans in action potential…
The dynamics of a relativistic blast wave propagating through magnetized medium is considered taking into account possible inhomogeneities of density and magnetic field and additional energy supply. Under the simplifying assumption of a…
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…
We present evidence that recurrent spiral activity, long manifested in simulations of disk galaxies, results from the super-position of a few transient spiral modes. Each mode lasts between 5 and 10 rotations at its corotation radius where…
The existence of scalar fields can be probed by observations of stochastic gravitational waves. Scalar fields mediate attractive forces, usually stronger than gravity, on the length scales shorter than their Compton wavelengths, which can…
The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the…
Nonlinear electromagnetic waves with superluminal phase velocity can propagate in the winds around isolated pulsars, and around some pulsars in binary systems. Using a short-wavelength approximation, we find and analyze an integrable system…