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The interaction of a massive binary and a non-self-gravitating circumbinary accretion disc is considered. The shape of the stationary twisted disc produced by the binary is calculated. It is shown that the inner part of the disc must lie in…
The genus statistics is studied using large $N$-body simulations for several cosmological models. We consider the effects of nonlinear gravitational evolution, smoothing the particle data in fully nonlinear regime, and the redshift-space…
Galaxy evolution is sensitive to how stars inject feedback into their surroundings. In particular, stellar feedback from star clusters strongly affects gas motions and the baryonic cycle, with more massive clusters having stronger effects.…
Motivated by the recent results of \citet{Lesur_Ogilvie10} on the transport properties of incompressible convection in protoplanetary discs, in this paper we study the role of compressibility and hence of another basic mode -- spiral…
In this paper we address the stability of resonantly forced density waves in dense planetary rings. Already by Goldreich & Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the…
The nonlinear evolution of a vortex sheet driven by the Kelvin--Helmholtz instability is characterized by the formation of a spiral possessing complex stretching and intensity patterns. We show that the power energy spectrum of a single…
We study a recently proposed nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. (80), 4221 (1998)]. A careful…
A numerical exploration of a gain-loss nonlinear Schr\"odinger equation was carried out utilizing over 180000 core hours to conduct more than 10000 unique simulations in an effort to characterize the model's six dimensional parameter space.…
Based on the Vlasov-Maxwell equations describing the self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a periodic focusing field has been studied. In an earlier…
We have discovered long-lived waves in two sets of numerical models of fast (marginally bound or unbound) flyby galaxy collisions, carried out independently with two different codes. In neither simulation set are the spirals the result of a…
We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…
We study the evolution of the fine-structure constant, $\alpha$, induced by non-linear density perturbations in the context of the simplest class of quintessence models with a non-minimal coupling to the electromagnetic field, in which the…
A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability relaxing the elastic energy by surface diffusion. The nonlinear and nonlocal dynamical equations of such films with wetting interactions are…
We demonstrate that numerical solutions of Burgers' equation can be obtained by a scale-totality algorithm for fluids of small viscosity (down to one billionth). Two sets of initial data, modelling simple shears and wall boundary layers,…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…
The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
This study investigates the nonlinear stability and dynamics of gravity-driven viscous films on a vertical rotating cylinder, considering both outer and inner surface flows with slip conditions at the cylinder wall. We develop an asymptotic…