Kinematics of interacting solitons in two-dimensional space

A simple kinematic approach to the description of the interaction between solitons is developed. It is applicable to both integrable and non-integrable two-dimensional models, including those commonly used for studying the surface and internal oceanic waves. This approach allows obtaining some important characteristics of the interaction between solitary waves propagating at an angle to each other. The developed theory is validated by comparison with the exact solutions of the Kadomtsev-Petviashvili equation and then applied to the observed interaction of solitary internal waves in a two-layer fluid within the two-dimensional Benjamin-Ono model

Structure formation in the oceanic subsurface bubble layer by an internal wave field

We model the effects of an internal wave on the structure of the oceanic subsurface bubble layer, generated by breaking surface waves.We consider two situations: when breaking is caused either by a strong sustained wind or by the direct interaction of surface waves with an internal wave. We find that the effects are twofold; bubbles are driven by the internal wave field and the injection of bubbles into the water is enhanced in downwelling areas behind the crests of the internal wave. We use an uncoupled problem formulation, substituting the solution for an internal wave in a two-layer fluid model into the equations describing the bubble dynamics. The latter equations are solved numerically, showing structure formation in the bubble layer for each of the two cases, when one of the aforementioned mechanisms dominates the other. © 2010 American Institute of Physics

Solitary Wave Interactions In Dispersive Equations Using Manton's Approach

We generalize the approach first proposed by Manton [Nuc. Phys. B {\bf 150}, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations that support such localized solutions. The approach is illustrated using as examples solitons in the Korteweg-de Vries equation, standing waves in the nonlinear Schr{\"o}dinger equation and kinks as well as breathers of the sine-Gordon equation.Comment: 5 pages, 4 figures, slightly modified version to appear in Phys. Rev.

Exact eigenstate analysis of finite-frequency conductivity in graphene

We employ the exact eigenstate basis formalism to study electrical conductivity in graphene, in the presence of short-range diagonal disorder and inter-valley scattering. We find that for disorder strength, $W \ge$ 5, the density of states is flat. We, then, make connection, using the MRG approach, with the work of Abrahams \textit{et al.} and find a very good agreement for disorder strength, $W$ = 5. For low disorder strength, $W$ = 2, we plot the energy-resolved current matrix elements squared for different locations of the Fermi energy from the band centre. We find that the states close to the band centre are more extended and falls of nearly as $1/E_l^{2}$ as we move away from the band centre. Further studies of current matrix elements versus disorder strength suggests a cross-over from weakly localized to a very weakly localized system. We calculate conductivity using Kubo Greenwood formula and show that, for low disorder strength, conductivity is in a good qualitative agreement with the experiments, even for the on-site disorder. The intensity plots of the eigenstates also reveal clear signatures of puddle formation for very small carrier concentration. We also make comparison with square lattice and find that graphene is more easily localized when subject to disorder.Comment: 11 pages,15 figure

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

ORIENTATIONAL ACOUSTIC NONLINEARITY IN FLUIDS WITH ANISOTROPIC PARTICLES

Les interactions non linéaires des ondes acoustiques induites par l'orientation des particules anisotropes dans un champ ultrasonore (effet Kerr acoustique) sont étudiées. L'analyse est menée pour un cristal liquide dans lequel la variation du paramètre d'ordre, la transition induite de l'état nématique à l'état isotrope, et réciproquement, sont possibles. Des estimations sont faites pour différents effets non linéaires dans un cristal liquide (auto modulation de phase, distorsion du profil d'onde, auto focalisation).Nonlinear self-action of acoustic waves due to the orientation of anisotropic particles in a sound field (the acoustic Kerr-effect) is considered. Analysis is performed for a liquid crystal in which an ultrasound changes the order parameter, the induced transition from nematic state into isotropic one and vice versa being possible. Estimations are made showing the real opportunity of observing different nonlinear effects (phase self-modulation, wave profile distortion, self-focusing) in a liquid crystal

Research note: the effect of strain amplitude produced by ultrasonic waves on its velocity

© 2018 European Association of Geoscientists & Engineers The effect of the amplitude of ultrasonic waves propagating through a sample is not often taken into account in laboratory experiments. However, ultrasonic waves can produce relatively large strain inside the sample, and thus change the properties of the sample. To investigate the effect of strain amplitude on the P-wave velocity, a series of ultrasonic wave propagation experiments were carried out on three different media. All measurements were performed at 1 MHz central frequency and at the strain levels inside propagating waves of ~3.0 × 10-6 to 6.0 × 10-5 without applying confining pressure to the sample. Strains in the waves were measured by a laser Doppler interferometer upon wave arrival on a free surface of the sample. The ultrasonic velocities were measured by a pair of P-wave transducers located at the same measuring point as the laser beam of the LDI. The effect of strain on P-wave velocity varied for different material. The P-wave velocity was calculated using both a first arrival and a first maximum peak at different applied voltage. The P-wave velocity remained unchanged for a pure elastic medium (aluminium); however, the velocity increased continuously with the increasing of the strain for polymethylmethacrylate and Gosford sandstone. For Gosford sandstone, velocity increases up to 0.8% with strain increase from 7.0 × 10-6 to 2.0 × 10-5. This effect of velocity increase with the strain induced by an ultrasonic wave can be explained by the in-elasticity of both the polymethylmethacrylate and Gosford sandstone samples