Localized Coherent Structures Research Articles

Linear and nonlinear quantum ion acoustic waves in a plasma with positive, negative ions and Fermi electron gas

Linear and nonlinear propagations of quantum ion acoustic waves in positive, negative ions and electron plasma have been vetted via the dispersion relation and Korteweg–de Vries equation, where the ions are inertial and electrons are inertialess. The quantum mechanical effects arising due to the quantum diffraction and Fermi–Dirac statistics for this system are taken into account. The existence, as well as the type (compressive/rarefactive) of solitary wave propagating in the system, is strongly dependent on the numerical value of dimensionless quantum parameter He. It is observed that negative ion population and ion mass ratio have emphatic influence on the phase velocity of ion acoustic wave and the propagation of localized coherent solitary structures at quantum scale in the system.

Impact of Terrain Heterogeneity on Coherent Structure Properties: Numerical Approach

A three-dimensional large-eddy simulation (LES) model, which includes the effects of plant–atmosphere interactions, is used to study the effects of surface inhomogeneities on near-surface coherent structures over an open field and behind a forest canopy. These simulated conditions are representative of two wind sectors of the Site Instrumental de Recherche par Teledetection Atmospherique (SIRTA) experimental site at the Institut Pierre Simon Laplace, Palaiseau, France. Coherent structure properties deduced from wavelet transforms of the simulated near-surface vertical velocity time series are not modified by upstream terrain heterogeneities, in agreement with site measurements. This feature is related to the nature of structures detected from the vertical velocity time series. The turbulence close to the surface seems composed of both local coherent structures and large coherent structures reflecting outer-layer properties, which depend on the overall surface heterogeneity or upstream heterogeneity. It is argued that the streamwise velocity is representative of these large outer-layer structures that impinge onto the ground through a top-down mechanism as identified through the space–time correlation of the wind velocity components. In contrast, the vertical velocity is more representative of small structures resulting from the impingement of the large outer-layer structures. These small structures represent locally-generated, active turbulence, which adjusts rapidly to local surface conditions, and consequently they are only weakly dependent on upstream heterogeneities.

On the theory of three-dimensional multihump solitons in active-dissipative media

Stable localized nonlinear coherent structures, i.e. solitons, play a key role in the stochastization of the processes occurring in active-dissipative media. In this study, three-dimensional multi-hump solitons are investigated for a model equation which qualitatively describes the wave processes in some physical systems. The existence of 3D multihump solitons is demonstrated numerically and the soliton behavior is studied. The results are generalized to describe multihump solitons in descending viscous-fluid layers [1]. An unusual physical phenomenon observed in experiments [1], namely, stable two-hump coherent structures on the surface of a downflowing viscous-fluid layer, is explained qualitatively.

Solitary wave propagation in quantum electron-positron plasmas

Existence of large amplitude stationary solitary wave structures in an unmagnetized electron-positron (e-p) plasma is studied using a quantum hydrodynamic (QHD) model that includes the quantum force (tunnelling) associated with the Bohm potential and the Fermi-dirac pressure law. It is found that in a quasi-neutral pair (e-p) plasma, where the dispersion is only due to the the quantum tunnelling effects, the large amplitude stationary solitary structure exists only when the normalized Mach speed,M <√2. Such solitary structures do not exist in absence of the Bohm potential term in an unmagnetized quasineutral pair (e-p) plasma. The system is shown to support only rarefactive stationary solitary waves. For such waves the amplitude, being independent of the quantum parameter H (the ratio of the electron plasmon to electron Fermi energy), decreases with the Mach number M, whereas the width increases with both M and H. The present theory is applicable to analyze the formation of localized coherent solitary structures at quantum scales in dense astrophysical objects as well as in intense laser fields.

Soliton and chaotic structures of dust ion-acoustic waves in quantum dusty plasmas

The quantum hydrodynamic model is employed to study the soliton and chaotic structures of dust ion-acoustic waves in quantum dusty plasmas consisting of electrons, ions, and negatively/positively charged dust particles. By means of the reductive perturbation technique, two-dimensional Davey–Stewartson (DS) system is derived. By improving the extended projective method and the extended tanh-function method, a separation of variables solution with arbitrary functions for the Davey–Stewartson system is obtained. Many soliton and chaotic structures such as localized nonlinear coherent structure, line-soliton structure, periodic wave pattern structure, Rössler and Lorenz chaotic structures are given. It is found that these structures are effected by the quantum effects.

New Exact Solutions and Localized Structures for (3+1)-Dimensional Burgers System

With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (3+1)-dimensional Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.

The structures and interactions of solitary waves in a (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation

The complete integrability of a (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion (CNLERD) equation using the technique of Painlev(P)-analysis is investigated. Using the formalism of Weiss et al (1983 J. Math. Phys. 24 522), the arbitrariness of the expansion coefficients are proved. Besides, following the Hirota's formalism (Hirota R 1980 Direct methods in soliton theory Soliton (Berlin: Springer)) combined to Weiss et al's methodology (Weiss et al 1984 J. Math. Phys. 25 13), the consistency of the truncation is shown. Thus, without the use of Kruskal's simplification, the Bcklund transformation (BT) of the equations is obtained via the truncation procedure. Taking into account the arbitrariness of the expansion coefficients in the foregoing truncation, a typical spectrum of localized coherent structures may be unearthed. The scattering behavior of such structures is also investigated.

Role of topological phase-defects in the parametric generation process

We show that topological phase-defects are spontaneously generated from noise fluctuations in the degenerate configuration of the parametric interaction. These localized coherent structures are shown to affect the coherence properties of the parametrically generated field. It is shown that the emergence of coherence in the fundamental field relies on a previously unrecognized process of mutual annihilation of pairs of neighboring phase-defects. More precisely, the density of phase-defects N, and the time correlation τc of the generated field, are shown to exhibit a power-law behavior with the propagation length, i.e., τc∝z1/4,N∝z-1/4.

LOCALIZED EXCITATIONS WITH AND WITHOUT PROPAGATING PROPERTIES IN (2+1)-DIMENSIONS VIA A REDUCTION APPROACH

In this paper, an objective reduction approach (a special conditional reduction approach) is presented. As a concrete application in nonlinear physical system, new types of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for the (2+1) -dimensional modified dispersive long-wave system are derived via the objective reduction approach. As special reduction cases based on the derived variable separation solutions, it is shown that some localized coherent structures like nonpropagating and propagating solitons with physical meaning exist in the (2+1) -dimensional modified dispersive long-wave system by prescribing different values of the arbitrary parameters in this short note.

Three-dimensional localized coherent structures of surface turbulence. I. Scenarios of two-dimensional–three-dimensional transition

The evolution of naturally excited disturbances on a thin liquid film falling down an inclined planar substrate undergoes several transitions between different wave regimes starting from two-dimensional (2D, one spatial dimension and height) solitary pulses at small Reynolds numbers to the “surface turbulence” stage for sufficiently large Reynolds numbers where the surface is randomly covered by localized three-dimensional (3D, two spatial dimensions and height) coherent structures. In this study, we analyze for the first time the instability of 2D pulses to 3D disturbances and the transitions of 2D pulses to fully developed 3D waves. The main instability mechanism responsible for the transition to 3D localized patterns is the Rayleigh instability of well-separated (isolated) 2D solitary waves. On the other hand, the physical mechanism for the 3D instability of 2D periodic waves and wave trains of 2D solitary waves sufficiently close to each other is not related to the Rayleigh instability but is due to wave-wave interaction and mass exchange between neighboring waves. These instabilities are characteristic of small inclination angles but under special conditions can be realized also for the vertical flow.

Three-dimensional localized coherent structures of surface turbulence. II. Λ solitons

We numerically construct Λ solitons as a function of the generalized Reynolds number δ. The numerical scheme is based on an impulse response analysis in which the nonlinear hump region is replaced with a Dirac delta function. We also examine the linear stability of Λ solitons with respect to three-dimensional disturbances. It is shown that the operator of the linearized system has both a discrete and a continuous spectrum. The discrete spectrum is always stable, while the continuous spectrum can be destabilized leading to a convective instability of Λ solitons. We demonstrate that the region of existence and stability of Λ solitons is 0.054&amp;lt;δ&amp;lt;0.51.

The functional separation method based on the singular manifold method

The functional separation method based on the singular manifold method may be devised to obtain a functional separation solution with arbitrary functions of a given nonlinear partial differential equation. Several examples are used to illustrate this approach, and their exact solutions are obtained. The localized coherent structures and their interaction properties are numerically studied on the basis of the exact solutions. The fission and fusion phenomena and the creation and annihilation phenomena of dromion-like structures are reported.

Ambipolar diffusion in complex plasma

A self-consistent model of the ambipolar diffusion of electrons and ions in complex (dusty) plasmas accounting for the local electric fields, the dust grain charging process, and the interaction of the plasma particles with the dust grains and neutrals is presented. The dependence of the diffusion coefficient on the interaction of the electrons and ions with the dust grains as well as with the neutrals are investigated. It is shown that increase of the dust density leads to a reduction of the diffusion scale length, and this effect is enhanced at higher electron densities. The dependence of the diffusion scale length on the neutral gas pressure is found to be given by a power law, where the absolute value of the power exponent decreases with increase of the dust density. The electric field gradient and its effects are shown to be significant and should thus be taken into account in studies of complex plasmas with not very small dust densities. The possibility of observing localized coherent dissipative nonlinear dust ion-acoustic structures in an asymmetrically discharged double plasma is discussed.

Trilinearization and localized coherent structures and periodic solutions for the (2 + 1) dimensional K-dV and NNV equations

In this paper, using a novel approach involving the truncated Laurent expansion in the Painlevé analysis of the (2 + 1) dimensional K-dV equation, we have trilinearized the evolution equation and obtained rather general classes of solutions in terms of arbitrary functions. The highlight of this method is that it allows us to construct generalized periodic structures corresponding to different manifolds in terms of Jacobian elliptic functions, and the exponentially decaying dromions turn out to be special cases of these solutions. We have also constructed multi-elliptic function solutions and multi-dromions and analysed their interactions. The analysis is also extended to the case of generalized Nizhnik–Novikov–Veselov (NNV) equation, which is also trilinearized and general class of solutions obtained.

Localized Excitations in a Dispersive Long Water-Wave System via an Extended Projective Approach

By means of an extended projective approach, a new type of variable separation excitation with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Based on the derived variable separation excitation, abundant localized coherent structures such as single-valued localized excitations, multiple-valued localized excitations and complex wave excitations are revealed by prescribing appropriate functions. - PACS numbers: 03.65.Ge, 05.45.Yv

Circular Couette cell for two-dimensional fluid dynamics experiments

A novel experiment to investigate fluid dynamics in quasi-two-dimensional flows has been built. A soap film is suspended horizontally in an annular channel with a rotating outer boundary, providing mean flow shear, and a vortex array is forced electromagnetically. The experiment will investigate sheared flow stability and the effect of mean flow shear on local vorticity and coherent structures. Particle image velocimetry measurements demonstrate the production of mean flow shear and induced vortices.

Two-Dimensional Turbulence Analysis Using High-Speed Visible Imaging in TJ-II Edge Plasmas

Two-dimensional edge plasma turbulence as measured by high-speed Hα imaging is investigated in the TJ-II stellarator. An image analysis method based on two-dimensional continuous wavelet transformation is introduced. This method detects localized coherent structures (blobs) in the images and extracts their geometrical characteristics (position, scale, orientation angle, and aspect ratio). This paper studies the impact of edge shear layers (both spontaneous and biased induced) on these geometrical aspects of blobs. Results show a reduction in the angular dispersion of k ∼ 1.2 to 1.4 cm−1 blobs as the shear layer (both spontaneous and biased induced) is established in the boundary, as well as a shift of the aspect ratio histogram toward higher values. The turbulence suppression induced by the biasing seems to be scale selective, more effectively suppressing k ∼ 1.4 cm−1, λ ∼ 4.5 cm structures than k ∼ 0.7 cm−1, λ ∼ 9.0 cm ones.

Optimized suppression of coherent noise from seismic data using the Karhunen-Loève transform

Signals obtained in land seismic surveys are usually contaminated with coherent noise, among which the ground roll (Rayleigh surface waves) is of major concern for it can severely degrade the quality of the information obtained from the seismic record. This paper presents an optimized filter based on the Karhunen-Loève transform for processing seismic images contaminated with ground roll. In this method, the contaminated region of the seismic record, to be processed by the filter, is selected in such way as to correspond to the maximum of a properly defined coherence index. The main advantages of the method are that the ground roll is suppressed with negligible distortion of the remnant reflection signals and that the filtering procedure can be automated. The image processing technique described in this study should also be relevant for other applications where coherent structures embedded in a complex spatiotemporal pattern need to be identified in a more refined way. In particular, it is argued that the method is appropriate for processing optical coherence tomography images whose quality is often degraded by coherent noise (speckle).

The Variable Separation Method and Exact Jacobi Elliptic Function Solutions for the Nizhnik-Novikov-Veselov Equation

Based on the singular structure analysis, the variable separation method is proposed for the Nizhnik–Novikov–Veselov equation to obtain a general functional separation solution containing three arbitrary functions. Choosing these arbitrary functions to be the Jacobi elliptic functions, a diversity of elliptic function solutions may be obtained for the equation of interest. The interaction property of the waves is numerically studied. The long wave limit gives the new type of localized coherent structures.

New Types of Localized Coherent Structures in the Bogoyavlenskii-Schiff Equation

Based on the singular structure analysis, we derive some new types of localized coherent structures for the Bogoyavlenskii-Schiff equation by suitably utilizing the arbitrary function present in the singular manifold equations.