151 research outputs found
A splitting lattice Boltzmann scheme for (2+1)-dimensional soliton solutions of the Kadomtsev-Petviashvili equation
Recently, considerable attention has been given to (2+1)-dimensional Kadomtsev-Petviashvili equations due to their extensive applications in solitons that widely exist in nonlinear science. Therefore, developing a reliable numerical algorithm for the Kadomtsev-Petviashvili equations is crucial. The lattice Boltzmann method, which has been an efficient simulation method in the last three decades, is a promising technique for solving Kadomtsev-Petviashvili equations. However, the traditional higher-order moment lattice Boltzmann model for the Kadomtsev-Petviashvili equations suffers from low accuracy because of error accumulation. To overcome this shortcoming, a splitting lattice Boltzmann scheme for (2+1)-dimensional Kadomtsev-Petviashvili-â… type equations is proposed in this paper. The variable substitution method is applied to transform the Kadomtsev-Petviashvili-â… type equation into two macroscopic equations. Two sets of distribution functions are employed to construct these two macroscopic equations. Moreover, three types of soliton solutions are numerically simulated by this algorithm. The numerical results imply that the splitting lattice Boltzmann schemes have an advantage over the traditional high-order moment lattice Boltzmann model in simulating the Kadomtsev-Petviashvili-â… type equations
Simulation of Magnetorheological Fluids Based on Lattice Boltzmann Method with Double Meshes
In order to study the rheological characteristics of magnetorheological fluids, a novel approach based on the two-component Lattice Boltzmann method with double meshes was proposed, and the micro-scale structures of magnetorheological fluids in different strength magnetic fields were simulated. The framework composed of three steps for the simulation of magnetorheological fluids was addressed, and the double meshes method was elaborated. Moreover, the various internal and external forces acting on the magnetic particles were analyzed and calculated. The two-component Lattice Boltzmann model was set up, and the flowchart for the simulation of magnetorheological fluids based on the two-component Lattice Boltzmann method with double meshes was designed. Finally, a physics experiment was carried out, and the simulation examples were provided. The comparison results indicated that the proposed approach was feasible, efficient, and outperforming others
Hydrodynamic scales of integrable many-particle systems
1. Introduction, 2. Dynamics of the classical Toda lattice, 3. Static
properties, 4. Dyson Brownian motion. , 5. Hydrodynamics for hard rods, 6.
Equations of generalized hydrodynamics, 7. Linearized hydrodynamics and GGE
dynamical correlations, 8. Domain wall initial states, 9. Toda fluid, 10.
Hydrodynamics of soliton gases, 11. Calogero models, 12. Discretized nonlinear
Schr\"odinger equation , 13. Hydrodynamics for the Lieb-Liniger -Bose
gas, 14. Quantum Toda lattice, 15. Beyond the Euler time scaleComment: 178 pages, 12 Figures. This a much enlarged and substantially
improved version of arXiv:2101.0652
Hyperbolic Techniques in Modelling, Analysis and Numerics
Several research areas are flourishing on the roots of the breakthroughs in conservation laws that took place in the last two decades. The meeting played a key role in providing contacts among the different branches that are currently developing. All the invitees shared the same common background that consists of the analytical and numerical techniques for nonlinear hyperbolic balance laws. However, their fields of applications and their levels of abstraction are very diverse. The workshop was the unique opportunity to share ideas about analytical issues like the fine-structure of singular solutions or the validity of entropy solution concepts. It turned out that generalized hyperbolic techniques are able to handle the challenges posed by new applications. The design of efficient structure preserving methods turned out to be the major line of development in numerical analysis
Soliton Gas: Theory, Numerics and Experiments
The concept of soliton gas was introduced in 1971 by V. Zakharov as an
infinite collection of weakly interacting solitons in the framework of
Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted
soliton gas, solitons with random parameters are almost non-overlapping. More
recently, the concept has been extended to dense gases in which solitons
strongly and continuously interact. The notion of soliton gas is inherently
associated with integrable wave systems described by nonlinear partial
differential equations like the KdV equation or the one-dimensional nonlinear
Schr\"odinger equation that can be solved using the inverse scattering
transform. Over the last few years, the field of soliton gases has received a
rapidly growing interest from both the theoretical and experimental points of
view. In particular, it has been realized that the soliton gas dynamics
underlies some fundamental nonlinear wave phenomena such as spontaneous
modulation instability and the formation of rogue waves. The recently
discovered deep connections of soliton gas theory with generalized
hydrodynamics have broadened the field and opened new fundamental questions
related to the soliton gas statistics and thermodynamics. We review the main
recent theoretical and experimental results in the field of soliton gas. The
key conceptual tools of the field, such as the inverse scattering transform,
the thermodynamic limit of finite-gap potentials and the Generalized Gibbs
Ensembles are introduced and various open questions and future challenges are
discussed.Comment: 35 pages, 8 figure
Modulated dust-acoustic wave packets in a plasma with non-isothermal electrons and ions
Nonlinear self-modulation of the dust acoustic waves is studied, in the
presence of non-thermal (non-Maxwellian) ion and electron populations. By
employing a multiple scale technique, a nonlinear Schrodinger-type equation
(NLSE) is derived for the wave amplitude. The influence of non-thermality, in
addition to obliqueness (between the propagation and modulation directions), on
the conditions for modulational instability to occur is discussed. Different
types of localized solutions (envelope excitations) which may possibly occur
are discussed, and the dependence of their characteristics on physical
parameters is traced. The ion deviation from a Maxwellian distribution comes
out to be more important than the electron analogous deviation alone. Both
yield a de-stabilizing effect on (the amplitude of) DAWs propagating in a dusty
plasma with negative dust grains. The opposite effect, namely a tendency
towards amplitude stabilization, is found for the case of positively charged
dust presence in the plasma.Comment: To appear in Journal of Plasma Physics (2004
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