225 research outputs found
Weakly nonlinear ion sound waves in gravitational systems
Ion sound waves are studied in a plasma subject to gravitational field. Such
systems are interesting by exhibiting a wave growth that is a result of energy
flux conservation in inhomogeneous systems. The increasing wave amplitude gives
rise to an enhanced interaction between waves and plasma particles that can be
modeled by a modified Korteweg-de Vries equation. Analytical results are
compared with numerical Particle-in-Cell simulations of the problem. Our code
assumes isothermally Boltzmann distributed electrons while the ion component is
treated as a collection of individual particles interacting through collective
electric fields. Deviations from quasi neutrality are allowed for.Comment: 30 pages, 9 figure
Contributions of plasma physics to chaos and nonlinear dynamics
This topical review focusses on the contributions of plasma physics to chaos
and nonlinear dynamics bringing new methods which are or can be used in other
scientific domains. It starts with the development of the theory of Hamiltonian
chaos, and then deals with order or quasi order, for instance adiabatic and
soliton theories. It ends with a shorter account of dissipative and high
dimensional Hamiltonian dynamics, and of quantum chaos. Most of these
contributions are a spin-off of the research on thermonuclear fusion by
magnetic confinement, which started in the fifties. Their presentation is both
exhaustive and compact. [15 April 2016
Selected Topics in Plasma Physics
This book is planned to introduce the advances topics of plasma physics for research scholars and postgraduate students. This book deals with basic concepts in plasma physics, non-equilibrium plasma modeling, space plasma applications, and plasma diagnostics. It also provides an overview of the linear and nonlinear aspects of plasma physics. Chapters cover such topics as plasma application in space propulsion, microwave–plasma interaction, plasma antennas, solitary waves, and plasma diagnostic techniques
Similar oscillations on both sides of a shock. Part I. Even-odd alternative dispersions and general assignments of Fourier dispersions towards a unfication of dispersion models
We consider assigning different dispersions for different dynamical modes,
particularly with the distinguishment and alternation of opposite signs for
alternative Fourier components. The Korteweg-de Vries (KdV) equation with
periodic boundary condition and longest-wave sinusoidal initial field, as used
by N. Zabusky and M. D. Kruskal, is chosen for our case study with such
alternating-dispersion of the Fourier modes of (normalized) even and odd
wavenumbers. Numerical results verify the capability of our new model to
produce two-sided (around the shock) oscillations, as appear on both sides of
some ion-acoustic and quantum shocks, not admitted by models such as the
KdV(-Burgers) equation, but also indicate even more, including singular
zero-dispersion limit or non-convergence to the classical shock (described by
the entropy solution), non-thermalization (of the Galerkin-truncated models)
and applicability to other models (showcased by the modified KdV equation with
cubic nonlinearity). A unification of various dispersive models, keeping the
essential mathematical elegance (such as the variational principle and
Hamiltonian formulation) of each, for phenomena with complicated dispersion
relation is thus suggested with a further explicit example of two even-order
dispersions (from the Hilbert transforms) extending the Benjamin-Ono model. The
most general situation can be simply formulated by the introduction of the
dispersive derivative, the indicator function and the Fourier transform,
resulting in an integro-differential dispersion equation. Other issues such as
the real-number order dispersion model and the transition from
non-thermalization to thermalization and, correspondingly, from regularization
to non-regularization for untruncated models are also briefly remarked
An augmented lagrangian approach for Euler-Korteweg type equations
On présente un modèle hyperbolique quasi-linéaire de premier ordre approximant les équations d'Euler-Korteweg (E-K), qui décrivent des écoulements de fluides compressibles dont l'énergie dépend du gradient de la densité. Le système E-K peut être vu comme les équations d'Euler-Lagrange d'un Lagrangien soumis à la conservation de la masse. Vu la présence du gradient de la densité dans le Lagrangien, des dérivées d'ordre élevé de la densité apparaissent dans les équations du mouvement. L'approche présentée ici permet d'obtenir un système d'équations hyperboliques qui approxime le système E-K. L'idée est d'introduire un nouveau paramètre d'ordre qui approxime la densité via une méthode de pénalisation classique. Le gradient de cette nouvelle variable remplace alors le gradient de la densité dans le Lagrangien, ce qui permet de construire le Lagrangien augmenté. Les équations d'Euler-Lagrange associées à celui-ci, sont des équations hyperboliques avec des termes sources raides et des vitesses de caractéristiques rapides. Ce système est analysé puis résolu numériquement en utilisant des schémas de type IMEX. En particulier, cette approche a été appliquée à l'équation de Schrödinger non-linéaire défocalisante (qui peut être réduite au système E-K via la transformée de Madelung), pour laquelle des comparaisons avec des solutions exactes et asymptotiques ont été faites, notamment pour des solitons gris et des ondes de choc dispersives. La même approche a été également appliquée aux équations de filmes minces avec capillarité, pour lesquelles une comparaison avec des résultats numériques de référence et des résultats expérimentaux a été faite. Il a été démontré que le modèle augmenté peut aussi bien s'appliquer pour des modèles dont le terme de capillarité est non-linéaire. Dans ce même cadre, une étude de gouttes stationnaires sur un substrat solide horizontal a été établie afin de classifier les profils possibles de gouttes selon leur énergie. Ceci a permis également de faire des comparaisons du modèle augmenté sur des solutions stationnaires. Enfin, une partie indépendante de ce travail est consacrée à l'étude des équations équivalentes associées aux schémas numériques, où l'on démontre que les conditions de stabilité qui dérivent d'une troncature de l'équation équivalente, n'a du sens que si la série correspondante dans l'espace de Fourier est convergente, sur les longueurs d'onde admissibles dans la pratique.An approximate first order quasilinear hyperbolic model for Euler-Korteweg (E-K) equations, describing compressible fluid flows whose energy depend on the gradient of density, is derived. E-K system can be seen as the Euler-Lagrange equations to a Lagrangian submitted to the mass conservation constraint. Due to the presence of the density gradient in the Lagrangian, one recovers high-order derivatives of density in the motion equations. The approach presented here permits us to obtain a system of hyperbolic equations that approximate E-K system. The idea is to introduce a new order parameter which approximates the density via a carefully chosen penalty method. The gradient of this new independent variable will then replace the original gradient of density in the Lagrangian, resulting in the so-called augmented Lagrangian. The Euler-Lagrange equations of the augmented Lagrangian result in a first order hyperbolic system with stiff source terms and fast characteristic speeds. Such a system is then analyzed and solved numerically by using IMEX schemes. In particular, this approach was applied to the defocusing nonlinear Schrödinger equation (which can be reduced to the E-K equations via the Madelung transform), for which a comparison with exact and asymptotic solutions, namely gray solitons and dispersive shock waves was performed. Then, the same approach was extended to thin film flows with capillarity, for which comparison of the numerical results with both reference numerical solutions and experimental results was performed. It was shown that the augmented model is also extendable to models with full nonlinear surface tension. In the same setting, a study of stationary droplets on a horizontal solid substrate was conducted in an attempt to classify droplet profiles depending on their energy forms. This also allowed to compare the augmented Lagrangian approach in the case of stationary solutions, and which showed excellent agreement with the reference solutions. Lastly, an independent part of this work is devoted to the study of modified equations associated to numerical schemes for stability purposes. It is shown that for a linear scheme, stability conditions which are obtained from a truncation of the associated modified equation, are only relevant if the corresponding series in Fourier space is convergent for the admissible wavenumbers
Rigorous coherent-structure theory for falling liquid films: Viscous dispersion effects on bound-state formation and self-organization
We examine the interaction of two-dimensional solitary pulses on falling
liquid films. We make use of the second-order model derived by Ruyer-Quil and
Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000);
Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a
weighted residuals technique. The model includes (second-order) viscous
dispersion effects which originate from the streamwise momentum equation and
tangential stress balance. These effects play a dispersive role that primarily
influences the shape of the capillary ripples in front of the solitary pulses.
We show that different physical parameters, such as surface tension and
viscosity, play a crucial role in the interaction between solitary pulses
giving rise eventually to the formation of bound states consisting of two or
more pulses separated by well-defined distances and travelling at the same
velocity. By developing a rigorous coherent-structure theory, we are able to
theoretically predict the pulse-separation distances for which bound states are
formed. Viscous dispersion affects the distances at which bound states are
observed. We show that the theory is in very good agreement with computations
of the second-order model. We also demonstrate that the presence of bound
states allows the film free surface to reach a self-organized state that can be
statistically described in terms of a gas of solitary waves separated by a
typical mean distance and characterized by a typical density
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