scholarly journals On the Generalized Kinetic Equation for Surface Gravity Waves, Blow-Up and Its Restraint

Fluids ◽  
2018 ◽  
Vol 4 (1) ◽  
pp. 2 ◽  
Author(s):  
David Andrade ◽  
Raphael Stuhlmeier ◽  
Michael Stiassnie
Keyword(s):  
Kinetic Equation ◽  
Blow Up ◽  
Kinetic Equations ◽  
Linear Interaction ◽  
Spectral Action ◽  
Ocean Surface Waves ◽  
Action Density ◽  
Numerical Tools ◽  
Generalized Kinetic Equation ◽  
Made In

This article is concerned with the non-linear interaction of homogeneous random ocean surface waves. Under this umbrella, numerous kinetic equations have been derived to study the evolution of the spectral action density, each employing slightly different assumptions. Using analytical and numerical tools, and providing exact formulas, we demonstrate that the recently derived generalized kinetic equation exhibits blow up in finite time for certain degenerate quartets of waves. This is discussed in light of the assumptions made in the derivation, and this equation is contrasted with other kinetic equations for the spectral action density.

Les équations cinétiques pour les systèmes réactifs. Initiation photochimique et thermique. Les coefficients de vitesse

1982 ◽  
Vol 60 (16) ◽  
pp. 2151-2158 ◽  
Author(s):  
Juan Veguillas ◽  
Miguel Angel Diaz Armentia ◽  
Angel Maria Gutierrez Terron
Keyword(s):  
Kinetic Equation ◽  
Cluster Expansion ◽  
Kinetic Equations ◽  
Master Equations ◽  
Rate Coefficients ◽  
Boltzmann Equations ◽  
Generalized Kinetic Equation

In a previous publication a method was developed for obtaining kinetic equations for a reacting system. In this publication that method is applied to a system [Formula: see text] whose initiation is a photodissociation. The reactive Hamiltonian has been found through Tani's generalized transformation. The generalized kinetic equation has been used. The cluster expansion of the collision superoperator has been obtained from the cluster expansion of the resolvent superoperator, by assuming that collisions are instantaneous. The generalized Boltzmann equations have been obtained. From the kinetic equations we have found the master equations and from them the rate coefficients have been identified.

A numerical solution of the kinetic equations for a spectrum of Langmuir turbulence

1984 ◽  
Vol 31 (2) ◽  
pp. 253-261
Author(s):  
Denis Hayward
Keyword(s):  
Numerical Solution ◽  
Relativistic Electron Beam ◽  
Final Section ◽  
Plasma Heating ◽  
Kinetic Equations ◽  
Langmuir Turbulence ◽  
Quick Method ◽  
Isothermal Plasma ◽  
Principal Contributor ◽  
Made In

The main properties of a kinetic wave equation in an isothermal plasma, Te ≈ Ti, are discussed and a quick method of numerical solution based on factorization of the kernel of an integral equation is outlined. As an illustration the method is applied to the problem of plasma heating with a relativistic electron beam and it is shown how the evolution of a spectrum of Langmuir turbulence is the principal contributor to the heating of the plasma. The technique allows an estimate of the error which is present in the stationary solution, and this is made in the final section.

Kinetic equations for plasmas subjected to a strong time-dependent extenal field. Part 2. The weak-interaction approximation

1974 ◽  
Vol 11 (3) ◽  
pp. 377-387 ◽  
Author(s):  
R. Balescu ◽  
J. H. Misguich
Keyword(s):  
Kinetic Equation ◽  
General Theory ◽  
Weak Interaction ◽  
Weak Coupling ◽  
Kinetic Equations ◽  
Time Dependent ◽  
External Fields ◽  
Interaction Approximation

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.

FRACTIONAL KINETIC EQUATIONS INVOLVING GENERALIZED V-FUNCTION VIA LAPLACE TRANSFORM

2021 ◽  
Vol 10 (5) ◽  
pp. 2593-2610
Author(s):  
Wagdi F.S. Ahmed ◽  
D.D. Pawar ◽  
W.D. Patil
Keyword(s):  
Kinetic Equation ◽  
Laplace Transform ◽  
Kinetic Equations ◽  
Graphical Interpretation ◽  
Fractional Kinetic Equation ◽  
Fractional Kinetic Equations

In this study, a new and further generalized form of the fractional kinetic equation involving the generalized V$-$function has been developed. We have discussed the manifold generality of the generalized V$-$function in terms of the solution of the fractional kinetic equation. Also, the graphical interpretation of the solutions by employing MATLAB is given. The results are very general in nature, and they can be used to generate a large number of known and novel results.

KINETIC EQUATION FOR A GAS WITH LONG-RANGE ATTRACTION

1967 ◽  
Vol 45 (11) ◽  
pp. 3555-3567 ◽  
Author(s):  
R. A. Elliott ◽  
Luis de Sobrino
Keyword(s):  
Kinetic Equation ◽  
Long Range ◽  
Short Range ◽  
Kinetic Equations ◽  
Perturbation Expansion ◽  
Interparticle Distance ◽  
Range Interaction ◽  
Short Range Repulsion ◽  
Self Consistent Field ◽  
Range Force

A classical gas whose particles interact through a weak long-range attraction and a strong short-range repulsion is studied. The Liouville equation is solved as an infinite-order perturbation expansion. The terms in this series are classified by Prigogine-type diagrams according to their order in the ratio of the range of the interaction to the average interparticle distance. It is shown that, provided the range of the short-range force is much less than the average interparticle distance which, in turn, is much less than the range of the long-range force, the terms can be grouped into two classes. The one class, represented by chain diagrams, constitutes the significant contributions of the short-range interaction; the other, represented by ring diagrams, makes up, apart from a self-consistent field term, the significant contributions from the long-range force. These contributions are summed to yield a kinetic equation. The orders of magnitude of the terms in this equation are compared for various ranges of the parameters of the system. Retaining only the dominant terms then produces a set of eight kinetic equations, each of which is valid for a definite range of the parameters of the system.

Long-term evolution of directional spectra of wind waves modelled by DNS and kinetic equations, and comparison with airborne measurements

2021 ◽  
Author(s):  
Sergei Annenkov ◽  
Victor Shrira ◽  
Leonel Romero ◽  
Ken Melville
Keyword(s):  
Angular Distribution ◽  
Kinetic Equation ◽  
Kinetic Theory ◽  
Wind Waves ◽  
Kinetic Equations ◽  
Spectral Peak ◽  
Angular Width ◽  
Angular Structure ◽  
Airborne Measurements ◽  
Steady Growth

<p>We consider the evolution of directional spectra of waves generated by constant and changing wind, modelling it by direct numerical simulation (DNS), based on the Zakharov equation. Results are compared with numerical simulations performed with the Hasselmann kinetic equation and the generalised kinetic equation, and with airborne measurements of waves generated by offshore wind, collected during the GOTEX experiment off the coast of Mexico. Modelling is performed with wind measured during the experiment, and the initial conditions are taken as the observed spectrum at the moment when wind waves prevail over swell after the initial part of the evolution.</p><p>Directional spreading is characterised by the second moment of the normalised angular distribution function, taken at selected wavenumbers relative to the spectral peak. We show that for scales longer than the spectral peak the angular spread predicted by the DNS is close to that predicted by both kinetic equations, but it underestimates the corresponding measured value, apparently due to the presence of swell. For the spectral peak and shorter waves, the DNS shows good agreement with the data. A notable feature is the steady growth of angular width at the spectral peak with time/fetch, in contrast to nearly constant width in the kinetic equations modelling. Dependence of angular width on wavenumber is shown to be much weaker than predicted by the kinetic equations. A more detailed consideration of the angular structure at the spectral peak at large fetches shows that the kinetic equations predict an angular distribution with a well-defined peak at the central angle, while the DNS reproduces the observed angular structure, with a flat peak over a range of angles.</p><p>In order to study in detail the differences between the predictions of the DNS and the kinetic equations modelling under idealised conditions, we also perform numerical simulations for the case of constant wind forcing. As in the previous case of forcing by real wind, the most striking difference between the kinetic equations and the DNS is the steady growth with time of angular width at the spectral peak, which is demonstrated by the DNS, but is not present in the modelling with the kinetic equations. We show that while the kinetic theory, both in the case of the Hasselmann equation and the generalised kinetic equation, predicts a relatively simple shape of the spectral peak, the DNS shows a more complicated structure, with a flat top and dependence of the peak position on angle. We discuss the approximations employed in the derivation of the kinetic theory and the possible causes of the found differences of directional structure.</p>

scholarly journals Fluid models with phase transition for kinetic equations in swarming

2020 ◽  
Vol 30 (10) ◽  
pp. 2023-2065 ◽  
Author(s):  
Mihaï Bostan ◽  
José Antonio Carrillo
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Kinetic Equation ◽  
Free Parameter ◽  
Kinetic Equations ◽  
Interaction Frequency ◽  
Fluid Models ◽  
Mean Velocity ◽  
Friction Forces ◽  
The Mean

We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case, the equilibria depend on the density and the orientation of the mean velocity, whereas the mean speed is not anymore a free parameter and a phase transition occurs in the homogeneous kinetic equation. We analyze the profile of equilibria for general potentials identifying a family of potentials leading to phase transitions. Finally, we derive the fluid equations when the interaction frequency becomes very large.

Collisional transport for a superthermal ion species in magnetized plasma

1986 ◽  
Vol 36 (3) ◽  
pp. 313-328 ◽  
Author(s):  
F. Cozzani ◽  
W. Horton
Keyword(s):  
Kinetic Equation ◽  
Transport Theory ◽  
A Priori ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
High Energy ◽  
Magnetized Plasma ◽  
Fractional Density ◽  
Background Ions ◽  
Ion Species

The transport theory of a high-energy ion species injected isotropically in a magnetized plasma is considered for arbitrary ratios of the high-energy ion cyclotron frequency to the collisional slowing down time. The assumptions of (i) low fractional density of the high-energy species and (ii) average ion speed faster than the thermal ions and slower than the electrons are used to decouple the kinetic equation for the high-energy species from the kinetic equations for background ions and electrons. The kinetic equation is solved by a Chapman–Enskog expansion in the strength of the gradients; an equation for the first correction to the lowest-order distribution function is obtained without scaling a priori the collision frequency with respect to the gyrofrequency. Various transport coefficients are explicitly calculated for the two cases of a weakly and a strongly magnetized plasma.

scholarly journals Multiple asymptotics of kinetic equations with internal states

2020 ◽  
Vol 30 (06) ◽  
pp. 1041-1073
Author(s):  
Benoit Perthame ◽  
Weiran Sun ◽  
Min Tang ◽  
Shugo Yasuda
Keyword(s):  
Kinetic Equation ◽  
Equilibrium Equation ◽  
Internal State ◽  
Kinetic Equations ◽  
Chemical Stimulus ◽  
Adaptation Time ◽  
Macroscopic Models ◽  
Internal States ◽  
New Type ◽  
Run And Tumble

The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However, the relation between the tumbling rate and the internal state of bacteria is poorly understood. This study aims at deriving macroscopic models as limits of the mesoscopic kinetic equation in different regimes. In particular, we are interested in the roles of the stiffness of the response and the adaptation time in the kinetic equation. Depending on the asymptotics chosen both the standard Keller–Segel equation and the flux-limited Keller–Segel (FLKS) equation can appear. An interesting mathematical issue arises with a new type of equilibrium equation leading to solution with singularities.

Generalized Kinetic Equation for Interaction between Liquid-Phase Silicon and Pyrolytic Carbon Surface

2019 ◽  
Vol 55 (7) ◽  
pp. 1277-1279
Author(s):  
I. L. Sinani ◽  
V. M. Bushuev ◽  
S. G. Lunegov
Keyword(s):  
Kinetic Equation ◽  
Liquid Phase ◽  
Pyrolytic Carbon ◽  
Carbon Surface ◽  
Generalized Kinetic Equation
Sign in / Sign up

Export Citation Format

Share Document