A modified truncation procedure for the BBGKY hierarchy

1969 ◽  
Vol 3 (1) ◽  
pp. 107-118 ◽  
Author(s):  
C. J. Myerscough
Keyword(s):  
Kinetic Equation ◽  
Physical Interpretation ◽  
Coulomb Potential ◽  
Kinetic Equations ◽  
Bbgky Hierarchy ◽  
Collision Integral ◽  
The Other ◽  
Standard Methods ◽  
Particle Separations ◽  
Number Of Authors

The approximations usually made to truncate the BBGKY hierarchy for a plasma are discussed; their failure at small inter-particle separations leads to divergence of the Balescu—Lenard collision integral. A number of authors have obtained convergent kinetic equations, often by rather complicated methods.It is shown here that, if the standard truncation procedure is modified in a way which makes it less obviously inconsistent for close approaches, the standard methods maybe closely followed in deriving a convergent collision integral which agrees to dominant order with the ‘cutoff’ Balescu—Lenard integral and with the other work on the problem. In fact, the kinetic equation obtained is identical with the Balescu—Lenard equation except that the Coulomb potential is replaced by another that is non-singular at the origin. A physical interpretation of this result is suggested.

The Cauchy problem for BBGKY hierarchy of quantum kinetic equations with coulomb potential

2009 ◽  
Author(s):  
M. Brokate ◽  
M. Yu. Rasulova ◽  
A. H. Siddiqi ◽  
M. Brokate ◽  
A. K. Gupta
Keyword(s):  
Cauchy Problem ◽  
Coulomb Potential ◽  
Kinetic Equations ◽  
Bbgky Hierarchy ◽  
The Cauchy Problem

scholarly journals DISTRIBUTION AND RACE COMPOSITION OF DOWNY MILDEW (Plasmopara halstedii (Farl.) Berl. and de Toni) IN BULGARIA / EXTENSION Y RAZAS DEL MILDIU (Plasmopara halstedii (Farl.) Berl. y de Toni) EN BULGARIA / ÉTENDUE ET RACES DE LA ROUILLE (Plasmopara halstedii (Farl.) Berl. and de Toni) EN BULGARIE

Helia ◽  
2000 ◽  
Vol 23 (33) ◽  
pp. 25-32
Author(s):  
P.S. Shindrova
Keyword(s):  
Downy Mildew ◽  
Resistance Gene ◽  
The Other ◽  
Plasmopara Halstedii ◽  
North West ◽  
North East ◽  
Race 1 ◽  
Race 2 ◽  
Production Areas ◽  
Number Of Authors

SUMMARY Downy mildew caused by the fungus Plasmopara halstedii is the main disease on sunflower in Bulgaria. In recent years a number of authors have reported the occurrence of new more virulent races of the pathogen. According to other authors these races demonstrate resistance to the fungicides used up to now. This fact is rather alarming and imposes the necessity of annual researches with the aim of following the changes in the downy mildew race variability. In the period 1995-1997 downy mildew isolates were collected from the following locations: Bourgas, Boyanovo, Karnobat, Ognyanovo, Selanovtsi, Kroushari, Lovech, Koubrat, Brashlyan, Sitovo, Tervel, Targovishte, IWS “Dobroudja” and Dobrich. The samples were assessed for virulence on a set of sunflower differential - lines under greenhouse conditions. The obtained results do not reveal a great race variability of downy mildew population in Bulgaria. In the period of study two races of the pathogen were identified: race 1 which infects the differential lines without genes for resistance to the pathogen. It is distributed in all sunflower production areas of the country. The other one is race 2. It is of limited distribution and has been registered in individual fields of north-east and north-west Bulgaria. It attacks the differential lines carrying the resistance gene Pl-1.

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.

scholarly journals Physico-chemical and Sensory Properties of Cookies Produced by Partial Substitution of Margarine with Avocado Pear (Persia americana)

2021 ◽  
Vol 13 (1) ◽  
pp. 96-104
Author(s):  
Jelili Babatunde Hussein ◽  
Joseph Idowu Olaniyi ◽  
Esther Anjikwi Msheliza ◽  
Seember Bernadette Kave
Keyword(s):  
Fatty Acids ◽  
Free Fatty Acids ◽  
Iodine Value ◽  
Peroxide Value ◽  
Crude Protein ◽  
The Other ◽  
Partial Substitution ◽  
Standard Methods ◽  
Physico Chemical ◽  
Sensory Qualities

The partial substitution of margarine with mature avocado pear pulp in the production of cookies was investigated. Five cookie samples were produced with avocado pear pulp and margarine blends in the ratios 80:20%, 70:30%, 60:40%, 50:50%, and 100% margarine serve as the control, labeled as B, C, D and E and A, respectively while the other ingredients used remain constant. The physico-chemical (proximate compositions, free fatty acids (FFA), iodine value, and peroxide value) and sensory qualities of the cookies were evaluated using standard methods. The results show ranged in moisture (11.13 to 14.60%), crude protein (6.93 to 7.83%), crude fat (16.00 to 18.03%), ash (1.40 to 2.09%), crude fiber (0.29 to 0.62%), carbohydrate (59.70 to 62.79%), FFA (0.35 to 1.01 mg KOH/g), iodine value (75.63 to 81.17 g I2/100 g) and peroxide value (2.96 to 5.27 meq/kg). The partial substitution of margarine with avocado pear pulp produced nutritious cookies with desirable organoleptic qualities. Also, the results demonstrated that cookies had acceptability up to a 30% level of substitution with avocado pear pulp. The findings indicated the feasibility of avocado pear pulp in fat-reduced cookies preparation, this will reduce the pressure in using only margarine in cookies making and diversify the use of avocado pear.

PHYSICAL INTERPRETATION OF BLACK HOLE EVAPORATION AS A VACUUM INSTABILITY

1992 ◽  
Vol 01 (01) ◽  
pp. 169-191 ◽  
Author(s):  
R. PARENTANI ◽  
R. BROUT
Keyword(s):  
Black Hole ◽  
Electric Field ◽  
Physical Interpretation ◽  
Particle Production ◽  
Pair Creation ◽  
The Other ◽  
Static Electric Field ◽  
Black Hole Evaporation ◽  
Tunneling Mechanism ◽  
Vacuum Instability

Using tunneling concepts which account for particle production in the cases of an accelerated detector and a static electric Field in Minkowski space, the more elusive case of black hole evaporation is analyzed in terms of a detailed tunneling mechanism. For the case of the incipient black hole (collapsing star) Hawking’s “heuristic” picture in terms of pair creation, wherein one member crosses the horizon to fall into the singularity as the other is emitted to infinity, is established. The inception of tunneling is due to the motion of the star’s surface, but its completion concerns traversal of the horizon, thereby reconciling varying schools of thought concerning this problem.

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>

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