KINETIC EQUATION DESCRIBING IRREVERSIBLE PROCESSES IN IONIZED GASES

1962 ◽  
Vol 40 (4) ◽  
pp. 463-519 ◽  
Author(s):  
Ta-You Wu ◽  
R. L. Rosenberg
Keyword(s):  
Kinetic Equation ◽  
General Theory ◽  
Time Reversal ◽  
Interaction Strength ◽  
Correlation Effect ◽  
Landau Damping ◽  
Irreversible Processes ◽  
Inhomogeneous System ◽  
First Order ◽  
Spatially Inhomogeneous

The present work deals with the formulation of the theory of irreversible processes in ionized gases on the basis of the theory of Bogoliubov for neutral gases. In an extension of the work of Guernsey and Uhlenbeck, the kinetic equation is obtained for a spatially inhomogeneous system in an approximation to the "first order" in the interaction strength (e2) and to all orders in the correlation effect (e2/v, v being the specific volume). The equation, unlike the usual Vlasov equation, is not invariant with respect to time-reversal and shows a genuine "damping" in the sense of an irreversible approach to equilibrium.In the present paper, brief discussions have also been given of the nature of a theory of irreversible processes, the so-called "divergence difficulty", due to the long-range Coulomb forces, the Landau damping, the recent general theory of irreversible processes of Prigogine and Balescu, and the theory of ionized gases of Balescu.

KINETIC EQUATION DESCRIBING IRREVERSIBLE PROCESSES IN IONIZED GASES, II

1963 ◽  
Vol 41 (7) ◽  
pp. 1193-1225
Author(s):  
R. L. Rosenberg ◽  
Ta-You Wu
Keyword(s):  
Kinetic Equation ◽  
Inhomogeneous Plasma ◽  
Effective Field ◽  
Collision Integral ◽  
Spatial Inhomogeneity ◽  
Irreversible Processes ◽  
First Order ◽  
Spatially Inhomogeneous ◽  
The Fourier Transform ◽  
The One

In a previous paper, the authors formulated the theory of irreversible processes in a spatially inhomogeneous plasma on the basis of Bogoliubov's theory as extended by Guernsey and Uhlenbeck. The kinetic equation, in terms of g(κ, n, t), the Fourier transform of the spatially inhomogeneous part f(r, n, t) of the one-particle distribution function F(r, n, t), has been obtained to the first order in 4πe2, all orders in (4πe2/ν), and the first order in κ which is related to the spatial inhomogeneity. In the present work, the mathematical part of the previous paper, especially the expansion in various orders in κ, has been revised. The kinetic equation is given in (33), in which are exhibited: (a) the stream term; (b) the corrections to the stream term arising from the "collisions"; (c) the Vlasov term; (d) the corrections, in the zeroth and the first order in κ, to the Vlasov term depending not only on the "static" effective field but also on the divergence of the mean current, these corrections being momentum-dependent and time-irreversible in nature; (e) the main "collision integral" which is time-irreversible, in the zeroth and the first order in κ.

Quantum Conductivity of Spatially Inhomogeneous Systems

2003 ◽  
Vol 789 ◽  
Author(s):  
Liudmila A. Pozhar
Keyword(s):  
Charge Density ◽  
Evolution Equations ◽  
Original Method ◽  
Theoretical Description ◽  
Inhomogeneous System ◽  
Inhomogeneous Systems ◽  
Spatially Inhomogeneous ◽  
Significant Step ◽  
Quantum Current ◽  
Electro Magnetic

ABSTRACTA fundamental quantum theory of conductivity of spatially inhomogeneous systems in weak electro-magnetic fields has been derived using a two-time Green function (TTGF)-based technique that generalizes the original method due to Zubarev and Tserkovnikov (ZT). Quantum current and charge density evolution equations are derived in a linear approximation with regard to the field potentials. Explicit expressions for the longitudinal and transverse conductivity, and dielectric and magnetic susceptibilities have been derived in terms of charge density - charge density and microcurrent - microcurrent TTGFs. The obtained theoretical description and formulae are applicable to any inhomogeneous system, such as artificial molecules, atomic and molecular clusters, thin films, interfacial systems, etc. In particular, the theory is designed to predict charge transport properties of small semiconductor quantum dots (QDs) and wells (QWs), and is a significant step toward realization of a concept of virtual (i.e., theory-based, computational) synthesis of electronic nanomaterials of prescribed electronic properties.

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.

scholarly journals General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions

2000 ◽  
Vol 84 (21) ◽  
pp. 4794-4797 ◽  
Author(s):  
M. Biskup ◽  
C. Borgs ◽  
J. T. Chayes ◽  
L. J. Kleinwaks ◽  
R. Kotecký
Keyword(s):  
Phase Transitions ◽  
General Theory ◽  
First Order ◽  
First Order Phase

DIFFERENTIAL EQUATIONS IN A HYPERCOMPLEX SYSTEM

2020 ◽  
Vol 69 (1) ◽  
pp. 7-11
Author(s):  
A.K. Abirov ◽  
◽  
N.K. Shazhdekeeva ◽  
T.N. Akhmurzina ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Inhomogeneous System ◽  
Homogeneous Solutions ◽  
First Order ◽  
Zero Divisors ◽  
Hypercomplex System ◽  
Independent Variable ◽  
The Right

The article considers the problem of solving an inhomogeneous first-order differential equation with a variable with a constant coefficient in a hypercomplex system. The structure of the solution in different cases of the right-hand side of the differential equation is determined. The structure of solving the equation in the case of the appearance of zero divisors is shown. It turns out that when the component of a hypercomplex function is a polynomial of an independent variable, the differential equation turns into an inhomogeneous system of real variables from n equations and its solution is determined by certain methods of the theory of differential equations. Thus, obtaining analytically homogeneous solutions of inhomogeneous differential equations in a hypercomplex system leads to an increase in the efficiency of modeling processes in various fields of science and technology.

Degradation of 4-nitrophenol using the Fenton process

2000 ◽  
Vol 42 (3-4) ◽  
pp. 155-160 ◽  
Author(s):  
Y.-S. Ma ◽  
S.-T. Huang ◽  
J.-G. Lin
Keyword(s):  
Kinetic Equation ◽  
Nitrogen Concentration ◽  
Order Kinetic ◽  
Fenton Process ◽  
Nitrogenous Compounds ◽  
First Order ◽  
Degradation Rate Constant ◽  
Before And After ◽  
Pseudo First Order ◽  
Order Kinetic Equation

In this study, The Fenton process was applied as a pretreatment method to treat industrial wastewater containing 4-nitrophenol (4-NP). The effect of oxidant dosages on the decomposition of 4-NP and the reaction kinetics were investigated. More than 99% of 4-NP was readily decomposed when the reaction was carried out at oxidant concentrations of 5 mM H2O2 and 5 mg/L Fe2+ for 2 hours. The total nitrogenous compounds and the nitrogen gas evolved, accounted for 88% of the initial nitrogen concentration. However, the maximum DOC removal efficiency was 30.6%; and only 1/3 of 4-NP was mineralized to carbon dioxide by the Fenton process. 4-NP degradation profiles fitted well into a pseudo first-order kinetic equation; degradation rate constant (min-1) of 4-NP increased from 4.3×10-3 to 66.1×10-3 with increasing dosages of H2O2 and Fe2+. In addition, the t value was calculated for studying the significance of simulation by the t-test. It was found that the t value was greater than the value for 99% confidence. This result suggested that the 4-NP decomposition profile could be described by the pseudo first-order kinetic equation. Biodegradability of 4-NP before and after the reaction was 0.018 and 0.594, respectively.

Part IV The ICC and its Applicable Law, 21 Co-Perpetration: German Dogmatik or German Invasion?

2015 ◽  
Author(s):  
David Ohlin Jens
Keyword(s):  
General Theory ◽  
Control Theory ◽  
International Law ◽  
Criminal Law ◽  
Historical Context ◽  
Legal Culture ◽  
Applicable Law ◽  
First Order

The current doctrines of co-perpetration, most notably the control theory of perpetration, are heavily influenced by German criminal law theory. To some critics, the ICC’s importation of Claus Roxin’s control theory is evidence that one legal culture is having an outsized influence on the direction of the Court’s jurisprudence. This chapter situates the current doctrines within historical context. It lays out the foundations of the ICC doctrine of co-perpetration and evaluates the most notable objections to it, including alternate versions of co-perpetration. The chapter argues that the criticism about the ICC becoming too weighted towards the criminal law approach of one particular system is unfair, since the Court engages in first-order questions of criminal law theory. Nevertheless, the criticism remains that the Court has done insufficient work to justify its methodology and properly ground its importation of domestic criminal law theory within a general theory of sources of international law.

Time violating amplitudes in the (3He, p) reactions

1988 ◽  
Vol 66 (7) ◽  
pp. 612-617 ◽  
Author(s):  
Ali E. Khalil
Keyword(s):  
Reaction Mechanism ◽  
Time Reversal ◽  
Born Approximation ◽  
Interaction Strength ◽  
Direct Reaction ◽  
Distorted Wave ◽  
Distorted Wave Born Approximation ◽  
Dwba Calculation ◽  
Hermitian Conjugate ◽  
The Difference

The difference between the polarization (P) of protons in the reaction (3He, [Formula: see text]) and the analyzing power (A) in the inverse reaction ([Formula: see text], 3He) has been calculated using a spin-independent isospin-independent, time reversal violating interaction in the form [α(r)[Formula: see text] + Hermitian conjugate]. The interaction strength is adjusted to be 1% of the time conserving optical potentials. A distorted-wave Born approximation (DWBA) calculation assuming a direct reaction mechanism has been performed. The relative values of the time violating amplitudes have no signatures for any measurable time violating effects.

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