Stimulated recombination in open systems

Muoz-Cobo, J. L.; Verdú, G.; Jiménez, Pedro Pablo Soriano; Pea, J.

doi:10.1103/physreva.34.2524

Cited by 2 publications

(3 citation statements)

References 3 publications

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“…Next, we split the stochastic variable

using Equation (65), in this approach the translation operators can be expanded in Taylor series [ 50 ]:

…”

Section: Methods To Obtain the Moments Of The Probability Distribumentioning

confidence: 99%

Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation

Muñoz-Cobo

Berna

2019

Entropy

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In this paper first, we review the physical root bases of chemical reaction networks as a Markov process in multidimensional vector space. Then we study the chemical reactions from a microscopic point of view, to obtain the expression for the propensities for the different reactions that can happen in the network. These chemical propensities, at a given time, depend on the system state at that time, and do not depend on the state at an earlier time indicating that we are dealing with Markov processes. Then the Chemical Master Equation (CME) is deduced for an arbitrary chemical network from a probability balance and it is expressed in terms of the reaction propensities. This CME governs the dynamics of the chemical system. Due to the difficulty to solve this equation two methods are studied, the first one is the probability generating function method or z-transform, which permits to obtain the evolution of the factorial moment of the system with time in an easiest way or after some manipulation the evolution of the polynomial moments. The second method studied is the expansion of the CME in terms of an order parameter (system volume). In this case we study first the expansion of the CME using the propensities obtained previously and splitting the molecular concentration into a deterministic part and a random part. An expression in terms of multinomial coefficients is obtained for the evolution of the probability of the random part. Then we study how to reconstruct the probability distribution from the moments using the maximum entropy principle. Finally, the previous methods are applied to simple chemical networks and the consistency of these methods is studied.

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“…Next, we split the stochastic variable

using Equation (65), in this approach the translation operators can be expanded in Taylor series [ 50 ]:

…”

Section: Methods To Obtain the Moments Of The Probability Distribumentioning

confidence: 99%

Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation

Muñoz-Cobo

Berna

2019

Entropy

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“…In general, this force depends on the position and particle velocity. If we denote by (rl, Vl) the phase space coordinates of the centre of a cell, of characteristic length ~ in position space and ~ in velocity space, we note that the points of this cell are defined by the map 6 (14) 16 :…”

Section: Ermentioning

confidence: 99%

“…The rate of change of the multivariate probability due to fusion events, which we denote by the supraindex f in the time derivative, will be given on account of expres-sion (4) and the master equation (2) where we have defined the step operators [14] (7)…”

Section: -Derivation Of the Master Equation In A D + T Plasmamentioning

confidence: 99%

Evolution equations of the expected phase space ion densities and correlation functions in a D+T plasma

Muñoz-Cobo

Verdú

1991

Il Nuovo Cimento D

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(ricevuto il 2 Luglio 1990; manoscritto revisionato ricevuto il 9 Aprile 1991) Summary. --In this paper we formulate a master equation approach describing a D + T thermonuclear plasma in a lumped phase space. From the first moments of this master equation and performing the pass to the continuous limit the evolution equations for the expected phase space ion densities emerge. Also we have obtained the evolution equations of the equal time correlation and covariance functions. Finally we have deduced the hydrodynamic equations that arise from a master equation approach.PACS 52.25 -Plasma properties. -Introduction.In the study of far from equilibrium hydrodynamic fluctuations, a master equation (ME) approach seems to be the natural and necessary method of description of such fluctuations [1,2]. However, such description must include the feedback of the fluctuations on the average behaviour [3]. The ME approach which accomplish this goal was developed by Brenig and Van der Broeck [4,5], which extended the Logan, Kac and Keizer [6,7] works, to include the effect of large fluctuations.Under plasma conditions, the motion of charged particles is determined by two types of interactions: i) close interactions, treated generally as binary collisions; ii) collective long-range interactions with many particles, that can be represented by electric and magnetic fields [8][9][10] which can be calculated with electromagnetic theory using the charge and current distribution, however we must observe that these electromagnetic fields are stochastic because they depend on the distribution of charged particles, and therefore the fluctuations in the distribution of charge particles give rise to fluctuations in these afore-mentioned electromagnetic fields which in turn affect the charge distributions.The simplest characterization of the nonequilibrium plasma uses a one-fluid magnetohydrodynamic picture (MHD). These equations are essentially those of the hydrodynamics, supplemented by terms appropriate to a conducting fluid, and by MaxweU's equations for the electromagnetic fields [11]. The next level of sophistica-89 -Il Nuovo Cimento D.1325

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Stimulated recombination in open systems

Cited by 2 publications

References 3 publications

Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation

Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation

Evolution equations of the expected phase space ion densities and correlation functions in a D+T plasma

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