The Master Equation for the Dissociation of a Dilute Diatomic Gas. VI. Solution of Coupled Sets of Master Equations

1972 ◽  
Vol 50 (6) ◽  
pp. 897-906 ◽  
Author(s):  
D. L. S. McElwain ◽  
H. O. Pritchard
Keyword(s):  
Relaxation Time ◽  
Differential Equations ◽  
Master Equation ◽  
Normal Mode ◽  
Rate Constants ◽  
Vibrational Relaxation ◽  
Master Equations ◽  
Diatomic Gas ◽  
Full Solution ◽  
Mode Technique

Three coupled sets of master equations, representing the equilibration of [Formula: see text] via atoms only, have been solved by the normal-mode technique; the set of 57 simultaneous differential equations describing the H2/D2/2HD system was considered as a suitable trial model. It was found that at times (t) in excess of the longest vibrational relaxation time, even though some of the populations in the system appeared highly non-Boltzmann, all the phenomenological rate constants were well-behaved: they were either constant and obeyed the rate–quotient law, or they were dependent on t2.The paper concludes with a discussion of the information required before a full solution of the [Formula: see text] reaction could be contemplated, and suggests methods by which an approximation to such a solution could be obtained.

The Master Equation for the Dissociation of a Dilute Diatomic Gas. XI. Vibrational Freezing in a Nozzle Flow

1974 ◽  
Vol 52 (6) ◽  
pp. 939-941 ◽  
Author(s):  
Nabil I. Labib ◽  
Huw O. Pritchard
Keyword(s):  
Relaxation Time ◽  
Energy Level ◽  
Master Equation ◽  
Rate Constant ◽  
Ground State ◽  
Vibrational Relaxation ◽  
Vibrational Energy ◽  
Nozzle Flow ◽  
Vibrational Energy Level ◽  
Diatomic Gas

A previously reported calculation on a model expansion in a nozzle flow is extended to the point where the whole vibrational energy "freezes" and the behavior of the vibrational relaxation time is examined. Starting with the high levels, each individual vibrational energy level becomes decoupled from the ground state in sequence, down to and including υ = 1; under these conditions, all measures of the vibrational relaxation time fail, but perhaps surprisingly the rate constant for recombination remains well defined.

scholarly journals Universal Constraints on Relaxation Times for d-Level GKLS Master Equations

2017 ◽  
Vol 24 (04) ◽  
pp. 1740009
Author(s):  
Gen Kimura ◽  
Shigeru Ajisaka ◽  
Kyouhei Watanabe
Keyword(s):  
Relaxation Time ◽  
Relaxation Rate ◽  
Master Equation ◽  
Experimental Test ◽  
Relaxation Times ◽  
Master Equations ◽  
Complete Positivity ◽  
Relaxation Rates ◽  
Markovian Dynamics ◽  
Inverse Relaxation Time

In 1976, Gorini, Kossakowski, Sudarshan and Lindblad independently discovered a general form of master equations for an open quantum Markovian dynamics. In honor of all the authors, the equation is nowadays called the GKLS master equation. In this paper, we show universal constraints on the relaxation times valid for any d-level GKLS master equations, which is a generalization of the well-known constraints for 2-level systems. Specifically, we show that any relaxation rate, the inverse-relaxation time, is not greater than half of the sum of all relaxation rates. Since the relaxation times are measurable in experiments, our constraints provide a direct experimental test for the validity of the GKLS master equations, and hence for the conditions of the complete positivity and Markovianity.

Singlet Methylene Removal Rate Constants from the (0,1,0) Vibrational Level: Enhancement via Complex-Mediated Vibrational Relaxation

2001 ◽  
Vol 215 (6) ◽  
Author(s):  
M.A. Buntine ◽  
G.J. Gutsche ◽  
W.S. Staker ◽  
M.W. Heaven ◽  
K.D. King ◽  
...  
Keyword(s):  
Vibrational Level ◽  
Rate Constants ◽  
Vibrational Relaxation ◽  
Flash Photolysis ◽  
Laser Flash Photolysis ◽  
Removal Rate ◽  
Laser Flash ◽  
Laser Absorption ◽  
Photolysis Laser ◽  
Singlet Methylene

The technique of laser flash photolysis/laser absorption has been used to obtain absolute removal rate constants for singlet methylene,

scholarly journals STUDY OF CARBON DIOXIDE ADSORPTION ON CHROMIUM OXIDE AND GALLIUM OXIDE CATALYSTS ON BASIS OF NON-LINEAR RELAXATION TIMES

2018 ◽  
Vol 61 (2) ◽  
pp. 46 ◽  
Author(s):  
Nikolay I. Kol'tsov
Keyword(s):  
Carbon Dioxide ◽  
Relaxation Time ◽  
Chromium Oxide ◽  
Rate Constants ◽  
Gallium Oxide ◽  
Relaxation Times ◽  
Oxide Catalysts ◽  
Linear Relaxation ◽  
Adsorption And Desorption ◽  
Non Linear

Recently the analysis of transient regimes of chemical reactions is paid much attention. This is due to the fact that the time-dependent relaxation modes prior to achieving steady states contain important information about the features of the reactions. During unsteady mode the changes in reactant concentrations and rate of the reaction in time are observed. These changes are due to their own relaxation processes, depending on the structure of the reaction mechanism. A complete study of the reaction mechanism involves the study of the relaxation characteristics both near and away from the stationary state. Linear relaxation time describes the local transient modes near the steady state and it is calculated as the time decrease deviations of reactant concentrations from steady-state values in the e-times. Non-linear relaxation time describes the overall behavior reactions and it can be evaluated through the reaction time from the initial state to a stationary. Depending on the structural features of reactions ratio to determine the non-linear relaxation time through of reactions parameters (rate constants stages and reactant concentrations) differ significantly. The establishment of such ratio for a particular reaction allows getting more information to identify the mechanism and the constituent rate constants of its stages. The mechanism of any catalytic reaction involves stages adsorption of one or more of the starting materials on the catalyst surface. As a rule these stages are initial remaining stages of chemical transformation of reactants adsorbed forms follow them. Therefore, it is necessary to have the data on these stages and rate constants of adsorption of reagents on the catalyst surface. Earlier by author the method for estimating the values of the rate constants of adsorption and desorption by linear relaxation times was described. This method was used for determine of mechanism and kinetic parameters of process of adsorption of carbon dioxide on the chromium oxide and gallium oxide catalysts. In this article the method for estimating the values of the rate constants of adsorption and desorption by non-linear relaxation times for this process is described. The previously found CO2 dissociative adsorption mechanism was proved by the obtained results. The intervals of values changes of the rate constants of adsorption and desorption of carbon dioxide on the gallium oxide and chromium oxide catalysts were defined.Forcitation:Kol’tsov N.I. Study of carbon dioxide adsorption on chromium oxide and gallium oxide catalysts on basis of non-linear relaxation times. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2018. V. 61. N 2. P. 46-52

On the breakdown of characteristics solutions in flows with vibrational relaxation

1967 ◽  
Vol 27 (1) ◽  
pp. 49-57 ◽  
Author(s):  
B. S. H. Rarity
Keyword(s):  
Relaxation Time ◽  
Mach Number ◽  
Supersonic Flow ◽  
Steady Flow ◽  
Speed Of Sound ◽  
Vibrational Relaxation ◽  
Precise Measure ◽  
Derivatives Of ◽  
Relaxing Gas ◽  
Flow Case

The breakdown of the characteristics solution in the neighbourhood of the leading frozen characteristic is investigated for the flow induced by a piston advancing with finite acceleration into a relaxing gas and for the steady supersonic flow of a relaxing gas into a smooth compressive corner. It is found that the point of breakdown moves outwards along the leading characteristic as the relaxation time decreases and that there is no breakdown of the solution on the leading characteristic if the gas has a sufficiently small, but non-zero, relaxation time. A precise measure of this relaxation time is derived. The paper deals only with points of breakdown determined by initial derivatives of the piston path or wall shape. In the steady-flow case, the Mach number based on the frozen speed of sound must be greater than unity.

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