Kinetic equations for the probability densities of non-Markovian processes. Evolution of moment and cumulant functions

1987 ◽  
Vol 30 (11) ◽  
pp. 959-968 ◽  
Author(s):  
V. A. Kazakov
Keyword(s):  
Kinetic Equations ◽  
Markovian Processes ◽  
Probability Densities ◽  
Cumulant Functions

Lifetime and Transit Time Distributions and Response Experiments in Chemical Kinetics

2006 ◽  
Author(s):  
John Ross ◽  
Igor Schreiber ◽  
Marcel O. Vlad
Keyword(s):  
Reaction Mechanism ◽  
Stationary State ◽  
Linear Response ◽  
Reaction Pathway ◽  
Kinetic Equations ◽  
Chemical Species ◽  
Main Idea ◽  
Stable Stationary State ◽  
Probability Densities ◽  
Mathematical Techniques

We discussed some aspects of the responses of chemical systems, linear or nonlinear, to perturbations on several earlier occasions. The first was the responses of the chemical species in a reaction mechanism (a network) in a nonequilibrium stable stationary state to a pulse in concentration of one species. We referred to this approach as the “pulse method” (see chapter 5 for theory and chapter 6 for experiments). Second, we studied the time series of the responses of concentrations to repeated random perturbations, the formulation of correlation functions from such measurements, and the construction of the correlation metric (see chapter 7 for theory and chapter 8 for experiments). Third, in the investigation of oscillatory chemical reactions we showed that the responses of a chemical system in a stable stationary state close to a Hopf bifurcation are related to the category of the oscillatory reaction and to the role of the essential species in the system (see chapter 11 for theory and experiments). In each of these cases the responses yield important information about the reaction pathway and the reaction mechanism. In this chapter we focus on the design of simple types of response experiments that make it possible to extract mechanistic and kinetic information from complex nonlinear reaction systems. The main idea is to use “neutral” labeled compounds (tracers), which have the same kinetic and transport properties as the unlabeled compounds. In our previous work we have shown that by using neutral tracers a class of response experiments can be described by linear response laws, even though the underlying kinetic equations are highly nonlinear. The linear response is not the result of a linearization procedure, but it is due to the use of neutral tracers. As a result the response is linear even for large perturbations, making it possible to investigate global nonlinear kinetics by making use of linear mathematical techniques. Moreover, the susceptibility functions from the response law are related to the probability densities of the lifetimes and transit times of the various chemical species, making it easy to establish a connection between the response data and the mechanism and kinetics of the process.

On Kinetic Equations in Heavy-Ion Physics

1996 ◽  
Vol 21 (5) ◽  
pp. 461-502 ◽  
Author(s):  
E. Suraud
Keyword(s):  
Kinetic Equations ◽  
Heavy Ion ◽  
Heavy Ion Physics

The Kinetics of Glucose Decomposition with Sulfate Reduction in the Anaerobic Fluidized Bed Reactor

1993 ◽  
Vol 28 (2) ◽  
pp. 135-144 ◽  
Author(s):  
S. Matsui ◽  
R. Ikemoto Yamamoto ◽  
Y. Tsuchiya ◽  
B. Inanc
Keyword(s):  
Sulfate Reduction ◽  
Fluidized Bed ◽  
Kinetic Equations ◽  
Fluidized Bed Reactor ◽  
Order Reaction ◽  
First Order Reaction ◽  
First Order ◽  
Glucose Decomposition ◽  
Reaction Equations ◽  
Kinetics Of

Using a fluidized bed reactor, experiments on glucose decomposition with and without sulfate reduction were conducted. Glucose in the reactor was mainly decomposed into lactate and ethanol. Lactate was mainly decomposed into propionate and acetate, while ethanol was decomposed into propionate, acetate, and hydrogen. Sulfate reduction was not involved in the decomposition of glucose, lactate, and ethanol, but was related to propionate and acetate decomposition. The stepwise reactions were modeled using either a Monod expression or first order reaction kinetics in respect to the reactions. The coefficients of the kinetic equations were determined experimentally. The modified Monod and first order reaction equations were effective at predicting concentrations of glucose, lactate, ethanol, propionate, acetate, and sulfate along the beight of the reactor. With sulfate reduction, propionate was decomposed into acetate, while without sulfate reduction, accumulation of propionate was observed in the reactor. Sulfate reduction accelerated propionate conversion into acetate by decreasing the hydrogen concentration.

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