The commutative property of strong-transition rate matrices

1979 ◽  
Vol 57 (21) ◽  
pp. 2793-2797 ◽  
Author(s):  
Huw O. Pritchard ◽  
Arunachalam Lakshmi
Keyword(s):  
Transition Rate ◽  
Transition Probabilities ◽  
Boltzmann Distribution ◽  
Unimolecular Reaction ◽  
Infinite Time ◽  
Relaxation Matrix ◽  
Reaction Theory ◽  
Strong Transition ◽  
Commutative Property

The (n − 1)-fold degenerate set of transition probabilities used in our recent reformulation of unimolecular reaction theory is operationally equivalent to the set of effective strong-transition probabilities introduced recently by Nordholm. We have found that the relaxation matrix corresponding to these transition probabilities commutes with any other relaxation matrix which will drive the same system to a Boltzmann distribution at infinite time. Some useful results stemming from this commutative property are presented; we expect that these results will help to clarify further the nature of the assumptions underlying strong- and effective strong-collision theories.

On the Unimolecular Decomposition of the tert-Butoxy Radical

1973 ◽  
Vol 51 (13) ◽  
pp. 2138-2140 ◽  
Author(s):  
C. K. Yip ◽  
H. O. Pritchard
Keyword(s):  
Pressure Dependence ◽  
Unimolecular Reaction ◽  
Unimolecular Decomposition ◽  
Reaction Theory ◽  
Butoxy Radical

It is argued that a large apparent pressure dependence in the rate of decomposition of the tert-butoxy radical should not be interpreted in terms of unimolecular reaction theory; the effect is probably heterogeneous in origin.

scholarly journals H 2 Control of Markovian Jump Systems with Input Saturation and Incomplete Knowledge of Transition Probabilities

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bum Yong Park
Keyword(s):  
Transition Rate ◽  
State Feedback ◽  
Transition Probabilities ◽  
Input Saturation ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Numerical Examples ◽  
Incomplete Knowledge ◽  
Matrix Polynomials ◽  
Jump Systems

This paper proposes an ℋ 2 state-feedback controller for Markovian jump systems with input saturation and incomplete knowledge of transition probabilities. The proposed controller is developed using second-order matrix polynomials of an incomplete transition rate to derive less conservative stabilization conditions. The proposed controller not only guarantees ℋ 2 performance but also rejects matched disturbances. The effectiveness of the proposed method is demonstrated using three numerical examples.

On joint exchangeability and conservative processes with stochastic rates

1976 ◽  
Vol 13 (3) ◽  
pp. 584-590 ◽  
Author(s):  
Roy Saunders
Keyword(s):  
Transition Rate ◽  
Transition Probabilities ◽  
Random Variables ◽  
Time Dependent ◽  
Previous Article ◽  
Initial State ◽  
Exchangeable Random Variables ◽  
Time Zero ◽  
Initial States

In a previous article Saunders (1975) investigated the form of transition probabilities for a generalization of conservative processes in which the usual transition rate parameters are replaced by time-dependent stochastic variables. The results of that investigation are given in terms of properties of exchangeable random variables and require that the process be in a particular initial state at time zero. This article removes the restriction on the initial state by using some properties of two sequences of jointly exchangeable variables. General results analogous to those obtained previously are shown to hold for general initial states.

Conservative processes with stochastic rates

1975 ◽  
Vol 12 (03) ◽  
pp. 447-456 ◽  
Author(s):  
Roy Saunders
Keyword(s):  
Transition Rate ◽  
Transition Probabilities ◽  
Random Variables ◽  
Time Dependent ◽  
Independent Random Variables ◽  
Exchangeable Random Variables

In this article we consider a generalisation of conservative processes in which the usual transition rate parameters are replaced by time-dependent stochastic variables. The main result of the article shows that these generalised processes which we call conservative processes with stochastic rates have transition probabilities which can be characterised in terms of exchangeable random variables in a manner similar to the characterisation of conservative processes in terms of independent random variables given by Bartlett (1949). We use this characterisation to obtain general expressions for the transition probabilities and to examine some limiting aspects of the processes. The carrier-borne epidemic is treated as a particular case of these generalised processes.

Simple Test of Unimolecular Reaction Theory

1967 ◽  
Vol 46 (11) ◽  
pp. 4504-4508 ◽  
Author(s):  
Richard K. Lyon
Keyword(s):  
Unimolecular Reaction ◽  
Simple Test ◽  
Reaction Theory

Detection of Ambient NO by Laser-Induced Photoacoustic Spectrometry Using A2Σ+ − X2Π (0,0) Transitions Near 226 nm

1996 ◽  
Vol 50 (2) ◽  
pp. 205-210 ◽  
Author(s):  
C. K. Williamson ◽  
R. L. Pastel ◽  
R. C. Sausa
Keyword(s):  
Transition Probabilities ◽  
Laser Energy ◽  
Boltzmann Distribution ◽  
Spectroscopic Techniques ◽  
Buffer Gas ◽  
Ambient Conditions ◽  
Model Calculations ◽  
Simulation Based ◽  
Photoacoustic Spectrometry ◽  
Trace Concentrations

Trace concentrations of NO are detected under ambient conditions by laser-induced photoacoustic spectroscopy. NO is excited via its A2Σ+-X2π (0,0) band with radiation near 226 nm, and the subsequent heat released is monitored by a microphone. Rotationally resolved photoacoustic spectra are recorded and fit with the use of a multiparameter computer simulation based on a Boltzmann distribution. Transition probabilities and rotational energies are used as input parameters. The effect of buffer gas pressure, buffer gas, laser energy, and NO concentration on the PA signal is investigated both experimentally and by model calculations. Limits of detection (LODs) of 1.2, 2.8, and 4.9 ppm are obtained for NO in Ar, N2, and air, respectively. The ultimate sensitivity of this approach is greater with LODs projected in the low-ppb range by utilizing higher laser energies and an improved system design. The results are compared with those of previous studies using complementary laser-based spectroscopic techniques.

On joint exchangeability and conservative processes with stochastic rates

1976 ◽  
Vol 13 (03) ◽  
pp. 584-590
Author(s):  
Roy Saunders
Keyword(s):  
Transition Rate ◽  
Transition Probabilities ◽  
Random Variables ◽  
Time Dependent ◽  
Previous Article ◽  
Initial State ◽  
Exchangeable Random Variables ◽  
Time Zero ◽  
Initial States

In a previous article Saunders (1975) investigated the form of transition probabilities for a generalization of conservative processes in which the usual transition rate parameters are replaced by time-dependent stochastic variables. The results of that investigation are given in terms of properties of exchangeable random variables and require that the process be in a particular initial state at time zero. This article removes the restriction on the initial state by using some properties of two sequences of jointly exchangeable variables. General results analogous to those obtained previously are shown to hold for general initial states.

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