Standard master equation technique

Using the standard master equation technique, we consider the continuous limit, supposing that w(x) and v(x) vary slightly from one bond to another. Then,... 

The simplest and most elegant theoretical technique operating in line with this leading idea is the Nakajima-Zwanzig projection method. By using this approach we are naturally led to replace the standard master equations. 

We are in position now to derive the Master equation for the density p x, t). Since the balance equations (3.121) and (3.122) are nonlinear, we cannot apply the standard technique of the Fourier—Laplace transforms directly. Instead we differentiate the density p(x, t) with respect to time ... 

By tracing out the atomic variables, i.e., Pc=TratomP we can obtain the information of the cavity fields. Following the standard techniques for the mixing interactions [4,84] we treat the cavity fields b, bf) linearly. Assuming that the atoms decay much more rapidly than the cavity fields, we can eliminate atomic variables adiabatically and derive the master equation of cavity modes i,2. For the case of Qi/Qomaster equation for Pc has the same form as Eq. (35), and the parameters are the same as in Eq. (36). Also we have taken 713=723=/ and Ki=K2=k for simplicity. The only difference lies in the dressed populations at steady state in the absence of the cavity fields. They are calculated as... 

Single-pulse shock tube studies of the thermal dehydrochlorination reactions of chlorocyclopentane and chlorocyclohexane at temperatures of 843-1021 K and pressures of 1.4-2.4 bar have been carried out using the comparative rate technique. Absolute rate constants provided a self-consistent temperature scale of use in comparison with chemical systems studied with different temperature standards. Quantum chemical methods have been used to compute the structure and energies of reactants, products, and transition states. The computations were used, in conjunction with experimentally determined rate constants, to develop Rice-Ramsperger-Kassel-Marcus (RRKM)/ Master Equation models and thereby allow extrapolation of the experimental data over an extended range of temperatures. 

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