Copyright © 1998–2012 by A. Miyoshi,
SSUMES reference manual - introduction to SSUMES
SSUMES reference manual -
introduction to SSUMES
The SSUMES program package consists of steady-state and
time-dependent solvers of
the master-equation for unimolecular dissociation, recombination, and
complex-forming (or chemically-activated) reactions.
It is mainly designed to
calculate the steady-state rate coefficients for the gas-phase reactions,
which are required for the modeling of reaction systems such as combustion
and atmospheric photooxidation reactions. For those who are mostly
interested in the time-dependent solutions to the master-equation,
it is recommendet to consider to use
the MultiWell Program Suite
by Prof. John R. Barker and
co-workers rather than SSUMES.
The master equation for the multiple-well multiple-channel reactions
can be represeted as,
The solver, diseig
, solves the eigenvalue problem,
by using LAPACK DSYEVR after symmetrizing the matrix.
According to the least-negative eigenvalue
hypothesis, the rate coefficients are calculated from the eigenvector
corresponding to the least-negative eigenvalue.
For the multiple-well reactions, the steady-state dissociation
described by eq (4) is not always the solution needed.
For the system with fairly high barrier between the isomers (wells),
sometimes, the solution needed is rather represented by,
This corresponds to the situation that the only one isomer (well-1) is
dominantly produced in the reaction system, but the isomerization reactions
are not so fast. The solver, dislit
, calculates the
steady-state distribution, n1,ss
for eq (5) by
iterative procedure, (6), starting from an initial guess,
The initial guess is the
Boltzmann distribution for the highest pressure at one temperature,
and the converged vector was used for the initial guess for the next
pressure. Thus the calculation is always done from higher pressure
to lower pressure, and the choice of the starting pressure may affect
the results in some cases.
solver is also useful to obtain the steady-state
solution (4). At some condition, especially in the mutiple-well
reactions, the least-negative eigenvalue is not always the solution needed.
This can be observed as the hop of the rate coefficients and
distribution during the pressure scans. For such cases, the iterative
procedure, (7), can be used to obtain the distribution from an initial
In other words, the distribution thus obtained does not necessarily
correspond to the least-negative eigenvalue.
The LAPACK DSYSV is used to solve the linear equations (6) or (7).
The solver, carate
, solves the master equation for chemically
activated reaction, assuming the steady-state,
by solving the linear equation system,
The LAPACK DSYSV is used to solve the linear equation (9).
The solver, catime
, calculates the time-dependent solution
to the master equation for chemically activated reaction,
for constant flux condition: kin
= 0) = 0
; and for the initial value
= 0 and n
= 0) =
The LSODES in ODEPACK is used to solve (10).