## Group Watson

Group Description Chemical reaction simulation matrices from Layne Watson and Jingwei Zhang. Virginia Tech, ltw at cs dot vtu doe yes, and jwzhang at the same domain. The ODE system \frac{dp}{dt}=Qp is what we call a chemical master equation (a Kolmogorov's backward/forward equation). Q is a sparse asymmetric matrix, whose off-diagonal entries are non-negative and row sum to zero. On each row, q_{ij}h gives the probability the system makes a transition from current state i to some other state j, in small time interval h. By "state", we mean a possible combination of number of molecules in each chemical species. Now, h is small enough so that only one reaction happens. In this way q_{ij} is nonzero only if there exists a chemical reaction that connects state i and j, i.e. j=i+s_k, s_k's are constant state vectors that correspond to every reaction. Say we have M reactions, then there are at most M+1 nonzero entries on each row of Q. On the other hand, the number of possible combination of molecules is huge, which means the dimension of Q is huge. The linear system we want to solve is (I - Q/lambda)x=b, and we have to solve it several times. (Here lambda is a constant). Problem.A is the Q matrix.
Displaying all 2 matrices
Id Name Group Rows Cols Nonzeros
1854 chem_master1 Watson 40,401 40,401 201,201
1855 Baumann Watson 112,211 112,211 748,331