## 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. |
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**all 2**collection matricesId | Name | Group | Rows | Cols | Nonzeros | Kind | Date | Download File |
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1854 | chem_master1 | Watson | 40,401 | 40,401 | 201,201 | 2D/3D Problem | 2007 | MATLAB Rutherford Boeing Matrix Market |

1855 | Baumann | Watson | 112,211 | 112,211 | 748,331 | 2D/3D Problem | 2007 | MATLAB Rutherford Boeing Matrix Market |