The Barrier Method: A Technique for Calculating Very Long Transition Times

In many dynamical systems there is a large separation of time scales between typical events and "rare" events which can be the cases of interest. Rare-event rates are quite difficult to compute numerically, but they are of considerable practical importance in many fields: for example transition times in chemical physics and extinction times in epidemiology can be very long, but are quite important. We present a very fast numerical technique that can be used to find long transition times (very small rates) in low-dimensional systems, even if they lack detailed balance. We illustrate the method for a bistable non-equilibrium system introduced by Maier and Stein and a two-dimensional (in parameter space) epidemiology model.Comment: 20 pages, 8 figure

Near-Infrared Kinetic Spectroscopy of the HO_2 and C_2H_5O_2 Self-Reactions and Cross Reactions

The self-reactions and cross reactions of the peroxy radicals HO_2 and C_2H_5O_2 and HO_2 were monitored using simultaneous independent spectroscopic probes to observe each radical species. Wavelength modulation (WM) near-infrared (NIR) spectroscopy was used to detect HO_2, and UV absorption monitored HO_2 and C_2H_5O_2. The temperature dependences of these reactions were investigated over a range of interest to tropospheric chemistry, 221−296 K. The Arrhenius expression determined for the cross reaction, k_2(T) = (6.01^(+1.95)_(−1.47)) × 10^(−13) exp((638 ± 73)/T) cm^3 molecules^(−1) s^(−1) is in agreement with other work from the literature. The measurements of the HO_2 self-reaction agreed with previous work from this lab and were not further refined.(1) The C_2H_5O_2 self-reaction is complicated by secondary production of HO_2. This experiment performed the first direct measurement of the self-reaction rate constant, as well as the branching fraction to the radical channel, in part by measurement of the secondary HO_2. The Arrhenius expression for the self-reaction rate constant is k_3(T) = (1.29^(+0.34)_(−0.27)) × 10^(−13)exp((−23 ± 61)/T) cm^3 molecules^(−1) s^(−1), and the branching fraction value is α = 0.28 ± 0.06, independent of temperature. These values are in disagreement with previous measurements based on end product studies of the branching fraction. The results suggest that better characterization of the products from RO_2 self-reactions are required

Computation of nucleation of a non-equilibrium first-order phase transition using a rare-event algorithm

We introduce a new Forward-Flux Sampling in Time (FFST) algorithm to efficiently measure transition times in rare-event processes in non-equilibrium systems, and apply it to study the first-order (discontinuous) kinetic transition in the Ziff-Gulari-Barshad model of catalytic surface reaction. The average time for the transition to take place, as well as both the spinodal and transition points, are clearly found by this method.Comment: 12 pages, 10 figure