A schematic diagram of a trajectory that passes from the reactants region of the conformation space to the products. The blue line represents the trajectory while it is fluctuating between the reactants and the transition region. The red line represents the transition path whose time duration gives a sample of the transit time, whereas the complete trajectory would be a sample of the first passage time.
A schematic diagram of a trajectory that passes from reactant surface (milestone 1, H 1), to product surface (milestone 4, H 4). The trajectory starts on H 1, at the phase space point represented by the filled black circle. The transit time for the transition from milestone 1 to 2 is denoted t 1, and is given by the time duration of the blue path—i.e., the time interval between last crossing the reactant surface (at the filled square) and arriving at milestone 2. The time for the trajectory to then carry on to H 4 without returning to the H 1, τ, is given by the red part of the path, and together t 1 + τ gives a sample of the transit time of the reaction.
A homopolymer translocating through a narrow pore. In MFPT calculations, a reflecting boundary is imposed on monomer 1 (dashed line).
(a) The MTT and (b) MLT plotted as a function of chain length, N. The straight lines are least squares fits of the 5 milestone M1TM data to functions of the form f(N) ∝ N α.
A schematic diagram of a trajectory that takes a transition path from milestone 1 to 4. Here the milestones are ordered by the reaction coordinate s(x) and milestones 2 and 3 are further broken up into MCM states (the quadrants of each milestone). The reactant (product) surface is taken to coincide with milestone 1(4). The blue path represents a A → β one-step transition path, which starts on the reactant surface and carries on to cluster β on milestone 2 without re-crossing the reactant surface. The duration of this path is denoted t β. The green path, on the other hand, is an example of a failed one step transition path, as it returns to the reactant surface before making a transition to a state in the transition region. The time τβ for the trajectory in β to carry onto the product surface B (milestone 4) without returning to the reactant surface is given by the red segment of the path, and together t β + τβ gives a sample of the transit time of the reaction.
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