Computer Simulations in Condensed Matter Systems: From by C. Dellago, P.G. Bolhuis, P.L. Geissler (auth.), Mauro

By C. Dellago, P.G. Bolhuis, P.L. Geissler (auth.), Mauro Ferrario Professor, Giovanni Ciccotti Professor, Kurt Binder Professor (eds.)

This huge and accomplished selection of lectures by way of world-leading specialists within the box introduces and stories all proper desktop simulation equipment and their functions in condensed subject structures. quantity 1 is an in-depth creation to an enormous spectrum of computational thoughts for statistical mechanical structures of condensed subject. it's going to let the graduate pupil and either the expert and nonspecialist researcher to get conversant in the instruments essential to perform numerical simulations at a sophisticated point. quantity 2 released as LNP 704 (ISBN 3-540-35283-X) is a set of cutting-edge surveys on numerical experiments conducted for numerous structures, starting from fabrics sciences to chemical biology.

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Additional info for Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 1

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Driving the system from A to B by controlling the wrong coordinate, on the other hand, leads to large hysteresis effects because such a procedure neglects important barriers that may exist in orthogonal directions. A good reaction coordinate should capture the essence of the dynamics and allow us to predict what a trajectory starting from a given configuration will most likely do. As we will see later, this is exactly what the committor does: it tells us about the probability to relax into A or B.

No definition of a reaction coordinate is necessary. Instead, it is sufficient to specify unambiguously the initial and the final state of the transition. This is a crucial feature of the method since information on the reaction coordinate is usually unavailable. Transition path sampling can therefore be used to study rare transitions between long-lived stable states in complex systems characterized by a rugged potential energy surface. Other path based methods that can be used to study rare events include the so called string method [7, 8] applicable to stochastic dynamics and methods based on the minimization of the classical action [9,10].

Since 354 C. Dellago et al. the pathways collected with transition path sampling are fully dynamical trajectories rather than artificial pathways such as minimum energy pathways or elastic bands, it is also possible to extract kinetic information from transition path sampling simulations. The first step in the application of transition path sampling consists in the definition of an appropriate path ensemble. This is what we will do next. 1 Path Probability It is convenient to discretize the continuous time evolution of the system and view a trajectory of length T as an ordered sequence of states: x(T ) ≡ {x0 , x∆t , x2∆t , .

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