Money supply and capital accumulation on the transition path revisited

Often, the dynamics of complex condensed materials is characterized by the presence of a wide range of different time scales, complicating the study of such processes with computer simulations. Consider, for instance, dynamical processes occurring in liquid water. Here, the fastest molecular processes are intramolecular vibrations with periods in the 10-20 fs range. The translational and rotational motions of water molecules occur on a significantly longer time scale. Typically, the direction of translational motion of a molecule persist for about 500 fs, corresponding to 50 vibrational periods. Hydrogen bonds, responsible for many of the unique properties of liquid water, have an average lifetime of about 1 ps and the rotational motion of water molecules stays correlated for about 10 ps. Much longer time scales are typically involved if covalent bonds are broken and formed. For instance, the average lifetime of a water molecule in liquid water before it dissociates and forms hydroxide and hydronium ions is on the order of 10 hours. This enormous range of time scales, spanning nearly 20 orders of magnitude, is a challenge for the computer simulator who wants to study such processes. In general, the dynamics of molecular systems can be explored on a computer with molecular

Two basic options exist for modeling transit path-choice in the travel forecasting process: including transit path-choice in a detailed mode choice model or using deterministic procedures to model transit path-choice through transit multipath, path-building algorithms. These two options require

of path used. The constraints of a network can consist of delivery/pickup time deadlines, network availability, the need to visit specific nodes of the network, or resource restrictions such as vehicle capacity, fleet size or transmission rates to name a few. We consider a class of path design problems

Despite a common parentage for most of the 20 century, Uzbekistan and Kazakhstan followed seemingly different paths in transition. Whereas Uzbekistan adopted a gradual and cautious approach to market reforms, Kazakhstan followed a more aggressive strategy. Yet, while Kazakhstan may have

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Transition path sampling, based on a statistical mechanics in trajectory space, is a set of computational methods for the simulation of rare events in complex systems. In these lecture notes we give an overview of these techniques and describe their statistical mechanical basis as well

We derive an new expression for the calculation of activation energies within the framework of transition path sampling. Using this expression one can determine activation energies without knowledge of the reaction mechanism, which is often unavailable for processes occurring in complex systems