No abstract

The nature of the Arrhenius activation energy and frequency factor is reexamined in terms of information now becoming available on the microscopic aspects of collisional reactions. It is pointed out that the activation energy is not generally equal to the threshold for reaction, and its correct conceptual meaning is discussed. The temperature dependence of this quantity and its relation to the threshold energy is developed for a number of representative forms of the energy dependence of the reaction cross-section (excitation function). The uses and limitations of the activation energy as a means of evaluating thresholds, excitation functions, and the presence of tunneling processes are discussed.

By manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks withPoisson and scale-free degree distributions. For both types of network, increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies. Surprisingly, in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization. As a result, they show an additional, advanced transition instead of a single synchronization threshold. This clusterenhanced synchronization of hubs may be relevant to the brain which is scale-free and highly clustered.