Sentence examples for many dynamical processes from inspiring English sources

Many dynamical processes contain both continuous and discrete elements simultaneously.

We therefore observe many dynamical processes being studied on top of these networks, such as diffusion processes [30, 31], synchronization [32, 33], percolation [34, 35], etc.

In spite of many obvious advantages, some models based on Brownian diffusion usually fail to provide a satisfactory description of many dynamical processes.

Unfortunately, many dynamical processes in cells do not follow these simple models, and in many instances it is not possible to obtain an analytical function through a theoretical analysis of a more complex model.

Since the introduction of fractional calculus of variations by Riewe [1], fractional calculus has played an important role in dealing with many natural dynamical processes.

The differential equations that we study describe many phenomena and dynamical processes in various fields, and they have attracted a great deal of attention of researchers in physical sciences, mathematics, biology, and economy.

"Unless nature reveals some exceptional feature in the CMB, it will be difficult to discriminate too many details about the dynamical processes occurring in the early universe," says Arjun Berera, a cosmologist at the University of Edinburgh in the United Kingdom.

The task of modeling these systems is made particularly challenging by the fact that the generation of the asymptotic explosion energies, although enormous (({sim}10^{44}~mathrm{J})), requires a rather subtle, percent-level imbalance between non-linear processes over many dynamical times.

Examples of such systems can be found in many disciplines of science and engineering such as physics, biomathematics, chemistry, dynamics of earthquakes, dynamical processes in porous media, material viscoelastic theory, and control theory of dynamical systems.

We show that judicious use of the empirical potential of Iyetomi et al. [18] leads to a credible model of the dynamical processes and correctly reproduces many aspects of the material.

Many dynamical systems in physics, chemistry, biology and engineering sciences have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes.