ii) A better theoretical understanding (strongly supported by the numerical approach in (i)) of the effects of symmetry breaking, interactions and integrability, in the non-equilibrium dynamics; especially with respect to the non-equilibrium transport of energy and particle throughout the systems as well as a universal description of the stationary states
(both equilibrium and non-equilibrium) that emerge at late times.
He covers the role of singular solutions of quantal equations in atomic physics, the classical description of crossings of energy terms and of charge exchange, classical stationary states
, understanding the role of the singular spin-spin interaction in the binding energy of two-electron atoms/ions, the last observed line in the spectral series of hydrogen lines in magnetized plasma: s revision of the Inglis-Tellor concept, and extrema in transition energies resulting not in satellites but in dips within spectral lines.
Among the topics are the topological analysis of metabolic networks based on Petri net theory, Petri nets for the steady-state analysis of metabolic systems, ontology-based standardizations of Petri net modeling for signaling pathways, analyzing stationary states
of a gene regulatory network using Petri nets, the impact of delays and noise on dopamine signal transduction, and modeling the molecular interactions in the flower development network of Arabidopsis thaliana.
The phase diagram exhibits a region of self-sustained current oscillations immersed in an area of stable stationary states
The author describes the origins of quantum mechanics, its mathematical tools and postulates, one- and three-dimensional problems, angular momentum, identical particles, approximation methods for stationary states
, scattering theory, time-dependent perturbation theory, and other related topics.
By using two different sets of parameters calculated around two different stationary states
, it was possible to significantly reduce system response overshoot.
3), where [mu] is a constant valid whatever is the state of the field, and [alpha] is a strictly positive function of time reducing to the constant c during the stationary states
of the field.
This particular example of the electron of an hydrogen atom shows that the ordinary stationary states
predicted by quantum mechanics can be seen as the effect of the vibration of a quantum of space at appropriate frequencies characteristic of that particle: the fact that the frequency is quantized implies that also the energy (in the entropy state) that a quantum of space acquires (as a consequence of that vibration) is quantized and a different quantum wavefunction will be associated with each of these values of energy.
As is well known, Smith refers to several types of stationary states
(Hollander 1987, pp.
1992], showing that when similar countries are considered, that is, differences in the stationary states
are accounted for, evidence of convergence appears.
In some cases, certain fluctuations may be amplified and invade the entire system, compelling it to evolve towards a new situation that may be qualitatively quite different from the stationary states
corresponding to minimum entropy production.
Thisconcerns non-thermal stationary states
, where we will shape an understanding of non-equilibrium phasediagrams and the associated phase transitions, in particular constructing a notion of driven quantumcriticality.