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Inhomogeneous Coherent States in Small-World Networks: Application to the Brain Networks
Bahruz Gadjiev,
Tatiana Progulova
Issue:
Volume 7, Issue 3, May 2019
Pages:
68-72
Received:
20 April 2019
Accepted:
11 June 2019
Published:
25 June 2019
Abstract: We study the dynamics of the processes in the small-world networks with a power-law degree distribution where every node is considered to be in one of the two available statuses. We present an algorithm for generation of such network and determine analytically a temporal dependence of the network nodes degrees and using the maximum entropy principle we define a degree distribution of the network. We discuss the results of the Ising discrete model for small-world networks and in the framework of the continuous approach using the principle of least action, we derive an equation of motion for the order parameter in these networks in the form of a fractional differential equation. The obtained equation enables the description of the problem of a spontaneous symmetry breaking in the system and determination of the spatio-temporal dependencies of the order parameter in varies stable phases of the system. In the cases of one and two component order parameters with taken into account major and secondary order parameters we obtain analytical solutions of the equation of motion for the order parameters and determine solutions for various regimes of the system functioning. We apply the obtained results to the description of the processes in the brain and discuss the problems of emergence of mind.
Abstract: We study the dynamics of the processes in the small-world networks with a power-law degree distribution where every node is considered to be in one of the two available statuses. We present an algorithm for generation of such network and determine analytically a temporal dependence of the network nodes degrees and using the maximum entropy principl...
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The Optics and Optimal Control Theory Interpretation of the Parametric Resonance
Nikolay Nikolaevitch Schitov
Issue:
Volume 7, Issue 3, May 2019
Pages:
73-83
Received:
22 April 2019
Accepted:
4 June 2019
Published:
26 June 2019
Abstract: The aim of the article is the elaboration of parametric resonance theory at piecewise constant frequency modulation. The investigation is based on the analogy with optics and optimal control theory (OCT) application. The exact expressions of oscillation frequency, gain/damping coefficients, dependencies of these coefficients on the modulation depth, duty ratio and initial phase are derived. First of all, the results obtained on the basis of the energy behavior analysis (at the conjunction conditions execution) in frictionless systems are presented. The well-known parametric resonance triggering condition is revised and adjusted. The heuristic feedback introduction (based on the energy behavior analysis) in the oscillation equation permits one to prove that the frequency modulation satisfying the parametric resonance condition is not necessary and sufficient condition of the oscillations unlimited increase. Their damping/shaking up formally corresponds by the frequency and duty ratio to the condition of the equality of optical paths to the quarter-wavelength characteristic of the interference filter or mirror. The unity of space-time coordinates shows itself in this specific form of the optical-mechanical analogy due to the general Hill’s equation description. It is marked that this equation theory underlies most of metamaterials advantages because all transport phenomena imply different wave – electromagnetic, acoustic, spin etc. propagation one way or another. The question about control uniqueness arises that is modulating frequency, duty ratio and signature sign uniqueness. Another question of characteristic index extremum at different controls is tightly bound with the former. The answers to these questions are obtained on the basis of OCT. The similarity of the optimal control problem solution and the one obtained at the heuristic feedback introduction through fundamental solutions product permits one to introduced the new form named general or mixed Hamiltonian along with the ordinary and OCT Hamiltonians. Besides this mixed Hamiltonian equality to zero together with the Wronskian constancy (almost everywhere) is the useful analogous in form to the Liouville’s theorem equation. The nonlinearity accounting using the OCT formalism is described too.
Abstract: The aim of the article is the elaboration of parametric resonance theory at piecewise constant frequency modulation. The investigation is based on the analogy with optics and optimal control theory (OCT) application. The exact expressions of oscillation frequency, gain/damping coefficients, dependencies of these coefficients on the modulation depth...
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Correlations of Heavy Quarks in Hot Deconfined Medium
Xinyu Li,
Xiaohan Eudora Song
Issue:
Volume 7, Issue 3, May 2019
Pages:
84-88
Received:
8 May 2019
Accepted:
4 June 2019
Published:
26 June 2019
Abstract: The early universe consists of bacis particles like quarks and gluons. Their interactions are controlled by strong interactions. In order to produce this new kind of matters, one can collide heavy ions. Large amount of energy will be transformed into particles. These particles form a matter with extremely high temperature. Usually this kind of matter can only be produced in heavy ion collisions, not nucleon collisions. But the recent experimental data indicate that it may also generate this kind of matter. The signal in nucleon collisions are taken as a baseline for heavy ion collisions, and other theoretical and experimental studies are based on this assumption that no hot medium is produced in nucleon collisions. If this new matter is also produced in nucleon collisions, this will affect the signals in heavy ion collisions. This work studies the momentum correlations of heavy quark pairs in the small colliding system such as proton-proton collisions based on the Langevin equation. With the production of deconfined hot medium, heavy quarks moving in the opposite direction can suffer energy loss and random kicks from the thermal medium. Moving in different directions, heavy quark and its anti-quark will suffer different random kicks from the thermal medium, which will change their momentum randomly. Their momentum correlations will be modified after moving out of the hot medium. Finally when heavy quark and anti-quark move out of the hot medium, their momentum is not in the opposite direction. Insteand, they move with a angular less than pi. We propose the momentum correlation of D mesons as a probe of the early stage of the proton-proton collisions, where the deconfined medium may be produced.
Abstract: The early universe consists of bacis particles like quarks and gluons. Their interactions are controlled by strong interactions. In order to produce this new kind of matters, one can collide heavy ions. Large amount of energy will be transformed into particles. These particles form a matter with extremely high temperature. Usually this kind of matt...
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Nuclear Alpha Decay in Field of Synchrotron Radiation
Issue:
Volume 7, Issue 3, May 2019
Pages:
89-92
Received:
11 April 2019
Accepted:
10 May 2019
Published:
4 July 2019
Abstract: We investigated before the possibility of modifying alpha decay rate by the influence of a laser radiation upon a nucleus. We showed that the laser radiation with the extreme achievable intensity slightly modifies the total rate of alpha decay. A different result may be probably obtained if it use synchrotron radiation for the irradiation of an alpha-active nucleus. At present, synchrotron radiation from the third generation synchrotrons has high brilliance, the photon energy may reach 200–300 keV and, in the future, it may be larger. These energies are comparable with nuclear ones and the effect from the influence of the synchrotron radiation upon alpha decay could be more significant. As it turned out, the change of the alpha decay rate of 238U isotope into the synchrotron radiation field from the third generation synchrotrons will be negligible.
Abstract: We investigated before the possibility of modifying alpha decay rate by the influence of a laser radiation upon a nucleus. We showed that the laser radiation with the extreme achievable intensity slightly modifies the total rate of alpha decay. A different result may be probably obtained if it use synchrotron radiation for the irradiation of an alp...
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