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1
Content available remote

Fractionl dynamics

100%
Magin R., Nigmatullin R.
Open Physics
|
2013
|
vol. 11
|
issue 6
615-616
2
Content available remote

Linear discrete systems with memory: a generalization of the Langmuir model

100%
Băleanu D., Nigmatullin R.
Open Physics
|
2013
|
vol. 11
|
issue 10
1233-1237
EN
In this manuscript we analyzed a general solution of the linear nonlocal Langmuir model within time scale calculus. Several generalizations of the Langmuir model are presented together with their exact corresponding solutions. The physical meaning of the proposed models are investigated and their corresponding geometries are reported.
3
Content available remote

Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum

81%
Nigmatullin R., Osokin S., Awrejcewicz J., Kudra G.
Open Physics
|
2014
|
vol. 12
|
issue 8
565-577
EN
In this paper we apply a new method of analysis of random behavior of chaotic systems based on the Prony decomposition. The generalized Prony spectrum (GPS) is used for quantitative description of a wide class of random functions when information about their probability distribution function is absent. The scaling properties of the random functions that keep their invariant properties on some range of scales help to fit the compressed function based on the Prony’s decomposition. In paper [1] the first author (RRN) found the physical interpretation of this decomposition that includes the conventional Fourier decomposition as a partial case. It has been proved also that the GPS can be used for detection of quasi-periodic processes that are appeared usually in the repeated or similar measurements. A triple physical pendulum is used as a chaotic system to obtain a chaotic behavior of displacement angles with one, two and three positive Lyapunov’s exponents (LEs). The chaotic behavior of these angles can be expressed in the form of amplitude-frequency response (AFR) that is extracted from the corresponding GPS and can serve as a specific ”fingerprint” characterizing the random behavior of the triple-pendulum system studied. This new quantitative presentation of random data opens additional possibilities in classification of chaotic responses and random behaviors of different complex systems.
4
Content available remote

Fractional Newtonian mechanics

81%
Baleanu D., Golmankhaneh A., Nigmatullin R., Golmankhaneh A.
Open Physics
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2010
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vol. 8
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issue 1
120-125
EN
In the present paper, we have introduced the generalized Newtonian law and fractional Langevin equation. We have derived potentials corresponding to different kinds of forces involving both the right and the left fractional derivatives. Illustrative examples have worked out to explain the formalism.
5
Content available remote

Self-similarity principle: the reduced description of randomness

81%
Nigmatullin R., Machado J., Menezes R.
|
EN
A new general fitting method based on the Self-Similar (SS) organization of random sequences is presented. The proposed analytical function helps to fit the response of many complex systems when their recorded data form a self-similar curve. The verified SS principle opens new possibilities for the fitting of economical, meteorological and other complex data when the mathematical model is absent but the reduced description in terms of some universal set of the fitting parameters is necessary. This fitting function is verified on economical (price of a commodity versus time) and weather (the Earth’s mean temperature surface data versus time) and for these nontrivial cases it becomes possible to receive a very good fit of initial data set. The general conditions of application of this fitting method describing the response of many complex systems and the forecast possibilities are discussed.
6
Content available remote

New method and treatment technique applied to interband transition in GaAs1−x Px ternary alloys

71%
Băleanu C.-M., Nigmatullin R., Cetin S., Băleanu D., Ozcelik S.
Open Physics
|
2011
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vol. 9
|
issue 3
729-739
EN
In this paper we presented a new method (Eigen-Coordinates (ECs)) that can be used for calculations of the critical points (CPs) energy of the interband-transition edges of the heterostructures. This new method is more accurate and complete in comparison with conventional ones and has a wide range of application for the calculation of the fitting parameters related to nontrivial functions that initially have nonlinear fitting parameters that are difficult to evaluate. The new method was applied to determine the CPs energies from the dielectric functions of the MBE grown GaAs1−xPx ternary alloys obtained using spectroscopic ellipsometry (SE) measurements at room temperature in the 0.5-5 eV photon energy region. The obtained results are in good agreement with the results of the other methods.
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