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System Dynamics Control through the Fractal Potential

100%
Timofte A., Casian Botez I., Scurtu D., Agop M.
Acta Physica Polonica A
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2011
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vol. 119
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issue 3
304-311
EN
Implications of the fractal potential in the system dynamics using an extended scale relativity model assuming the fractal character of the particle movements, are established. So, in the dissipative approximation of the model it is shown that the fractal potential comes from the non-differentiability of the space-time, i.e. by means of imaginary part of a complex speed field. In the dispersive approximation of the same model, the fractalization of the differential part of the complex speed field induces a normalized fractal potential which controls through coherence the system dynamics. In such context the type I superconductivity results: the temperature dependences of the superconducting parameter, the accumulator effect etc.
2
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Fractal Transport Phenomena through the Scale Relativity Model

100%
Colotin M., Pompilian G., Nica P., Gurlui S., Paun V., Agop M.
Acta Physica Polonica A
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2009
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vol. 116
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issue 2
157-164
EN
A correspondence between Nottale's scale relativity model and Cresson's mathematical procedures is analyzed. It results that the "synchronization" of the movements at different scales (fractal scale, differential scale etc.) gives conductive type properties to the fractal fluid, while the absence of "synchronization" is inducing properties of convective type. The behavior of a conductive fractal fluid is illustrated through the numerical simulation of plasma diffusion that is generated by laser ablation. Rotational and irrotational convective behaviors of a fractal fluid are established. Particularly, at Compton spatial and temporal scales, the irrotational behavior implies the standard Schrödinger equation.
3
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RKKY Interaction in Coupled Quantum Dots

100%
Bak Z., Jaroszewicz R., Gruhn W.
Acta Physica Polonica A
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2009
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vol. 115
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issue 1
342-344
EN
Assuming that quantum dots are treated as artificial impurities we consider the Ruderman-Kittel-Kasuya-Yosida interaction between their localized magnetic moments. We prove that due to the quantum confinement the carriers that mediate interactions can exhibit fractional spectral dimension. Basing on this result we discuss magnetic interactions in coupled system of quantum dots and leads.
4
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Wave-Particle Duality through a Hydrodynamic Model of the Fractal Space-Time Theory

100%
Agop M., Nica P., Harabagiu A.
Acta Physica Polonica A
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2008
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vol. 113
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issue 6
1571-1588
EN
Considering that the microparticle movements take place on fractal curves, the wave-particle duality is studied in the fractal space-time theory (scale relativity theory). The Nottale model was extended by assuming arbitrary fractal dimension, D_F, of the fractal curves and third-order terms in the equation of motion of a complex speed field. It results that, in a fractal fluid, the convection, dissipation, and dispersion are reciprocally compensating at any scale (differentiable or non-differentiable), whereas a generalized Schrödinger equation is obtained for an irrotational movement of the fractal fluid. The absence of the dispersion implies a generalized Navier-Stokes type equation and the usual Schrödinger equation results for the irrotational movement in D_F=2 of the fractal fluid. The absence of dissipation implies a generalized Korteweg-de Vries type equation. In such conjecture, the duality is analyzed through a hydrodynamic formulation. At the differentiable scale, the duality is achieved by the flowing regimes of the fractal fluid, while at the non-differentiable scale, a fractal potential controls, through the coherence, the duality.
5
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Some Aspects Concerning the "Memorization Effect" in Complex Fluid

100%
Agop M., Ochiuz L., Timofte D., Barlescu V., Danila M., Gheorghita L., Paun V., Solovastru L., Popa C.
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vol. 126
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issue 3
663-670
EN
In the frame of a non-standard scale relativity model, the specific momentum, states density and internal energy conservations laws are obtained. The chaoticity, either through turbulence in the fractal hydrodynamics approach, or through stochasticization in the Schrödinger type approach, is generated only by the non-differentiability of the movement trajectories of the complex fluid entities. Using the conservation laws mentioned above, by numerical simulations, hysteretic type effects (dynamics of hysteretic cycles) occur.
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