Maricel Agop

Cantorian E(∞) space-time and generalized superconductivity

Abstract In fractal space-time theory we built a superconducting model for generalized fields (electromagnetic and linear gravitation): generalized Maxwell and Londons equations, generalized Meissner and shielding effects, oscillation modes in thin cylindrical generalized superconductors (generalized supertrons) and generalized superconductivity as a gauge theory. In such a context the atomic, planetary and double galaxies systems are self-organized as fractal superconducting structures. The Cantorian E (∞) structure of space-time implies a two-dimensional cnoidal distribution of the particles concentration for the solid–liquid interface and allows the evaluation of the kinetic moment of a neutron star.

Wave-particle duality and superconductivity in Weyl-Dirac theories

In the Gregorash–Papini–Wood approach to the Weyl–Dirac theory, some superconducting properties of the wave equation are analysed. In a special topology, for a constant modulus of the wavefunction, the phase gradient verifies an effect analogous to the gravitational Meissner effect (there is no momentum transfer between the wave and the particle, and the wave–particle duality is achieved by self-tunnelling). Through the gravitational Meissner effect the oscillation modes of a particle are cnoidal, and in a superconducting cylinder a quantum fluid moving along its axis is self-focusing. The matching between quantum hydrodynamics and wave mechanics is similar to the quantization of the gravitational fluxoid, and their unmatching is analogous to the gravitational analogue of the Aharonov–Bohm effect. The absence of the gravitational Meissner effect implies a permanent transfer of momentum between the wave and the particle such as the interior of the particle structured like a lattice. By defining a free energy we show that the wave–particle duality is equivalent to a normal–superconducting phase transition. In this context by generalizing the one-dimensional solution of the WD equation to the two-dimensional case, one can induce a superconducting state by in-phase oscillations of a vortex lattice.

Focusing and Guiding Charged Particles using Two-layer Superconducting Tubes: A Theoretical Approach.

A theoretical model of self-focusing of an impulse electron beam in a two-layered superconducting tube is designed. The self-focusing force is calculated and, by defining the pair breaking time of the superconducting pair, it is shown that this is conditioned among others by the ratio of the beam pulse period to the pair breaking time. The model is validated by evaluating both the breaking time and the focusing length.

Cantorian-fractal space-time and particles in a generalized magnetic field

Abstract In the fractal space-time theory the generalized precession, the generalized Stern–Gerlach experiment, the generalized Zeeman effect, the generalized Landaus levels and the generalized fractional quantum Hall effect are analyzed. The Cantorian structure of space-time implies the supplemental decreasing rate of the Ecliptic tilt, the “global” quantization in units of 36 km s−1 and the filling factor ν=1/2n+1.

The isotope effect coefficient dependence on nonstoichiometry for single CuO layer superconductors

Considering that the variation of the critical temperature can be explained if the impurity potential acts only by the non-spin-flip part, in the presence of either a pure d-wave or anisotropic s-wave gap symmetry, and inserting the pair-breaking time dependence on temperature, we obtain a quantitative expression for the isotope effect coefficient α as a function of measured critical temperature Tc maximal critical temperature T and degree of anisotropy of the energy gap. Our result predicts the achievement of a large range of values in α for different ratios T/Tc. Introducing the dependence of the critical temperature and pair-breaking time on dopant content for a single Cuue5f8O layer superconductors, we can describe the variation of the isotope effect coefficient with nonstoichiometry for these materials. The result for the case of anisotropic s-wave gap symmetry is in good agreement with the experimental data.