The interaction between a cylindrical magnet and a superconducting hollow cylinder in the Meissner state was analyzed using a dipole-dipole model. Analytical expression of the levitation force was derived as a function of the magnetic moment, radius of the magnet, radius, and thickness of the superconductor sample. The effect of the magnet's dimensions on the levitation force was studied. The obtained results show that there is strong dependence of the levitation force on the magnetic dipole orientation at a small magnet-superconductor distance.

A frequency chirped continuous wave laser beam incident upon a resonant, two-level atomic absorber is seen to evolve into a Jacobi elliptic pulse-train solution to the Maxwell-Bloch equations. Experimental pulse-train envelopes are found in good agreement with numerical and analytical predictions.

The interaction between a monolayer of fine ferromagnetic particles and a semi-infinite superconductor has been investigated in the mixed state. The frozen and diamagnetic images model was employed to calculate the levitation force as a function of the levitation height as well as the temperature of the monolayer under the zero-field-cooled (ZFC) and the field-cooled (FC) conditions. Results showed the well-known monotonic decrease of the levitation force as a function of the levitation height while it increases rapidly as a function of temperature up to saturation. As a result of the first order approximation used in our calculations in which the interaction was represented by the forces between the magnetic dipoles and their images, the levitation force was dominated by the diamagnetic properties rather than the flux pinning effects of the superconductor for small values of levitation heights compared to the initial field cooling height.

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A new mathematical identity is suggested to describe narrow band phase modulation and other similar physical problems instead of using the Bessel function. Bessel functions are extensively used in mathematical physics [1,2], electromagnetic wave propagation and scattering [3,4], and communication system theory [3,5,6]. Such phenomena must often be approximated by appropriate formulas since there is no closed form solution or expression, which usually leads to complex mathematical solutions [5,7]. Comparisons are made between the exact solution numerically calculated and graphed with the new mathematical identities’ prediction of phase modulation behavior. The proposed mathematical identity matches the results very well, leading to simpler analysis of such physical behavior