Investigation of the trajectories of a magnetized particle in the equatorial plane of a magnetic dipole

Денисов, В И; Kozar, A. V.; Sharikhin, V. F.

doi:10.3103/s0027134910030021

Cited by 4 publications

(1 citation statement)

References 2 publications

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“…A good description of the major numerical methods is given, for example, in [1][2][3][4][5][6]. Here they allow numerical modelling of complicated physical processes [7][8][9][10][11][12][13][14][15][16][17][18][19], including multidimensional heat transfer in rectangles and cylinders [20][21][22][23]. However, proper understanding of the solutions and of the obtained results can be best done when they are obtained in analytical form.…”

Section: Introductionmentioning

confidence: 99%

Operational Approach and Solutions of Hyperbolic Heat Conduction Equations

Zhukovsky

2016

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Abstract:We studied physical problems related to heat transport and the corresponding differential equations, which describe a wider range of physical processes. The operational method was employed to construct particular solutions for them. Inverse differential operators and operational exponent as well as operational definitions and operational rules for generalized orthogonal polynomials were used together with integral transforms and special functions. Examples of an electric charge in a constant electric field passing under a potential barrier and of heat diffusion were compared and explored in two dimensions. Non-Fourier heat propagation models were studied and compared with each other and with Fourier heat transfer. Exact analytical solutions for the hyperbolic heat equation and for its extensions were explored. The exact analytical solution for the Guyer-Krumhansl type heat equation was derived. Using the latter, the heat surge propagation and relaxation was studied for the Guyer-Krumhansl heat transport model, for the Cattaneo and for the Fourier models. The comparison between them was drawn. Space-time propagation of a power-exponential function and of a periodic signal, obeying the Fourier law, the hyperbolic heat equation and its extended Guyer-Krumhansl form were studied by the operational technique. The role of various terms in the equations was explored and their influence on the solutions demonstrated. The accordance of the solutions with maximum principle is discussed. The application of our theoretical study for heat propagation in thin films is considered. The examples of the relaxation of the initial laser flash, the wide heat spot, and the harmonic function are considered and solved analytically.

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