Abstracts of papers for

Previous issue vol. 42, no. 3 (2001)

vol. 42, no. 4 (2001)

Next issue vol. 43, no. 1 (2002)

Contents of issue 4, vol. 42

1. J. Przeszowski: Gauge symmetry in models of high temperature superconductors
2. S. Poria, C. Mamaloukas, G.C. Layek and H.P. Mazumdar: Some effects of a transverse magnetic field on the flow of a viscous conducting fluid produced by an oscillating plane wall
3. A. Drzewiecki and B. Maruszewski: Doping and mass transfer in fullerenes
4. E. Radzikowska: Micropolar model of high-temperature superconductors
5. S. Bytner, A. Gałka and B. Gambin: Effective properties of layered piezoelectric material with gradient of polarization
6. V. Nichoga, P. Dub and Z. Kaczmarek: Hollow ellipsoid of rotation as a physical model of tubular cylindrical ferromagnetic core
7. J. Cabański: Exact method of solution of torsional vibrations problem for discontinuous viscoelastic shaft with oscillators

   Brief Notes

8. W. Skrzeczanowski, J. Owsik, A. Długaszek, J. Janucki, M. Nowakowski and A. Zarwalska: Portable low uncertainty calorimetric standard for energy unit of pulse laser radiation

J. Przeszowski: Gauge symmetry in models of high temperature superconductors

Gauge symmetry which appears in the slave-mode approach to the t-J model of high temperature superconductivity is presented. The mean field analysis of these microscopic models lead to the continuum gauge field systems with infinitely strong coupling constant. The viability of the perturbative calculations (with finite coupling constant) are illustrated with a particularly simple field theory model. Exact resummation of the perturbation series is discussed for the Heisenberg model of strongly interacting spins in 1+1 dimensions which is approximated by the Schwinger model.

Contents

S. Poria, C. Mamaloukas, G.C. Layek and H.P. Mazumdar: Some effects of a transverse magnetic field on the flow of a viscous conducting fluid produced by an oscillating plane wall

In this paper, the unsteady unidirectional motion of an incompressible vicous fluid, produced by sinusoidal oscillation of a rigid plane wall and subjected to a uniform magnetic field acting perpendicularly to the flow direction is investigated. The basic equation, governing the motion of such a flow is expressed in non-dimensional form. It is shown that this equation admits two solutions which satisfy the respective sets of boundary and initial conditions. The results, showing the development of the velocity field in time for different values of the magnetic parameter, are presented graphically and discussed.

Contents

A. Drzewiecki and B. Maruszewski: Doping and mass transfer in fullerenes

A crystalline solid of C₆₀ (a fullerene) is expected to be an insulator or a semiconductor. However, one of the most striking properties of C₆₀ - related materials is the observation of relatively high temperature superconductivity in alkali metal doped M₃C₆₀ and in various alkaline earth doped compounds. So, the interstitial diffusion of impurities considerably influences the superconductivity phase. The value of the critical temperature below which the superconducting phase exists strongly depends on many other external influences (electromagnetic, thermal, mechanical, etc.). The paper deals with construction of a phenomenological macroscopic model of interactions between physical fields in fullerenes, basing on the extended thermodynamics with internal variables and with the use of Liu's theorem in order to apply the entropy inequality. Two types of the mass diffusion have been taken into account constructing the model.

Contents

E. Radzikowska: Micropolar model of high-temperature superconductors

The micropolar continuum theory is applied to superconductors of type II containing a vortex lattice. The classical electrodynamic theory of micropolar continua is supplemented by quantum-mechanical notions describing the phenomenon of superconductivity. A variational principle for dissipative processes taking place in high-temperature superconductors is formulated. The electromagnetic, mechanical and thermal fields interactions in superconductors are considered. Finally, the complete system of field equations describing these interactions is obtained together with the constitutive relations and the jump conditions on the discontinuity surface.

Contents

S. Bytner, A. Gałka and B. Gambin: Effective properties of layered piezoelectric material with gradient of polarization

In the paper, homogenization of heterogeneous piezoelectricity with polarization gradient is performed to obtain effective material coefficients. The method of two-scale asymptotic expansion is used and the layered composite structure is analysed in details.

Contents

V. Nichoga, P. Dub and Z. Kaczmarek: Hollow ellipsoid of rotation as a physical model of tubular cylindrical ferromagnetic core

Induction sensors with cores in the shape of hollow cylinder are widely used because of such advantages as decrease of mass and simplicity of manufacturing cores with defined geometry. Replacement of a real tubular cylindrical core by the model in the shape of hollow ellipsoid of rotation with equal values of relative lengths, ferromagnetic volumes and fluxes, that is proposed in the article, allows to find the calculation algorithms for determination of electromagnetic parameters of cylindrical rod with solid and tubular cores. The obtained algorithms take into account the influence of both the geometry and magnetic properties of core material on the electromagnetic parameters and are suitable for engineering calculations.

Contents

J. Cabański: Exact method of solution of torsional vibrations problem for discontinuous viscoelastic shaft with oscillators

In this paper a generalized, exact method for solving the problems of torsional vibrations of a non-continuous viscoelastic shaft with oscillators has been presented. The oscillators are attached to the shaft by means of the visco-elastic constraints. The vibrations of this compound system are described by the set of conjugated, partial and ordinary differential equations. The separation of the variables in the complex Hilbert space, the obtained results from the analysis of the boundary-value problems and the proved generalized orthogonality of complex eigenvectors have been used to obtain the solution for free vibrations of the system at the arbitrary initial conditions. Finally, by applying the harmonic moment of the forced vibrations, the problem of the shaft has been solved. In the herein presented method, the operational generalized principles [6] have been applied.

Contents

W. Skrzeczanowski, J. Owsik, A. Długaszek, J. Janucki, M. Nowakowski and A. Zarwalska: Portable low uncertainty calorimetric standard for energy unit of pulse laser radiation

New instrument for metrology applications in measurements of laser pulse energy is presented. Due to its parameters it can be used as a standard for unit of energy of pulse laser radiation. The instrument consists of a control unit, three different sources of laser radiation, two receivers of optical signal, and a laptop. The whole system can be easily transported enabling one to carry out measurements in situ, at customers, not only in laboratory conditions. A method of measurement used in operation of the standard is described. Main characteristics of the standard are shown. Methods of calculation of uncertainties of measurement during laser energy meters calibration by means of our standard are also presented.

Contents