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Spin Waves in Two and Three Dimensional Magnetic Materials

Wijesinhe H. s., Wijewardena Gamalath K. A. I. L.

International Letters of Chemistry, Physics and Astronomy

2015

Vol. 49

35--47

The equations of motion for the dynamic properties of spin waves in three dimensions were obtained using Heisenberg model and solved for two and three dimensional lattices analytically up to an exponential operator representation. The second order Suzuki Trotter decomposition method was extended to incorporate second nearest interaction parameters into the numerical solution. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for two dimensional lattice as well as three dimensional simple cubic and bcc lattices. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor presenting the variation of energy transfer with respect to momentum transfer of spin waves. Second order Suzuki Trotter algorithm used conserved the energy.

The Heisenberg modelling procedure and applications to process control

Höskuldsson A.

Applied Mathematics and Computer Science

1998

Vol. 8, no 4

755-773

The Heisenberg modelling procedure is presented. The underlying idea is to define the basic modelling units that describe the modelling task. The associated algorithm gives a simultaneous expansion of the data matrix X and its generalised inverse X+. The procedure is applied to linear regression, time sedes analysis, Kalman filtering and nonlinear modelling. Some applications to Statistical Process Control (SPC) are described. Applications of the Heisenberg modelling procedure give new algorithms in different fields. The advantage of the procedure is that it gives stable estimates of parameters.