Browsing by Author "Waldron, J. T."

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    Exact Analytic Formula for the Correlation Time of a Single-Domain Ferromagnetic Particle
    (1994) Coffey, William T.; Crothers, D. S. F.; Kalmykov, Yuri P.; Massawe, Estomih S.; Waldron, J. T.
    Exact solutions for the longitudinal relaxation time T∥ and the complex susceptibility χ∥(ω) of a thermally agitated single-domain ferromagnetic particle are presented for the simple uniaxial potential of the crystalline anisotropy considered by Brown [Phys. Rev. 130, 1677 (1963)]. This is accomplished by expanding the spatial part of the distribution function of magnetic-moment orientations on the unit sphere in the Fokker-Planck equation in Legendre polynomials. This leads to the three-term recurrence relation for the Laplace transform of the decay functions. The recurrence relation may be solved exactly in terms of continued fractions. The zero-frequency limit of the solution yields an analytic formula for T∥ as a series of confluent hypergeometric (Kummer) functions which is easily tabulated for all potential-barrier heights. The asymptotic formula for T∥ of Brown is recovered in the limit of high barriers. On conversion of the exact solution for T∥ to integral form, it is shown using the method of steepest descents that an asymptotic correction to Brown’s high-barrier result is necessary. The inadequacy of the effective-eigenvalue method as applied to the calculation of T∥ is discussed.
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    Exact Analytic Formula for the Correlation Times for Single Domain Ferromagnetic Particles.
    (Elsevier, 1993) Coffey, William T.; Crothers, D. S. F.; Kalmykov, Yuri P.; Massawe, Estomih S.; Waldron, J. T.
    Exact solutions for the longitudinal relaxation time T∥ and the complex susceptibility χ∥(ω) of a thermally agitated single domain ferromagnetic particle are presented for the simple uniaxial (Maier-Saupe) potential of the crystalline anisotropy considered by Brown [Phys. Rev. 130 (1963) 1677].
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    Exact Solution for the Correlation Times of Dielectric Relaxation of a Single Axis Rotator with Two Equivalent Sites
    (1993) Coffey, William T.; Kalmykov, Yuri P.; Massawe, Estomih S.; Waldron, J. T.
    It is shown how exact formulas for the longitudinal and transverse dielectric correlation times and complex polar&ability tensor, of a single axis rotator with two equivalent sites may be found. This is accomplished by writing the Laplace transforms of the dipole autocorrelation functions as three term recurrence relations and solving them in terms of continued fractions. The solution of these recurrence relations, in the zero frequency limit, yields the correlation times in terms of modified Bessel functions of the first kind. The previous result of Lauritzen and Zwanzig for the longitudinal relaxation time, based on an asymptotic expansion of the SturmLiouville equation, is regained in the limit of high potential barriers.