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  • 1
    Electronic Resource
    Electronic Resource
    Longitudinal dynamic susceptibility of superparamagnetic particles with cubic anisotropy (1999)
    Springer
    Journal of experimental and theoretical physics 88 (1999), S. 58-65 
    Details
    ISSN: 1090-6509
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the linear response of a system of single-domain ferromagnetic particles with cubic magnetic anisotropy to a weak external a.c. magnetic field. By averaging the Gilbert equation with a fluctuating field for the magnetization of an individual particle we derive a system of recurrence equations for the spectra of equilibrium correlation functions describing the longitudinal relaxation of the system. We find the solution of this system by using matrix continued fractions. We also evaluate the longitudinal relaxation time and the spectrum of the complex-valued magnetic susceptibility. Finally, we show that the nature of susceptibility dispersion is determined by the anisotropy and dissipation parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.558764
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  • 2
    Electronic Resource
    Electronic Resource
    Longitudinal complex magnetic susceptibility of superparamagnetic particles with cubic anisotropy (1998)
    Springer
    Physics of the solid state 40 (1998), S. 1721-1722 
    Details
    ISSN: 1063-7834
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The dynamic susceptibility spectrum of single-domain particles with cubic anisotropy has been calculated within the continuous diffusion model throughout the total range of anisotropy-and damping-parameter variation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.1130643
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  • 3
    Electronic Resource
    Electronic Resource
    Complex magnetic susceptibility of uniaxial superparamagnetic particles in a strong static magnetic field (1998)
    Springer
    Physics of the solid state 40 (1998), S. 1492-1499 
    Details
    ISSN: 1063-7834
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The magnetic relaxation of a system of single-domain ferromagnetic particles in the presence of a strong static magnetic field directed at an arbitrary angle relative to the particle anisotropy axis is investigated. A system of linear difference-differential equations for the moments (averaged spherical harmonics) is derived without recourse to the Fokker-Planck equation by averaging Gilbert’s equations with a fluctuating field. An exact solution (in terms of matrix continuous fractions) is found for this system. The relaxation times and spectra of the complex magnetic susceptibility are calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.1130584
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  • 4
    Electronic Resource
    Electronic Resource
    Calculating coefficients for a system of moment equations used to describe the magnetization kinetics of a superparamagnetic particle in a fluctuating field (1999)
    Springer
    Physics of the solid state 41 (1999), S. 1854-1861 
    Details
    ISSN: 1063-7834
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A system of equations is derived for moments [averages of spherical harmonics 〈Y l,m 〉(t)] that determine the dynamics of the magnetization M of a superparamagnetic particle in a fluctuating field. The system is derived by representing the Gilbert equation in a fluctuating field, and the corresponding Fokker-Planck equation for the distribution function of M, in terms of angular momentum operators, which in turn makes it possible to express the coefficients of the system of moment equations in terms of Clebsch-Gordan coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.1131113
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  • 5
    Electronic Resource
    Electronic Resource
    Nonlinear response of superparamagnetic particles to a sudden change of a high constant magnetic field (2000)
    Springer
    Physics of the solid state 42 (2000), S. 918-924 
    Details
    ISSN: 1063-7834
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For a system of superparamagnetic particles in a high external constant magnetic field, a technique for calculating the nonlinear response to a sudden change in the field direction and magnitude is proposed. A set of momentary equations for the averaged spherical harmonics, which is derived from the Fokker-Planck equation for the magnetization-orientation distribution function is the basis of this technique. As an example, the nonlinear response of a system of particles with anisotropy of the easy-axis type is examined. For this case, a solution to the momentary equations is obtained by using matrix continued fractions. The magnetization relaxation time and the spectrum of the relaxation function are calculated for typical values of anisotropy, dissipation, and nonlinearity parameters. It is shown that the magnetization kinetics is essentially dependent on these parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.1131312
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  • 6
    Electronic Resource
    Electronic Resource
    Rotational diffusion and dielectric relaxation of linear molecules in a cubic potential (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 3644-3653 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The dielectric relaxation of molecular impurities in cubic crystals is treated by averaging the Langevin equation for noninertial rotational Brownian motion of a linear rotator in a cubic potential, so that the system of linear differential-recurrence equations for the appropriate equilibrium correlation functions is derived without recourse to the diffusion (Smoluchowski) equation. The solution of this system is expressed in terms of matrix continued fractions that allows us to evaluate the dielectric relaxation time τ and the low frequency spectrum of the complex susceptibility χ(ω). The behavior of τ and χ(ω) is investigated for all ranges of the anisotropy energy (σ) parameter. The results obtained are compared both with previously available solutions and asymptotic estimates based on the Kramers escape rate theory in the overdamped limit. It is shown that the relaxation processes in a cubic potential are very similar to those in a double-well potential. They are governed and can be described by two distinct mechanisms — overbarrier and intrawell relaxation. Simple analytic formulas for χ(ω) and τ are also presented. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479645
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  • 7
    Electronic Resource
    Electronic Resource
    Steady state response of the nonlinear dielectric relaxation and birefringence in strong superimposed ac and dc bias electric fields: Polar and polarizable molecules (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 2916-2923 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Both nonlinear dielectric relaxation and dynamic Kerr effect responses of an assembly of polar and anisotropically polarizable molecules acted on by strong superimposed external dc E0 and ac E1(t)=E1 cos ωt electric fields are evaluated in the context of the rotational diffusion model in the noninertial limit. The relaxation functions fn(t) (the expectation value of the Legendre polynomials Pn), which are appropriate to describe these nonlinear relaxation phenomena, are calculated by expanding them as a Fourier series in the time domain. An infinite hierarchy of recurrence relations for these Fourier amplitudes of fn(t) is obtained, the solution of which is expressed in terms of an infinite matrix continued fraction, so allowing us to evaluate the dynamic characteristics of the electric polarization and birefringence. For a weak ac field, the results predicted by the theory are in complete agreement with previous solutions obtained by perturbation methods. The solutions for the particular cases, where only either permanent or induced dipole moments are taken into account, can easily be extracted from the general solution. Diagrams of the frequency behavior of the in-phase and out-of-phase components of the electric birefringence and polarization are presented showing pronounced nonlinear effects due to the high ac field. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.480864
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  • 8
    Electronic Resource
    Electronic Resource
    Transient dielectric and birefringence relaxation of a system of rigid polar particles in strong dc electric fields (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 6484-6490 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The problem of the nonlinear transient response of a system of rigid dipolar particles (macromolecules) diluted in a nonpolar solvent to a sudden change of an external dc field both in magnitude and direction is considered. On solving the noninertial Fokker–Planck equation for the rotational Brownian motion of a dipolar particle, the relaxation functions and relaxation times are calculated for the transient dynamic Kerr effect and nonlinear dielectric relaxation. This is accomplished by using the matrix-continued fraction method, which allows one to find the solution of the infinite hierarchy of differential-recurrence relations for the first- (electric polarization) and second- (electric birefringence) order transient responses of ensemble averages of the spherical harmonics (relaxation functions). The results are compared with solutions previously obtained and illustrated by plots for the relaxation times and spectra of the relaxation functions. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478551
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  • 9
    Electronic Resource
    Electronic Resource
    Exact analytic solution for the correlation time of a Brownian particle in a double-well potential from the Langevin equation (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 2112-2118 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The correlation time of the positional autocorrelation function is calculated exactly for one-dimensional translational Brownian motion of a particle in a 2–4 double-well potential in the noninertial limit. The calculations are carried out using the method of direct conversion (by averaging) of the Langevin equation for a nonlinear stochastic system to a set of differential–recurrence relations. These, in the present problem, reduce on taking the Laplace transform, to a three-term recurrence relation. Thus the correlation time Tc of the positional autocorrelation function may be formally expressed as a sum of products of infinite continued fractions which may be represented in series form as a sum of two term products of Whittaker's parabolic cylinder functions. The sum of this series may be expressed as an integral using the integral representation of the parabolic cylinder functions and subsequently the Taylor expansion of the error function, thus yielding the exact solution for Tc. This solution is in numerical agreement with that obtained by Perico et al. [J. Chem. Phys. 98, 564 (1993)] using the first passage time approach while previous asymptotic results obtained by solving the underlying Smoluchowski equation are recovered in the limit of high barrier heights. A simple empirical formula which provides a close approximation to the exact solution for all barrier heights is also given. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472079
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  • 10
    Electronic Resource
    Electronic Resource
    Exact solution for the correlation times of dielectric relaxation of a single axis rotator with two equivalent sites (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 4011-4023 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It is shown how exact formulas for the longitudinal and transverse dielectric correlation times and complex polarizability 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 Sturm–Liouville equation, is regained in the limit of high potential barriers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.466097
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