The nonlinear dielectric relaxation ac stationary response of an assembly of rigid polar molecules acted on by strong superimposed external dc E0 and ac E1(t)=E(1) cos omegat electric fields is evaluated in the context of the noninertial rotational diffusion model. The calculation proceeds by expanding the relaxation functions f(n)(t) (the expectation value of the Legendre polynomials P(n)), which describe the nonlinear relaxation of the system, as a Fourier series in the time domain. Hence, an infinite hierarchy of recurrence equations for the Fourier components of f(n)(t) is obtained. The exact solution of this hierarchy can be obtained in terms of a matrix continued fraction, so allowing us to evaluate the ac nonlinear response. For a weak ac field our results are in complete agreement with previous solutions obtained by perturbation methods. Diagrams showing the behavior of the in-phase and out-of-phase components of the electric polarization are presented.

We address the issue of inter-particle dipolar interactions in the context of magnetic hyperthermia. More precisely, the main question dealt with here is concerned with the conditions under which the specific absorption rate is enhanced or reduced by dipolar interactions. For this purpose, we propose a theory for the calculation of the AC susceptibility, and thereby the specific absorption rate, for a monodisperse two-dimensional assembly of nanoparticles with oriented anisotropy, in the presence of a DC magnetic field, in addition to the AC magnetic field. We also study the competition between the dipolar interactions and the DC field, both in the transverse and longitudinal configurations. In both cases, we find that the specific absorption rate has a maximum at some critical DC field that depends on the inter-particle separation. In the longitudinal setup, this critical field falls well within the range of experiments.

Based on the temperature behavior of the entropy increment induced by the probing electric field in the isotropic phase of mesogenic compounds belonging to the homologous series C(n)H(2n+1)PhCOOPhCN ( n = 4-10), it is found that an ability to the dipolar aggregation of the molecules depends on the alkyl tail length, and, in particular, the ability is strongly reinforced when the number n changes from 7 to 8. The role of the molecular structure in the self-assembling process is discussed.

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The nonlinear effects arising from the first and second hyperpolarizabilities on the Kerr effect relaxation response of an ensemble of polar and anisotropically polarizable molecules in a strong dc electric field are studied by solving the infinite hierarchy of differential-recurrence relations underlying the noninertial Fokker–Planck (Smoluchowski) equation. The step-on solution is obtained by using the matrix continued fraction methods. An expression for the Kerr effect relaxation time is derived as well following the procedure of Kalmykov, Déjardin, and Coffey [Phys. Rev. E 55, 2509 (1997)] which is in full agreement with the matrix continued fraction expression. For small values of the electric field, it is shown that the first hyperpolarizability contributes to increasing the Kerr effect relaxation time while the second hyperpolarizability shifts the maximum of the relaxation time toward the lowest electric fields on increasing the value of this maximum. The dual nature of essentially two relaxation processes is also emphasized by plotting the Kerr effect relaxation spectra for various values of the first and second hyperpolarizability parameters.

The nonlinear impedance of a point Josephson junction is calculated under various conditions for the resistively shunted junction model in the presence of noise. The calculation proceeds by solving the Langevin equation for the mechanical problem of a Brownian particle in a tilted cosine potential in the presence of a strong ac force ignoring inertial effects. The exact solution of the infinite hierarchy of equations for the moments ͑expectation values of the Fourier components of the phase angle͒, which describe the dynamics of the junction, is expressed in terms of a matrix continued fraction. This solution allows one to evaluate the nonlinear response of the junction ͑nonlinear microwave impedance, for example͒ to an ac microwave current of arbitrary amplitude. Strong nonlinear effects in the resistance and the reactance are observed for large ac currents as is demonstrated by plotting the nonlinear response characteristics as a function of the model parameters. For weak ac currents and low noise strengths, our results agree closely with previously available linear response and nonlinear response noiseless solutions, respectively. Applications of the model to the interpretation of recent experimental data found in the literature for the nonlinear behavior of microwave impedance of superconducting weak links are discussed.

The dielectric relaxation spectroscopy is used for studying the orientational molecular dynamics in the isotropic (I) and nematic (N) phases of two mesogenic liquids composed of the molecules of similar structure and length, but of an essentially different polarity: n-heptylcyanobiphenyl, C(7)H(15)PhPhCN, 7CB (molecular dipole moment mu approximately 5D) and 4-(trans-4'-n-hexylcyclohexyl)isothiocyanatobenzene, C(6)H(13)CyHxPhNCS, 6CHBT (mu approximately 2.5D); advantageously, the temperatures of the I-N phase transition for the two compounds are very close to each other (T(NI) = 316.6 +/- 0.2 K). It is shown that regardless of the differences in polarity of 7CB and 6CHBT molecules and their abilities in dipolar aggregation, the values and temperature dependences of the relaxation time (corresponding to the rotational diffusion of the molecules around their short axis) are very close to each other, in both the isotropic and nematic phases of the liquids studied. Therefore, the data show that the dielectric relaxation processes occurring in dipolar liquids in the isotropic and nematic states lead through the rotational diffusion of individual molecules and the diffusion seems to be not influenced by the intermolecular interactions.

We develop a general formalism for analyzing the ferromagnetic resonance characteristics of a magnetic dimer consisting of two magnetic elements (in a horizontal or vertical configuration) coupled by dipolar interaction, taking account of their finite-size and aspect ratio. We study the effect on the resonance frequency and resonance field of the applied magnetic field (in amplitude and direction), the inter-element coupling, and the uniaxial anisotropy in various configurations. We obtain analytical expressions for the resonance frequency in various regimes of the interlayer coupling. We (numerically) investigate the behavior of the resonance field in the corresponding regimes. The critical value of the applied magnetic field at which the resonance frequency vanishes may be an increasing or a decreasing function of the dimer's coupling, depending on the anisotropy configuration. It is also a function of the nanomagnets aspect ratio in the case of in-plane anisotropy. This and several other results of this work, when compared with experiments using the standard ferromagnetic resonance with fixed frequency, or the network analyzer with varying frequency and applied magnetic field, provide a useful means for characterizing the effective anisotropy and coupling within systems of stacked or assembled nanomagnets.Comment: 22 Pages, 13 Figure