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  • 1
    Electronic Resource
    Electronic Resource
    Decrease in frequency of maximum far-infra-red power absorption of polar fluids with temperature (1986)
    Springer
    Il nuovo cimento della Società Italiana di Fisica 8 (1986), S. 369-378 
    Details
    ISSN: 0392-6737
    Keywords: Infra-red and Raman spectra and scattering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Description / Table of Contents: Riassunto Si mostra come l'inerente non linearità delle equazioni di moto di dipoli accoppiati spiega qualitativamente un numero di comportamenti dello spettro osservato nel lontano infrarosso di fluidi polari. Questi includono il decremento quasi lineare della posizione del picco del coefficiente di assorbimento di potenza FIR con l'aumento della temperatura e l'indipendenza della temperatura dell'ampiezza di banda.
    Notes: Summary It is shown how the inherent nonlinearity of the equations of motion of coupled dipoles qualitatively explains a number of features of the observed far-infra-red spectrum of polar fluids. These include the almost linear increasing temperature and the temperature independence of the band width.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02450572
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  • 2
    Electronic Resource
    Electronic Resource
    On the derivation of the Debye theory of dielectric relaxation from the Langevin equation in the presence of the driving field (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 724-729 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It is shown how the Debye results for the behavior of an assembly of dipoles subjected to step-on, step-off, and ac fields which are usually obtained by calculating the linear response from the Smoluchowski equation may also be obtained from the Langevin equation by using a transformation of that equation suggested by Frood and Lal. This transformation allows one to calculate the linear response from the Langevin equation even in the presence of a driving field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459522
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  • 3
    Electronic Resource
    Electronic Resource
    Anomalous dielectric relaxation in the context of the Debye model of noninertial rotational diffusion (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 6422-6426 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Debye theory of dielectric relaxation of an assembly of polar molecules is reformulated using a fractional noninertial Fokker–Planck equation for the purpose of extending that theory to explain anomalous dielectric relaxation. The fractional Fourier–Planck equation in question is a generalization of the Smoluchowski equation for the dynamics of Brownian particles in configuration space to include anomalous relaxation. It is shown that this model can reproduce nonexponential Cole–Cole-type anomalous dielectric relaxation behavior and that it reduces to the classical Debye model of rotational diffusion when the anomalous exponent is unity. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1460860
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  • 4
    Electronic Resource
    Electronic Resource
    Inertial effects in the nonlinear transient relaxation of Brownian particles in strong external electric fields (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 9895-9904 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A method of calculation of the nonlinear transient response of an assembly of fixed axis (two-dimensional) rotators due to sudden changes of a strong external dc electric field is presented. The infinite hierarchy of differential-recurrence relations for the decay functions describing the relaxation of the system is derived by averaging the underlying inertial Langevin equation. The solution for the one-sided Fourier transform of this hierarchy is obtained in terms of matrix continued fractions. The integral relaxation time and the spectrum of the electric polarization for various kinds of nonlinear transient responses (step-on, step-off, rapidly rotating field) are calculated for typical values of the model parameters. Both exhibit pronounced nonlinear effects due to the strong dc field. Analytical equations for the quantities of interest are presented for particular cases (in the overdamped and low damping limits, etc.). © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1415443
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  • 5
    Electronic Resource
    Electronic Resource
    Mean first passage times of Brownian rotators from differential recurrence relations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 8350-8355 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An exact method of calculation of mean first passage times (analogous to that previously used [W. T. Coffey, Yu. P. Kalmykov, E. S. Massawe, and J. T. Waldron, J. Chem. Phys. 99, 4011 (1993)] for the correlation time) is developed in terms of continued fractions from the zero frequency limit of the Laplace transform of the set of differential recurrence relations generated by the Fokker–Planck or Langevin equations. The method because it is based on a Floquet representation avoids the use of quadratures and so may be easily generalized to multidegree of freedom systems by the use of matrix continued fractions. The procedure is illustrated by considering the mean first passage time of a fixed axis rotator with two equivalent sites. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.480176
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  • 6
    Electronic Resource
    Electronic Resource
    On the derivation of the Debye theory of dielectric relaxation from the Langevin equation in the presence of the driving field. II. Inclusion of inertial effects for rotation in three dimensions (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 2026-2035 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It is shown how the inertial response in the presence of a driving field of an assembly of molecules free to rotate in space (with dipole–dipole coupling effects ignored) may be obtained by direct averaging of the Langevin equation. The procedure is illustrated by considering the linear dielectric response of an assembly of needle like rotators choosing as variables in the Langevin equation the Hermite polynomials in the angular velocities and the associated Legendre functions of order l. This leads directly, using the statistical properties of the white noise driving torques, to the differential–difference equations which govern the dielectric response. These are converted into an infinite set of linear simultaneous first order differential equations which are solved by successively limiting the size of the transition matrix to 2×2, 3×3, etc. The continued fraction solution previously obtained by Sack is recovered using this procedure. The 2×2 approximation to the solution, effectively corresponding to the Rocard equation, is discussed in relation to recent far infrared absorption measurements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461001
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  • 7
    Electronic Resource
    Electronic Resource
    Application of free rotational models of molecular reorientation to the explanation of high frequency effects in dielectric relaxation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 5300-5306 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Exact solutions obtained by Gross [J. Chem. Phys. 23, 1415 (1955)] and Sack [Proc. Phys. Soc. London, Sect. B 70, 402 (1957)] for the complex polarizability of assemblies of nonelectrically interacting rotators subjected to a variety of collisions and various approximations to that quantity, specifically the Rocard equation are reappraised in view of recent attempts to use a variety of forms of that equation for the interpretation of far infrared resonance absorption spectra. It is shown that for small values of the inertial parameter (heavy damping) the Rocard equation yields a really good approximation for the complex polarizability only for the small collision model considered by Gross and Sack. In the case of large inertial parameter values it is emphasized by means of plots of the complex polarizability that such an approximation always exhibits behavior characteristic of a sharply resonant system, i.e., a pronounced absorption peak well in excess of the Debye peak and a strongly negative real part, while the exact complex polarizability spectrum for the same parameter values merely displays inertia corrected Debye relaxation. Therefore, an explanation of the resonant term other than that based on a Rocard equation with a large inertial parameter must be sought as that equation strictly applies to inertia corrected Debye (heavily damped) relaxation only. The application of the itinerant oscillator model and the three variable Mori theory to the problem is discussed in view of this conclusion.© 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478424
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  • 8
    Electronic Resource
    Electronic Resource
    Closed form solution of the itinerant oscillator model of molecular libration (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 7625-7628 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It is shown by using self-consistent (so that action and reaction torques are fully accounted for) expressions for the viscous drag and white noise terms in the equations of motion of the fixed axis rotator version of the itinerant oscillator model that the characteristic (secular) equation of the system automatically factorizes. Hence all the correlation functions of the model (which consists of a "cage" of dipolar molecules surrounding a tagged molecule) may be given in closed form. In particular, the orientational correlation functions of the tagged molecule become the products of single particle ones namely those of a free Brownian rotator and a damped harmonic oscillator while the orientational correlation functions of the cage are simply those of the free Brownian rotator. The equations of motion of the system likewise decouple when the restrictions of small oscillations and of rotation about a fixed axis are removed. Thus, irrespective of the form of the interaction potential between the cage and the tagged molecule, the relaxation modes of the system separate into those of the tagged molecule and those of its surroundings which behave as an inertia corrected free Brownian rotator. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.473765
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  • 9
    Electronic Resource
    Electronic Resource
    Dipole–dipole interaction and anisotropy effects in the itinerant oscillator model (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 4960-4967 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The itinerant oscillator model whereby a typical molecule of a polar fluid may exhibit librational motion under the influence of the field of its large cage of neighboring dipoles is examined when the restriction of rotation about a common fixed axis is removed, both cage and tagged molecule now being free to rotate about a common fixed point of themselves. It is shown that the equations of motion of the system cannot, in general, be decomposed into the equations of motion of the tagged molecule relative to the cage and that of the cage alone on account of the Coriolis torques. If, however, one can make the assumption that the cage is much more massive than the tagged molecule so that in a short time (essentially a time less than the Debye relaxation time of the cage so that the cage represents a slowly relaxing local structure) after the removal of an external uniform field the cage remains virtually at rest relative to the tagged molecule, then the dipole autocorrelation function of the tagged molecule is approximately the product of the autocorrelation function of the cage and the autocorrelation functions of the motion of the tagged molecule relative to the cage. The behavior of the model, with a cage–dipole interaction potential including both the permanent and induced dipole terms in the noninertial limit is discussed using the above assumption. It is shown that the inclusion of the induced dipole term essentially creates an asymmetric bistable interaction potential in which a relaxation process indicative of a slow overbarrier (activation) process coexists with the relatively fast relaxation modes in the wells of the potentials [as predicted by Polemino and Freed, Adv. Chem. Phys. 83, 89 (1993) in their numerical analysis of the model]. The conditions under which the fast relaxation processes may come to dominate the overall relaxation behavior are discussed by analogy with superparamagnetic relaxation [cf. Coffey, Crothers, and Kalmykov, Phys. Rev. E 55, 4812 (1997)]. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.474859
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  • 10
    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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