Debye Relaxation Equation Research Articles

Dynamic Response of a Nonlinear Fabry-Perot Etalon for Various Medium Response Times

In this work, the switching nonlinear dynamics of a Fabry-Perot etalon are studied. The method used to complete the solution of the differential equations for the nonlinear medium. The Debye relaxation equations solved numerically to predict the behavior of the cavity for modulated input power. The response of the cavity filled with materials of different response time is depicted. For a material with a response time equal to = 50 ns, the cavity switches after about (100 ns). Notice that there is always a finite time delay before the cavity switches. The switch up time is much longer than the cavity build-up time of the corresponding linear cavity which was found to be of the order of a few round-trip times. The slowing down of the cavity response occurs when the incident intensity is approximately equal to the critical switching intensity. This effect is called critical slowing down. As a result, the response of the cavity is much slower than what could be expected from the steady state analysis. The reflected intensity and the change in round-trip phase have similar dynamic response. In this research, the matlap programs are used to study the switching dynamics of a Fabry-Perot etalon.

Excess wing physics and nearly constant loss in glasses

Excess wings and nearly constant loss are almost universal nonequilibrium phenomena in glass formers. Both lack an accepted theoretical foundation. A model-free and unified theoretical description for these phenomena is presented that encompasses also fast -processes, emergent Debye peaks, and the relaxation strength of the boson peak. The theory is model-free in the same way as the classical Debye relaxation equation for orientational polarisation. It is based on generalizing time flow from translation semigroups to composite time translation-convolution semigroups. Composite translation-convolution fits have less parameters than traditional fits. They need only one dynamic scaling exponent, while four are needed in Havriliak–Negami fits. For glycerol the single dynamic exponent in the translation-convolution fit is found to be temperature-independent.

A High-Sensitivity Microfluidic Sensor Based on a Substrate Integrated Waveguide Re-Entrant Cavity for Complex Permittivity Measurement of Liquids.

In this study, a novel non-invasive and contactless microwave sensor using a square substrate integrated waveguide (SIW) re-entrant cavity is proposed for complex permittivity measurement of chemical solutions. The working principle of this sensor is based on cavity perturbation technique, in which the resonant properties of cavity are utilized as signatures to extract the dielectric information of liquid under test (LUT). A winding microfluidic channel is designed and embedded in the gap region of the cavity to obtain a strong interaction between the induced electric field and LUT, thus achieving a high sensitivity. Also, a mathematical predictive model which quantitatively associates the resonant properties of the sensor with the dielectric constant of LUT is developed through numerical analysis. Using this predictive model, quick and accurate extraction of the complex permittivity of LUT can be easily realized. The performance of this sensor is then experimentally validated by four pure chemicals (hexane, ethyl acetate, DMSO and water) together with a set of acetone/water mixtures in various concentrations. Experimental results demonstrate that the designed sensor is capable of characterizing the complex permittivities of various liquids with an accuracy of higher than 96.76% (compared with the theoretical values obtained by Debye relaxation equations), and it is also available for quantifying the concentration ratio of a given binary mixture.

Multirelaxation Generalized Refractive Mixing Dielectric Model of Moist Soils

In this letter, a multirelaxation generalized refractive mixing dielectric model (GRMDM) for moist soil is proposed and substantiated in the frequency range from 0.04 to 26.5 GHz. This model is based on the methodology of a single-relaxation GRMDM which accounts only for the dipole relaxation of water molecules in the gigahertz frequency range. The proposed multirelaxation GRMDM takes into account both the dipole (Debye) and ionic (Maxwell-Wagner) relaxations of soil water molecules. For this purpose, it uses a two-frequency Debye relaxation equation for the dielectric spectra of bound water. The spectroscopic parameters of the multirelaxation GRMDM were derived by fitting the spectra calculated by this model to the respective measured ones. The main advantage of this model is that it predicts the complex dielectric constant of moist soils throughout the megahertz and gigahertz frequency ranges with the same error as the single-relaxation GRMDM does only in the gigahertz range.

A FDTD formulation for high order dispersive media of muscle-equivalent

In this paper, shift operator finite-difference time-domain (SO-FDTD) method is applied for the calculation of the dispersive medium. The high efficiency and accuracy of this method is verified by calculating the reflection of the plane electromagnetic wave impinging on a muscle slab. For human tissues where multiterm Debye relaxation equations must generally be used. We describe a new differential equation approach, which can be used for general dispersive media. In this method D( t) is expressed in terms of E( t) by means of a differential equation involving D, E, and their time derivatives. The method is illustrated by means of example of media for which relative permittivity is given by a multiterm Debye equation, and for an approximate two-thirds muscle-equivalent model of the human body.

Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I

The string model for the glass transition can quantitatively describe the universal α-relaxation in glassformers, including the average relaxation time, the distribution function of the relaxation time, and the relaxation strength as functions of temperature. The string relaxation equation (SRE) of the model, at high enough temperatures, simplifies to the well-known single particle mean-field Debye relaxation equation, and at low enough temperatures to the well-known Rouse–Zimm relaxation equation that describes the relaxation dynamics of linear macromolecules. However, its initial condition, necessary to the further model predictions of glassy dynamics, has not been solved. In this paper, the special initial condition (SIC) of the SRE, i.e. for straight strings and the dielectric spectrum technique that is one of the most common methods to measure the glassy dynamics, was solved exactly. It should be expected that the obtained SIC would benefit the solution of the general initial condition of the SRE of the string model, i.e. for stochastically spatially configurating strings, as will be described in separate publications.

Dielectric relaxation study in electron-irradiated ferroelectric poly(vinylidene fluoride-trifluoroethylene) (80/20 mol%) copolymer

The relaxor ferroelectric (RFE) behavior in high-energy electron-irradiated poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] 80/20 mol % copolymer system is characterized over a broad frequency and temperature range. The dielectric properties remarkably vary with the irradiated dose in terms of the change from normal ferroelectric (FE) to RFE phase. During the RFE–paraelectric (PE) transition, the dielectric constants, as a function of temperature, can be described by the Vogel–Fulcher (V–F) relation. It has been found that the relationship between the real and imaginary part of dielectric constant in irradiated copolymer can be well fitted with modified Cole–Cole equation and Debye relaxation equation, exhibiting similar features as inorganic RFEs. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2972–2980, 2005

Diffuse Dielectric Anomaly in Ferroelectric Materials

It has not been clear whether the diffuse dielectric anomaly by Debye-type dielectric relaxation is extrinsic or intrinsic in origin although it has been frequently found in ferroelectric materials regardless of their structures and ferroelectric properties. We experimentally investigated the extrinsic nature of the diffuse dielectric anomaly in ferroelectric oxides and sulfide such as BaTiO3, Pb0.9La0.1TiO3, and SnP2S6. The advanced fitting method using the modified Debye relaxation equation was introduced in order to explain the temperature dependent behavior of the diffuse dielectric anomaly. It was confirmed that the diffuse dielectric anomaly was a competitive phenomenon between the dielectric relaxation and the electrical conduction of the relaxing species. It was also proved that the activation energy of the dielectric relaxation should be always higher than the conductivity activation energy of the relaxing species in the diffuse dielectric anomaly.

Diffuse dielectric anomaly in perovskite-type ferroelectric oxides in the temperature range of 400–700 °C

The diffuse dielectric anomaly by the dielectric relaxation found at the high-temperature region of 400–700 °C was investigated in perovskite-type ferroelectric oxides such as BaTiO3, (Pb,La)TiO3, and (Pb,La)(Zr,Ti)O3 ceramics. We observed that the diffuse dielectric anomaly in perovskite oxides was strongly affected by oxygen-related processing parameters. We have modified the Debye relaxation equation by introducing the mobile dipole of the thermal motion of oxygen vacancies in order to explain the temperature-dependent behavior of the diffuse dielectric anomaly. A relationship between the dielectric polarization/relaxation and the electrical conduction by the thermal motion of oxygen vacancies was microscopically suggested to explain the origin of the diffuse dielectric anomaly found at 400–700 °C in perovskite-type ferroelectric oxides.

FCC-HCP Transformation-Related Internal Friction in Fe–Mn Alloys

Abstract The e  reversible transformation has been studied in Fe-14 wt.% Mn and Fe-21 wt.% Mn alloys which are known to exhibit a weak shape memory effect. The internal friction changes and the associated elastic modulus changes were measured using the high frequency (40 kHz) composite oscillator technique in the temperature range 20–350°C in which the e  transformation occurs. The strain-induced amplitude dependent internal friction was measured in order to evaluate changes in the dislocation structure that occur during the transformations and to identify the transformation mechanism involved. The study revealed that the propagation of the e/γ interface boundary during the e  γ transformation is a thermally activated relaxation process obeying the Debye relaxation equation. The internal friction data were used to determine the activation energy of the process responsible for the martensitic transformation. The damping peak is observed at temperatures where both phases coexist and is due to the motion ...

Structure and dielectric properties of ferroelectricpyridinium perrhenate crystals

The crystal and molecular structure of a new ferroelectric[C5H6N]+ReO4- was determined by the x-raydiffraction method at 350 K, 293 K and 220 K. In all three phasesits structure is orthorhombic, with the following sequence of spacegroups: Cmcm Cmc21 Pbca. In the twohigh-temperature phases, the pyridinium cations are disordered whilethe anions are ordered. The low-temperature phase is fully ordered.The complex permittivity of a ferroelectric single crystal ofpyridinium perrhenate was measured in the frequency range from 1 kHzto 13 MHz. The results confirm the order-disorder nature of thecontinuous ferroelectric phase transition at T1 = 336 K.In the vicinity of the ferroelectric phase transition, thephenomenon of critical slowing down was detected. Thedielectric relaxation in the paraelectric phase can be described bythe Debye relaxation equation with a single relaxation time. Thenature of the ferroelectricity is related to the degree of disorderof the pyridinium cation as well as to the appearance and thealignment of the dipole moment of the ReO4- anion.

Effect of Material Response Time on Optical Bistability in Nonlinear Distributed Feedback Gratings

The dynamic behaviors of nonlinear periodic waveguides with a finite material response time have been investigated by numerically solving both the coupled-mode equations and Debye relaxation equation. When the response time of the nonlinearity is more than the transit time through the grating, a modulational instability is sufficiently suppressed and one can obtain optical bistability. Unlike a nonlinear Fabry-Perot resonator or ring resonators, overshoot in the transmission never takes place in the case of zero detuning. However, a relaxation (or damped) oscillation always takes place in the presence of detuning. It is also found that the switch-on time depends on the material response time and the switch-off time is almost independent of it.

Effects of gradient of polarization on dielectric relaxation

We present a non-equilibrium thermodynamic model to describe diffusion effects in dielectric materials with spatial inhomogeneities in the polarization vector and with local viscoelastic effects. The model presented here is a generalization of the Debye relaxation equation including inertial effect, and contributions from the spatial inhomogeneities of the polarization vector, together with a contribution from the antisymmetric stress tensor via the divergence operator. At the same time, a Maxwell viscoelastic-relaxation type equation for the antisymmetric stress tensor is proposed to describe the time evolution of this tensor. On the other hand, a generalized hydrodynamics model for the dielectric memory for short wave length and high frequencies is obtained, by considering the linearized complete set of differential equations of the model. By working in the Fourier–Laplace space, the dielectric susceptibility is obtained and their main features are described and compared with π and α dielectric relaxation.

Critical Slowing Down in Ferroelectric Pyridinium Tetrafluoroborate

Complex permittivity of a ferroelectric single crystal of PyBF4 was measured in the frequency range from 1 kHz to 13 MHz. In the vicinity of ferroelectric phase transition, the phenomenon of critical slowing down was detected. The dielectric relaxation in that crystal can be described by the Debye relaxation equation with a single relaxation time. The results suggest the order–disorder nature of the continuous ferroelectric phase transition.

Effects of symmetric and antisymmetric stress tensors on N- and α-dielectric relaxations

We present a generalized hydrodynamic model for dielectric relaxation to describe the effect of spatial inhomogeneities in the polarization fluctuations in viscoelastic fluids. The model is a generalization of the simple Debye relaxation equation with the addition of the gradient of the total stress tensor. The two known modes of relaxation, N- and α-absorption can be incorporated in the model semiquantitatively, since we do not know the actual parameters involved. The comparison between our results and the experimental response reported for the N- and α-modes in polymers, shows that the predicted intensities of the loss peaks are well represented. However, at lower and higher frequencies the predicted curves deviate from the experimental ones.

Complete FDTD analysis of microwave heating processes in frequency-dependent and temperature-dependent media

It Is well known that the temperature rise in a material modifies its physical properties and, particularly, its dielectric permittivity. The dissipated electromagnetic power involved in microwave heating processes depending on /spl epsi/(/spl omega/), the electrical characteristics of the heated media must vary with the temperature to achieve realistic simulations. In this paper, we present a fast and accurate algorithm allowing, through a combined electromagnetic and thermal procedure, to take into account the influence of the temperature on the electrical properties of materials. First, the temperature dependence of the complex permittivity ruled by a Debye relaxation equation is investigated, and a realistic model is proposed and validated. Then, a frequency-dependent finite-differences time-domain ((FD)/sup 2/TD) method is used to assess the instantaneous electromagnetic power lost by dielectric hysteresis. Within the same iteration, a time-scaled form of the heat transfer equation allows one to calculate the temperature distribution in the heated medium and then to correct the dielectric properties of the material using the proposed model. These new characteristics will be taken into account by the EM solver at the next iteration. This combined algorithm allows a significant reduction of computation time. An application to a microwave oven is proposed.

A frequency-dependent finite-difference time-domain formulation for general dispersive media

A weakness of the finite-difference-time-domain (FDTD) method is that dispersion of the dielectric properties of the scattering/absorbing body is often ignored and frequency-independent properties are generally taken. While this is not a disadvantage for CW or narrowband irradiation, the results thus obtained may be highly erroneous for short pulses where ultrawide bandwidths are involved. In some recent publications, procedures based on a convolution integral describing D(t) in terms of E(t) are given for media for which the complex permittivity in *( omega ) may be described by a single-order Debye relaxation equation or a modified version thereof. Procedures are, however, needed for general dispersive media for which in *( omega ) and mu *( omega ) may be expressible in terms of rational functions, or for human tissues for which multiterm Debye relaxation equations must generally be used. The authors describe a new differential equation approach, which can be used for general dispersive media. In this method D(t) in terms of E(t) by means of a differential equation involving E, and their time derivatives. The method is illustrated for several examples. >

Dielectric properties of female human breast tissue measured in vitro at 3.2 GHz

Complex permittivities of in vitro diseased and undiseased human female breast tissues have been measured at 3.2 GHz using a resonant cavity technique. Experimental data are compared with models predicted from mixture equations. Measured permittivity data lie within limits set by two-phase mixture theory, but some conductivity data are in excess of those expected. At any particular microwave frequency in all tissue of a given type, the relationship between permittivity and conductivity may be parameterized using the Debye relaxation equations. It is concluded that the dielectric relaxation of tissue water is not the only dispersive process occurring at this frequency: dielectric relaxation of bound water and the tail end of a beta -dispersion may also contribute to the dielectric properties. The similarity of the dielectric properties of benign and malignant breast tumours measured suggest that in vivo dielectric imaging methods will not be capable of distinguishing them.

A frequency-dependent finite-difference time-domain formulation for induced current calculations in human beings.

The finite-difference time-domain (FDTD) method has been used to calculate SARs and induced currents involving whole-body or partial-body exposures of models to spatially uniform or nonuniform (far-field or near-field), to sinusoidally varying EM fields, or to transient fields such as those associated with electromagnetic pulses. However, a weakness of the FDTD algorithm is that the dispersion of the tissue's dielectric properties is ignored and frequency-independent properties are assumed. Although this is permissible for continuous-wave or narrow-band irradiation, the results may be highly erroneous for short pulses, in which ultra-wide bandwidths are involved. In some recent publications, procedures are described for one- and two-dimensional problems for media in which the complex permittivity epsilon * (omega) may be described by a single-order Debye relaxation equation or a modified version thereof. These procedures based on a convolution integral describing D(t) in terms of E(t) cannot be extended to human tissues for which multiterm Debye relaxation equations must generally be used. We describe here a new differential-equation approach that can be used for general dispersive media. We illustrate the use of this approach by one- and three-dimensional examples of media for which epsilon * (omega) is given by a multiterm Debye equation, and for an approximate two-thirds muscle-equivalent model of the human body. Based on a single run involving a Gaussian pulse, the frequency-dependent FDTD [(FD)2TD] method allows calculations of SARs and induced currents at various frequencies by taking the Fourier components of the induced E fields. The (FD)2TD method can also be used to calculate coupling of the short (ultra-wideband) pulses to the human body.

A study of dielectric dispersions of bacteriorhodopsin

Dielectric measurements in the MHz region of bacteriorhodopsin (bR) in aqueous solution have shown the existence of β1-dispersion with five distinct parts. This dispersion and the β-dispersion at low frequencies conform approximately to the Debye relaxation equations. The derived apparent relaxation times showed dependence on various physical parameters. The relaxation effect at low frequencies is attributed to the reorientation of bR chromophore within the purple membrane (PM) fragments. The mechanism which gives rise to the β1-dispersion may well be due to the Maxwell-Wagner effect, although the first two parts of the dispersion could also be attributed to counterion relaxation or to bR reorientation.