Field-dependent dielectric coefficient

Consequently, while the effect of an electric field dependence of both drift mobility and diffusion coefficient and also hydrodynamic repulsion decreases, the recombination probability, dielectric saturation and relaxation effects increase the recombination probability. 

In order to compare calculated and experimentally observed phase portraits it is necessary to know very exactly all the coefficients of the describing nonlinear differential Equation 14.3. Therefore, different methods of determination of the nonlinear coefficient in the Duffing equation have been compared. In the paraelectric phase the value of the nonlinear dielectric coefficient B is determined by measuring the shift of the resonance frequency in dependence on the amplitude of the excitation ( [1], [5]). In the ferroelectric phase three different methods are used in order to determine B. Firstly, the coefficient B is calculated in the framework of the Landau theory from the coefficient of the high temperature phase (e.g. [4]). This means B = const, and B has the same values above and below the phase transition. Secondly, the shift of the resonance frequency of the resonator in the ferroelectric phase as a function of the driving field is used in order to determine the coefficient B. The amplitude of the exciting field is smaller than the coercive field and does not produce polarization reversal during the measurements of the shift of the resonance frequency. In the third method the coefficient B was determined by the values of the spontaneous polarization... 

It is known that the value of dielectric constant is a function of the local electric field. Since the electric field near the interface is not a constant, but a function of distance from it, the further refinement of EDL theory and potential profile at the BLM interface should include this positional dependency of dielectric coefficient. The local value of this coefficient is of course a measure of the influence of uncharged species such as water or lipid molecules on the interaction between charges in their vicinity. The dielectric coefficient of bulk aqueous electrolyte at... 

Note 4. The Number of Dipoles per Unit Volume (Sec. 98). Between 25 and 100°C the value of 1 /t for water rises from TV to , while the increment in the value of l/(t — 1) is nearly the same, namely, from rs to TfV- Similarly in any solvent whose dielectric constant is large compared with unity the temperature coefficients of l/(e — 1) and of 1/e are nearly equal. In comparing the behavior of different solvents, let us consider now how the loss of entropy in an applied field will depend upon n, the number of dipoles per unit volume. Let us ask what will be the behavior if (e — 1) is nearly proportional to n/T as it is in the case of a polar gas. In this case we have l/(e — 1) nearly proportional to T/n and since in a liquid n is almost independent of T, wc have... 

The study of behavior of many-electron systems such as atoms, molecules, and solids under the action of time-dependent (TD) external fields, which includes interaction with radiation, has been an important area of research. In the linear response regime, where one considers the external held to cause a small perturbation to the initial ground state of the system, one can obtain many important physical quantities such as polarizabilities, dielectric functions, excitation energies, photoabsorption spectra, van der Waals coefficients, etc. In many situations, for example, in the case of interaction of many-electron systems with strong laser held, however, it is necessary to go beyond linear response for investigation of the properties. Since a full theoretical description based on accurate solution of TD Schrodinger equation is not yet within the reach of computational capabilities, new methods which can efficiently handle the TD many-electron correlations need to be explored, and time-dependent density functional theory (TDDFT) is one such valuable approach. 

It is also important to realize that piezoelectricity implies a linear coupling between dielectric displacement and strain, for example. However, in many ferroelectric materials, this response is linear only over a relatively limited field range (See for example, Figure 2.2). Non-linearity is especially important in ferroelectric materials which show a strong extrinsic contribution to the piezoelectric response [5], In addition, it is quite common for the response to be hysteretic. The amount of hysteresis that is observed depends strongly on the measurement conditions. Larger amplitude excitations often result in larger extrinsic contributions to the coefficients, and more non-linearity and hysteresis in the response. 

The nematic mean-field U, the molecule-field interaction potential, WE, and the induced dipole moment, ju d, are evaluated at different orientations using Equation (2.263), and then the coefficients of their expansion on a basis of Wigner rotation matrices can be calculated, according to Equation (2.268). The permittivity is obtained by a self-consistency procedure, because the energy WE and the induced dipole moment / md, as well as the reaction field contribution to the nematic distribution function p( l), themselves depend on the dielectric permittivity. 

The coefficient AHam itself varies with separation /. It takes the form of a sum over all frequencies at which fluctuations can occur wherein each term depends on the frequency-dependent responses of materials A, B, and m to electromagnetic fields. These responses are written in terms of "dielectric" functions sA, b, and em that are extracted from absorption spectra. It is the differences in these dielectric responses that create interactions. To first approximation,... 

The disadvantage of this simple relationship is that it does not show how coefficient K depends on the frequency of dielectric dispersion (expression for the frequency dependence see p. 48). Nevertheless, Eq. (26) implies that a dry plastic foam may be considered as a laminated two-phase system of the type dielectric — gas with layers ariat ed parallel to the electric field lines. This conclusion is based on the well-known observation that a linear dependence (Eq. (26)) indicates a precise solution to the problem of dielectric permeability of a laminated dielectric with layers parallel to the field. 

The method is based on the magnetorefractive effect (MRE). The MRE is the variation of the complex refractive index (dielectric function) of a material due to change in its conductivity at IR frequencies when a magnetic field is applied. A direct measure of the changes of dielectric properties of a material can be performed by determining its reflection and transmission coefficients. Hence, IR transmission or reflection spectroscopy can provide a direct tool for probing the spin-dependent conductivity in GMR and TMR [5,6]. 

As shown by Mie " and Debye,the electromagnetic field of the light scattered by a sphere can be presented as an infinite series over associated Legendre polynomials, P (cos0), multiphed by spherical Bessel functions, (InrlX). The coefficients in this series must be determined from the boundary conditions and afterward can be used to calculate the angular dependence of the amplitude and polarization of the scattered field. Different boundary conditions were imposed in the case of conducting or dielectric materials of the sphere and of the medium. 

If the film cannot be freely deformed in its plane, the piezoelectric current is called t/33 or dj. If the variation in the electric field is measured per unit of stress, g coefficients are obtained that are connected by the correlation of g = d/e where e is the dielectric constant depending on the film thickness. Constants g and tf are most widely used in the design of electromechanical transducers. The yield from the conversion of mechanical energy into electrical energy is represented by the electromechanical coupling coefficient ATjby Eq. (3.3). 

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