Permittivity profiles

T.J. Cui and C.H. Liang, Reconstruction of the permittivity profile of an inhomogeneous medium using an equivalent network method, 1993, IEEE Trans. Antennas Propagat., 41, pp. 1719-1726. 

This expression, however, only deals with a single molecular dipole and as many such dipoles would be required to describe the overall membrane dipole potential but as a mean-field expression, this term is practical and culmulatively offers the approximation of the estimated dipolar organisation shown in Fig. 4. A further complication, however, involves the solvent environment and this too is also often dealt with as a mean field or in a continuum manner. But the relative permittivity (or dielectric constant) (sr) cannot be considered to possess the same value throughout the multiphase system represented by a membrane in an aqueous medium. The permittivity profile has been measured to vary from about 78.5 in the bulk aqueous... 

Near-field scanning microwave microscopy (NSMM) is another system that has been used for label-free detection of both DNA and RNA molecules (42). NSMM monitors the microwave reflectance, a factor that depends on the dielectric permittivity profile across the microarray surface (42). This parameter is, in turn, dependent on the length and surface coverage of the strands, as well as on the hybridization state of the molecules (e.g., unhybridized single-stranded probe vs. hybridized duplex). NSMM technique demonstrated an acceptable resolution (potentially less than 50 pm) and comparable sensitivity to the fluorescent detection (42). 

Let us consider an optical waveguide consisting of three homogeneous media (Fig. 1) with a permittivity profile ... 

In the perturbation theory, we assume that the magnetic field vector hy of a surface plasmon supported by a general planar waveguide with and without the refractive index profile perturbation is described by Eq. 18. For the unperturbed and perturbed waveguide with permittivity profiles e(x) and s(x) = s(x) + Ss(x), respectively, this equation can be rewritten as ... 

For a small permittivity profile perturbation (x) <3C fi(x), we can assume that the modal field remains unchanged hy = hy) and the modal propagation constant is altered only slightly <3C ) ). Then, Eq. 52 can be reduced... 

Two main types of refractive index perturbations will be discussed here in detail. The first type is a homogeneous change in the refractive index in the whole superstrate. Fig. 13, (herein referred as to bulk refractive index change), which can be described by a change in the permittivity profile, e(x) s(x), where ... 

A change in the surface plasmon propagation constant induced by a surface refractive index change occurring within a layer with a thickness h can be calculated by substituting the perturbation of the permittivity profile Eq. 55 and the field distribution of the surface plasmon Eq. 48 into Eq. 53. After a straightforward mathematical manipulation we obtain ... 

Stern, H.A., Feller, S.E. Calculation of the dielectric permittivity profile for a nonuniform system Application to a lipid bilayer simulation. J. Chem. Phys. 2003,118,3401-12. 

T.M. Habashy, W.C. Chew, and E.Y. Chow, Simultaneous reconstruction of permittivity and conductivity profiles in a radially inhomogeneous slab, Radio Sci., 1986,21,... 

The theory of wideband complex permittivity of water described in the review drastically differs from the empirical double Debye representation [17, 54] of the complex permittivity given for water by formula (280b). Evolution of the employed potential profiles, in which a dipole moves, explored by a dynamic linear-response method can be illustrated as follows ... 

The profile in the upper funnel clearly shows the step of permittivity applied to the system, whereas the profile after the lower funnel is clearly spread. This shows us that the... 

Ek]uatlon (5.5.31) expresses volume fraction profiles. From a z) the dielectric displacement D(z), which is the product of the dielectric permittivity e eiz] and the electric field strength (z), follows from standard electrostatics (see (1.4.5.12 and 16) ... 

One of the first attempts at modeling SOFCs with KMC simulations was reported by Modak and Lusk [32]. In their study, their model was restricted to capture the behavior of the electrolyte, YSZ, as a function of the open-circuit voltage, and comparisons were made with analytical predictions (Guoy-Chapman model). The paper focused on the oxygen concentration distribution within the electrolyte at the TPB, the voltage profile across the electrolyte, and the electric field within the electrolyte. Furthermore, the influences of the temperature and relative permittivity of the electrolyte on these features were captured. In order to accelerate the convergence of the simulations and to facilitate comparison with analytic models, a one-dimensional (1-D) model was implemented, and the cathode and anode structures and reactions were completely neglected. 

The fractional derivative technique is used for the description of diverse physical phenomena (e.g., Refs. 208-215). Apparently, Blumen et al. [189] were the first to use fractal concepts in the analysis of anomalous relaxation. The same problem was treated in Refs. 190,194,200-203, again using the fractional derivative approach. An excellent review of the use of fractional derivative operators for the analysis of various physical phenomena can be found in Ref. 208. Yet, however, there seems to be little understanding of the relationship between the fractional derivative operator and/or differential equations derived therefrom (which are used for the description of various transport phenomena, such as transport of a quantum particle through a potential barrier in fractal structures, or transmission of electromagnetic waves through a medium with a fractal-like profile of dielectric permittivity, etc.), and the fractal dimension of a medium. 

Consider a dispersive material (with a homogeneous, linear, isotropic, and lossy profile), whose electrical frequency dependence is described by the variation of complex permittivity s(co) as... 

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