En-Bo Wei

The nonlinear effective dielectric response of graded composites

The perturbation method is developed to deal with the effective nonlinear dielectric responses of weakly nonlinear graded composites, which consist of the graded inclusion with a linear dielectric function of spatial variables of inclusion material. For Kerr-like nonlinear graded composites, as an example in two dimensions, we have used the perturbation method to solve the boundary value problems of potentials, and studied the effective responses of nonlinear graded composites, where a cylindrical inclusion with linear dielectric function and nonlinear dielectric constant is randomly embedded in a homogeneous host with linear and nonlinear dielectric constants. For the exponential function and the power-law dielectric profiles of cylindrical inclusions, in the dilute limit, we have derived the formulae of effective nonlinear responses of both graded nonlinear composites.

Effective dielectric response of nonlinear composites with external ac and dc electric field

The perturbation method is developed to investigate the effective nonlinear dielectric response of Kerr composites when the external ac and dc electric field is applied. Under the external ac and dc electric field E-app=E-a(1+sin omegat), the effective coupling nonlinear response can be induced by the cubic nonlinearity of Kerr nonlinear materials at the zero frequency, the finite basic frequency omega, the second and the third harmonics, 2omega and 3omega, and so on. As an example, we have investigated the cylindrical inclusions randomly embedded in a host and derived the formulas of the effective nonlinear dielectric response at harmonics in dilute limit. For a higher concentration of inclusions, we have proposed a nonlinear effective-medium approximation by introducing the general effective nonlinear response. With the relationships between the effective nonlinear response at harmonics and the general effective nonlinear response, we have derived a set of formulas of the effective nonlinear dielectric responses at harmonics for a larger volume fraction

Effective ac response in weakly nonlinear composites

The perturbation method is developed to deal with the problem of determining the effective nonlinear conductivity of Kerr-like nonlinear media under an external ac electric field. As an example, we have considered the cylindrical inclusion embedded in a host under the sinusoidal external field E1 sin (ωt) + E3 sin (3ωt) with frequencies ω and 3ω. The potentials of composites at higher harmonics are derived in both local inclusion particle and host regions. The effective responses of bulk nonlinear composites at basic frequency and harmonics are given for cylindrical composites in the dilute limit. Moreover, the relationships between the nonlinear effective responses at the basic frequency and the third harmonics are derived.

Effective ac response of graded colloidal suspensions

The alternating current (ac) response has been investigated theoretically in colloidal suspensions consisting of suspended radially inhomogeneous graded particles having complex permittivity profiles under an external ac electric field. The gradation in the colloidal particles is modeled by physically motivated graded profiles as the dielectric function may only vary slightly along the radius, while the conductivity profile may vary rapidly along the radius. More precisely, the dielectric function is assumed to be a constant, while the conductivity has a power-law dependence on the radius variable r, namely, epsilon(i)(r)=A+cr(k)/(i omega). In previous attempts, this model was solved numerically via the differential effective dipole approximation. In this work, we will demonstrate the existence of exact analytical solutions of the local potentials in the graded particles in terms of the hypergeometric functions, and hence the effective ac response is calculated in the dilute limit. Our exact results will be applied to graded biological cell suspensions. Extensions to nonlinear ac response will be discussed.

Dielectric response of composites with graded cylindrical particles

Effective dielectric responses of graded cylindrical composites are investigated when an external uniform field is applied to the composites. Considering linear random composites of cylindrical particles with a specific dielectric function, which varies along the radial direction of the particles, we have studied three cases of dielectric profiles: exponential function, linear and power-law profiles. For each case, the effective dielectric response of graded composites is given on the basis of exact solutions of the local potentials of composites in the dilute limit. For a larger volume fraction, we have proposed an effective medium approximation to estimate the effective dielectric response.

Dielectric response of graded composites having general power-law-graded cylindrical inclusions

The dielectric response of graded composites having general power-law-graded cylindrical inclusions under a uniform applied electric field is investigated. The dielectric profile of the cylindrical inclusions is modeled by the equation epsilon(i)(r)=c(b+r)(k) (where r is the radius of the cylindrical inclusions and c, b and k are parameters). Analytical solutions for the local electrical potentials are derived in terms of hypergeometric functions and the effective dielectric response of the graded composites is predicted in the dilute limit. Moreover, for a simple power-law dielectric profile epsilon(i)(r) = cr(k) and a linear dielectric profile epsilon(i)(r) = c(b + r), analytical expressions of the electrical potentials and the effective dielectric response are derived exactly from our results by taking the limits b -> 0 and k -> 1, respectively. For a higher concentration of inclusions, the effective dielectric response is estimated by an effective-medium approximation. In addition, we have discussed the effective response of graded cylindrical composites with a more complex dielectric profile of inclusion, epsilon(i)(r)=c(b+r)(k)e(beta r). (c) 2005 American Institute of Physics.

Analysis of cost functions for retrieving sea surface salinity

Two kinds of Bayesian-based cost functions (i.e., the unconstrained cost function and parameter-constrained cost function) are investigated for retrieving the sea surface salinity (SSS). In low SSS regions, we have analyzed the sensitivity of the two cost functions to geophysical parameters. The results show that the unconstrained cost function is valid for retrieving several parameters (including SSS, wind speed and significant wave height), and the constrained cost function, which largely depends on the accuracy of reference values, may lead to large retrieval biases. Furthermore, as a retrieval parameter, the sea surface temperature (SST) can result in the divergence of other geophysical parameters in an unconstrained cost function due to the strong sensitivity of brightness temperature to SST. By using the unconstrained cost function and the simulated brightness temperature TB with white noises, the retrieval biases of SSS are discussed with the following two procedures. Procedure a): the simulated TB values are first averaged, and then SSS is retrieved. Procedure b): the SSS is directly retrieved from the simulated TB, and then the retrieved SSS values are averaged. The results indicate that, for low SSS and SST distributions, the SSS retrieval by procedure a) has less biases compared with that by procedure b), while the two procedures give almost the same retrieval results for high SSS and SST sea regions.

The wavelet analysis of satellite sea surface temperature in the South China Sea and the Pacific Ocean

Using wavelet transform, the sea surface temperature (SST) during the period of 1982–1999 of the South China Sea and the equatorial Pacific, from datasets of NOAA/AVHRR, was analyzed. It is shown that there are 4- and 8-year interannual oscillations in the eastern equatorial Pacific and 8-year interannual oscillation in the western equatorial Pacific. In terms of attractive time-frequency localization and multi-scale properties of wavelet transform, as shown by the Morlet wavelet, it is found that an in-phase coupling oscillation occurs between the SCS and the equatorial Pacific. The SST changes of SCS will have echoed every event of EI Niño (abnormally warm) and La Niño (abnormally cold) in the equatorial Pacific. There is a positive correlation between the SCS and the western equatorial Pacific in the 8-year time-scale. Evidence is presented that the SST anomalies of the equatorial Pacific influence the SST of the SCS.

Higher order response of nonlinear composite in external AC electric field

The fifth-order effective nonlinear responses at fundament frequency and higher-order harmonics are given for nonlinear composites, which obey a current-field relation of the form J = sigmaE + x\E\(2) E, if a sinusoidal alternating current (AC) external field with finite frequency omega is applied. As two examples, we have investigated the cylinder and spherical inclusion embedded in a host and, for larger volume fraction, also derived the formulae of effective nonlinear responses at higher-order harmonics by the aid of the general effective response definition. Furthermore, the relationships between effective nonlinear responses at harmonics are given

Brightness Temperature Model of Sea Foam Layer at L-band

Permittivity of a sea foam layer is very important in investigating ocean brightness temperature model. At microwave frequency, the Rayleigh method is developed to estimate the effective permittivity of the sea foam layer. To simplify the tedious calculation of sea foam effective permittivity at L band (1.4 GHz), Pade’ approximation is adopted to fit the sea foam effective permittivity computed by the Rayleigh method. With this fitting formula, a new brightness temperature model of sea foam layer defined by certain geophysical parameters, such as air volume fraction (AVF), sea surface temperature (SST), sea surface salinity (SSS) and thickness of foam layer d, is given. Furthermore, the sensitivities of the brightness temperature model to SST, SSS, d and AVF of a sea foam layer at L band are discussed. The sensitivities are ranked from most to least in the order: (1) d; (2) AVF; (3) SSS; (4) SST. This result indicates that the measurement errors of d and AVF have significant impacts on the retrievals of SSS and SST. With the experimental brightness temperature data, the SSS and AFV are retrieved by cost function.