Quasi-homogeneous Media Research Articles

A versatile coupled progress variable/REDIM model for auto-ignition and combustion

In this work, we present a reduced model for treating chemical reactions in combustion simulations, with special attention on combustion in IC engines. The model which is based on low-dimensional manifolds in state space, is able to describe auto-ignition, burning in quasi homogeneous media as well as chemical reactions which are strongly coupled with molecular transport, like, e.g., in flame propagation. A coupling scheme is developed for existing concepts for reduced treatment of combustion, namely a progress variable model (PVM) and the reaction-diffusion manifold approach (REDIM). We discuss a simple, robust method for this coupling, based on an additional variable, namely the normalized strength of molecular transport. The implementation and behavior of the resulting coupled model are shown. To demonstrate the performance of the model, numerical simulations of representative combustion scenarios are performed, both with fully detailed calculations and with the reduced model. The comparison of results obtained with detailed and reduced computation shows that the strongly reduced model, which requires only five independent variables in total, still can accurately predict a wide range of combustion-relevant scenarios.

Spectral shifts and spectral switches of light generated by scattering of arbitrary coherent waves from a quasi-homogeneous media.

Within the accuracy of the Born approximation, it is shown that the light, which is generated by the scattering of an arbitrary coherent polychromatic wave from a quasi-homogeneous (QH) media can, display both spectral shifts and spectral switches. In our study, a pair of Young's pinholes is utilized to modulate spatial coherence of the incident plane wave before it interacts with the scatterer. The spectral shifts are found to be highly dependent of the scattering angle, the correlation length of scatterer and the Young's configuration parameter. Moreover, the spectral shifts can be converted from the red shift to blue one provided that the correlation length of scatterer is small enough. Derived results are confirmed by numerical simulations where influences of various factors on the spectrum are analyzed in detail.

Application of the Hanbury Brown–Twiss effect to scattering from quasi-homogeneous media

The scattering from a wide class of random scatterers, so-called quasi homogeneous scattering media, is studied by the use of the Hanbury Brown–Twiss effect. In particular the two-point correlation of intensity fluctuations and their variance in the far field are analyzed. A new reciprocity relation is derived, and expressions for the correlation of intensity fluctuations for several different types of scattering potentials are obtained. The results indicate the possibility of distinguishing, for example, hollow scatterers from solid ones.

强度相关场对比度测量准均匀介质散射势强度的理论研究

强度相关场对比度测量准均匀介质散射势强度的理论研究

Propagation of the light generated by quasi-homogeneous sources through quasi-homogeneous media

The spectral density of the quasi-homogeneous (QH) light has been known when it scatters on QH media or propagates in free space. The case that QH sources are surrounded by QH media is proposed in this paper. Under the paraxial approximation, the spectral density of the QH light propagating through QH media is derived. A modified scaling law for the propagation of the QH light through QH media is also obtained. This law also holds true in the far field beyond the paraxial approximation.

Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media

We study the coherence properties of the field generated by beam radiated from quasi-homogeneous (QH) electromagnetic source scattering on QH media. Formulas for the spectral density and spectral degree of coherence of the three dimensional scattered field are derived. The results show under assumption that the diagonal correlation coefficients of the source are proportional to each other, the far field of the scattered light satisfy two reciprocity relations analogous to that in the scalar case, that, the spectral density is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential; the spectral degree of coherence is proportional to the convolution of the diagonal correlation coefficients and the strength of the scattering potential.

Scattering of light from quasi-homogeneous sources by quasi-homogeneous media

The field generated by scattering of light from a quasi-homogeneous source on a quasi-homogeneous, random medium is investigated. It is found that, within the accuracy of the first-order Born approximation, the far field satisfies two reciprocity relations (sometimes called uncertainty relations). One of them implies that the spectral density (or spectral intensity) is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential. The other implies that the spectral degree of coherence of the far field is proportional to the convolution of the correlation coefficient of the source and the spatial Fourier transform of the strength of the scattering potential. While the case we consider might seem restrictive, it is actually quite general. For instance, the quasi-homogeneous source model can be used to describe the generation of beams with different coherence properties and different angular spreads. In addition, the quasi-homogeneous scattering model adequately describes a wide class of turbulent media, including a stratified, turbulent atmosphere and confined plasmas.

Current-voltage characteristics of ultrafine-grained ferroelectric Pb(Zr, Ti)O3 thin films

Room-temperature current-voltage dependence of ultrafine-grained ferroelectric Pb(Zr, Ti)O3 thin films has been investigated. Both strong varistor type behavior and space charge limited conduction (SCLC) were observed. Differences in the current-voltage characteristics are attributed to differences in the nature of the grain boundaries resulting from variations in processing conditions. The strong varistor type behavior is believed to be due to the presence of highly resistive grain boundaries and thus may be termed grain boundary limited conduction (GBLC). A double-depletion-layer barrier model is used to describe the origin of high resistivity of the grain boundaries. It is suggested that the barrier height varies significantly with the applied field due to the nonlinear ferroelectric polarization, and that the barrier is overcome by tunneling at sufficiently high fields. In some other cases, the resistivity of the grain boundaries is comparable to that of the grains, and therefore the intrinsically heterogeneous films degenerate into quasi-homogeneous media, to which the SCLC theory is applicable. As such, a unified grain boundary modeling reconciles different types of conduction mechanisms in the ultrafine-grained ferroelectric thin films. This grain boundary modeling also well accounts for some other dc-related phenomena observed, including abnormal current-voltage dependencies, remanent polarization effect, electrode interface effect, and unusual charging and discharging transients. In addition, many other electrical properties of the ferroelectric films may be better understood by taking the effect of grain boundaries into account.

Comparison of the Born and the Rytov approximations for scattering on quasi-homogeneous media

A comparison is made of the distribution of the intensity of light in the far zone, scattered by a class of model media, as predicted by the first Born and the first Rytov approximations. The model media are quasi-homogeneous, random scatterers, whose spatial fluctuations are governed by gaussian statistics. The results are illustrated by numerical examples. It is found that for directions of scattering which do not coincide with the forward direction, or are not too close to it, the predictions of the two theories are essentially identical, provided that the integrated strength of the dielectric fluctuations is sufficiently small; under these circumstances the first Born approximation is believed to be reasonably accurate.

Scattering from quasi-homogeneous media

In analogy with the concept of a quasi-homogeneous source, the concept of a quasi-homogeneous random, time-independent medium is introduced. The scattering on such a medium is considered within the accuracy of the first Born approximation. Expressions are derived for the radiant intensity (the differential scattering cross-section) of the scattered field and for its degree of spatial coherence. These quantities and the quantities that characterize the correlation properties of the scatterer are found to obey interesting reciprocity relations.