Plane-parallel Layer Research Articles

Influence of high hydrostatic pressure on the optical properties of minced fish proteins

In the functioning of various biological systems, an extremely important role is played by the dynamic properties of optically anisotropic protein macromolecules, such as translational movements, temporal correlations, and transfer processes, which are determined by the surface charge, molecular weight, molecular shape, and the nature of intermolecular interactions. An experimental study of the influence of high hydrostatic pressure on the optical properties of pike perch minced fish proteins at room temperature was carried out in this work. The intensities of the radiation transmitted through a thin plane-parallel layer of minced fish were measured, which was subjected to hydrostatic compression at a rate of ≈3 MPa/s and ≈17 MPa/s. It was found that with increasing pressure, the intensity of the transmitted light decreases nonmonotonically; in this case, the experimental plots of the I(P) dependence show the presence of broad attenuation bands of the intensity of the radiation transmitted through the sample, located at pressures of about 150, 300, and 700 MPa. The observed attenuation bands are associated with the appearance of scattering centers formed as a result of denaturation of macromolecules of proteins of various types with different functional purposes contained in the muscle tissue of pike perch.

Reflection of Light from a Layer of a Hyperbolic Metamaterial

We have investigated specific features of reflection of a plane elliptically polarized electromagnetic wave that is incident from an isotropic nonabsorbing medium onto a plane-parallel layer of a hyperbolic metamaterial the optical axis of which is parallel to the interface, while the diagonal values of the dielectric permittivity are smaller than the dielectric permittivity of the isotropic medium. Depending on the angle of incidence and the angle between the plane of incidence and the optical axis of the hyperbolic metamaterial, regimes are possible in which either an ordinary wave or an extraordinary wave, or both waves decay outward from the interface, and, in the latter case, for some values of these angles, the decay may be nonexponential. For these three regimes, the reflection coefficient from a layer of an ITO/Ag nanostructure has been calculated numerically. Upon variation in the polarization of the incident wave, the energy reflection coefficient changes from minimum to maximum values, which depend on the layer thickness. As distinct from conventional anisotropic media, in all cases, the maximum value of the reflection coefficient tends to unity with increasing layer thickness. If the amplitude of an ordinary or extraordinary wave does not decrease outward from the interface boundary, the minimal reflection coefficient periodically turns to zero with increasing layer thickness due to interference. In the case in which both waves decay, with this decay being nonexponential under certain incidence conditions, the minimum reflection coefficient turns to zero at a certain layer thickness, and then tends to unity.

Parameterized Transmittance Model for Atmospheric and Surface Solar Radiations

This work describes a transmittance model that evaluates global solar irradiation through the atmospheric column and at surface. The model is based on appropriate determination of the transmission coefficients of the different atmospheric constituents in a plane parallel layers frame and estimates the downward solar fluxes from the upper limit of the atmosphere. In testing this model, we first considered the purely molecular atmosphere to parameterize descending solar fluxes, which allowed us to estimate the attenuation due to atmospheric gases at specific times of the day when the irradiation at ground level is known. The results thus obtained show that the molecular atmosphere has a maximum reduction rate of incident flux (at the Top Of Atmosphere) of 20% with daily profiles that are homogeneous with extraterrestrial fluxes. Considering the turbid and cloudy atmosphere in which the multiple scattering phenomenon is taken into account, we obtain at ground level fluctuating profiles with attenuation rates reaching 64% depending on the time instant in the day. The comparison of our results with the experimental data obtained at the Yaounde site on one hand and with the results of the CLIRAD-SW model on the other hand shows at monthly scale high correlation, of the order of 0.998. Moreover at monthly time scale, the precision which for some hourly values is relatively low tends towards a net improvement on the seasonal scale where it extends over a narrow domain ranging from 0.02% to 1.66%.

Features of the Residual Velocity Ellipsoid of Hot Subdwarfs from the Gaia DR2 Catalog

The evolution of the parameters of the residual velocity ellipsoid of hot subdwarfs (HSDs) with their position relative to the Galactic plane is traced, using the HSDs selected by Geier et al. from the Gaia DR2 catalog. Parameters of the Galactic rotation are determined for two $|z|$ zones. These are used to estimate the gradient of the circular rotation velocity, $V_0,$ versus $|z|,$ found to be $\Delta V_0/\Delta |z|=-71\pm7$ km s$^{-1}$ kpc$^{-1}$. The size of the residual velocity ellipsoid is $(\sigma_1,\sigma_2,\sigma_3)=(36.1,27.6,22.8)\pm(0.4,0.8,0.6)$ km/s for HSDs at $|z|<0.5$ kpc and $(\sigma_1,\sigma_2,\sigma_3)=(56.9,55.8,39.7)\pm(0.9,1.1,0.8)$ km/s for HSDs at $|z|\geq0.5$ kpc. When forming the HSD residual velocities, the Galactic rotation was taken into account using individual approaches for each $z$ zone. Parameters of the residual velocity ellipsoids for HSDs located in four plane-parallel layers are also determined. The size of the ellipsoid increases with $z,$ and the inclination of the first axis relative to the Galactic plane also increases. This inclination is close to zero in zones close to the Galactic plane, $z\sim\pm0.2$ kpc, and rises to $\mp12\pm4^\circ$ for $z\sim\pm0.9$ kpc.

Light scattering by densely packed optically soft particle systems, with consideration of the particle agglomeration and dependent scattering.

Light scattering and radiative transfer in optically soft particle systems are important problems in many fields of natural sciences and engineering, such as biology, ocean optics, atmospheric science, solar energy utilization, and so on. Due to the effects of particle agglomeration and dependent scattering, the radiative transfer problem will become more complex with the increase of particle volume fraction. In this study, the scattering properties and radiative transfer characteristics of densely packed optically soft particle systems, with consideration of the effects of dependent scattering and particle agglomeration, are investigated. The dependent scattering properties of densely packed silicon-dioxide spherical particles embedded in water are calculated by using the Lorenz-Mie theory and Percus-Yevick sticky hard-sphere model. The directional-hemispherical reflectance of the dispersed plane-parallel layer is obtained by using the Monte Carlo method. The results show that dependent scattering and particle agglomeration have significant influence on the scattering properties of particles. With the increase of particle agglomeration degree, the scattering coefficients and asymmetry factors of the particles increase obviously, which can be even larger than the results for independent scattering under certain circumstances. Due to the combined interaction of multiple scattering, dependent scattering, and particle agglomeration, for different size particles, the variation tendency of the hemispherical reflectance is obviously different with increasing particle agglomeration degree.

Reflection and transmission of elastic waves by a fluid-filled crack located in a poroelastic formation

Elastic wave propagation in the system: porous saturated half-space – plane-parallel layer (crack) filled with a viscous fluid – porous saturated half-space is considered in this paper. Reflection and transmission coefficients of compressional and shear waves propagating in such system are calculated. Within the frame of validity of the single-scattering approximation, an expression for the complex wave number of the compressional wave propagating in a rock containing a system of thin parallel layers (cracks) is obtained. The performed calculations have shown that this wave presents strong velocity dispersion, especially at low frequencies corresponding to seismic measurements. The reflection coefficient of the elastic compressional wave incident at the boundary between the elastic half-space and porous fractured medium is calculated. It was shown that the reflection coefficient of this wave strongly depends on the frequency, especially in the low frequency range. This frequency dependence is determined by the intensive hydrodynamic flows (mesoscopic flow) generated at the boundary between the cracks and the porous matrix. The importance of the effects associated with these mesoscopic flows is illustrated by calculations of synthetic seismograms.

Application of the Photometric Theory of the Radiance Field in the Problems of Electron Scattering

The physical model of the radiance field is similar in some aspects to the elementary particle transport theory under the assumptions of the classical mechanics. Disregarding the differences in the used nomenclatures, it can be shown that the transport equations for the radiance field are identical to those for the particle flux density. Since the end of the 19th century, both theories have been developing in parallel, thereby enriching each other. In other words, a breakthrough, which has been made in one theory, readily contributes to the significant progress in another one. Nowadays the accuracy achieved in the experiments with particles is close to the limit, which allows validating the relationships derived within the light scattering theory. Besides, the experiments with particles are free from uncertainties in the scattering medium, which are typical for atmospheric remote sensing applications. In this paper, a new algorithm is described, which is derived by analogies between these theories. It is applied for calculating the electron flux elastically scattered by plane-parallel layers of a solid with the strongly forward peaked phase functions. The calculations are compared against the experimental angular distributions of electrons, which are elastically reflected by the two-layer solid samples.

Radiative transfer in dispersed media: Considering the effect of host medium absorption on particle scattering

For many practical radiative transfer problems in dispersed media, the host medium surrounding the particles is absorbing rather than lossless, therefore it may lead to inaccurate results when the effect of host medium absorption on particle scattering is neglected. This paper presents a systematical investigation on the radiative transfer problems for three different cases of refractive indexes for spherical particles embedded in an absorbing medium. The single-scattering properties of the particles are calculated using the recently developed public-domain Lorenz-Mie program for the case of an absorbing host medium. The directional-hemispherical reflectance and transmittance for a plane-parallel layer of spherical particles are obtained by using the Monte Carlo method. The effects of host medium absorption, particle size parameter and size distribution on the radiative transfer characteristics are discussed. The results show that neglecting the effect of host medium absorption on particle scattering will underestimate the directional-hemispherical reflectance and transmittance to some extent. Meanwhile, the errors caused by using the conventional Lorenz–Mie theory increase obviously with increase of host medium absorption index and particle size parameter. For the case of monodisperse particles embedded in an absorbing thin layer (i.e., with layer thickness of 0.05 mm and host medium absorption index of 0.01), the relative error of hemispherical reflectances increases approximate linearly from 5.9% to 59.4% with the particle size parameter increases from 1.0 to 40.

Direct prediction of bidirectional reflectance by dense particulate deposits

To observe and study the effects of the volume packing density on polarimetric scattering by deposited particulate materials, a comparison is made between the vector radiative transport equation (VRTE) and the plane wave plane parallel (PWPP) models for the polarized bidirectional reflectance and transmittance from plane parallel layers of randomly distributed, wavelength–sized particles. Calculations have been performed on ice and mineral materials with refractive indices of m=1.31 and m=1.5+0.01i respectively. In these simulations, particle volume fraction ranges from around 0.05–0.3 for deposits consisting of spherical particles with size parameters of one and two.It is found that the PWPP model results converge to those predicted by the VRTE at small ( ∼ 5% or less) particle volume fractions. At higher volume fractions, the difference between the PWPP and VRTE results depends strongly on the particle size and refractive index, yet not so much on the optical thickness (equivalently, volume of particles per unit area of layer).PWPP simulation results of coherent backscattering effects – brightness opposition and polarization opposition effects – for ice and mineral particles are also represented. Their dependency on the particle volume fraction and particle size has been discussed.

Errors induced by the neglect of polarization in radiance calculations for three-dimensional cloudy atmospheres

Remote sensing instruments observe radiation being scattered and absorbed by molecules, aerosol particles, cloud droplets and ice crystals. In order to interpret and accurately model such observations, the vector radiative transfer equation needs to be solved, because scattering polarizes the initially unpolarized incoming solar radiation. A widely used approximation in radiative transfer theory is the neglect of polarization which allows to greatly simplify the radiative transfer equation.It is well known that the error caused by multiple Rayleigh scattering can be larger than 10%, depending on wavelength and sun-observer geometry (Mishchenko et al., 1994 [1]). For homogeneous plane-parallel layers of liquid cloud droplets the error is comparatively small (below 1%) (Hansen, 1971 [2]). Therefore, in radiative transfer modelling for cloud remote sensing polarization is mostly neglected. However, in reality clouds are not plane-parallel layers of water droplets but complex three-dimensional (3D) structures and observations of clouds usually include pixels consisting of clear and cloudy parts. In this study we revisit the question of the magnitude of the error due to the neglect of polarization in radiative transfer theory for a realistic 3D cloudy atmosphere.We apply the Monte Carlo radiative transfer model MYSTIC with and without neglecting polarization and compare the results. At a phase angle of 90° and 400 nm wavelength we find the maximum overestimation error of about 8% for complete clear-sky conditions. The error is reduced to about 6% in clear-sky regions surrounded by clouds due to scattering from clouds into the clear regions. Within the clouds the error is up to 4% with the highest values in cloud shadows. In backscattering direction the radiance is underestimated by about 5% in clear regions between clouds. For other sun-observer geometries, the error ranges between the two extremes. The error decreases with wavelength and in the absorption bands.

Reflective properties of melt ponds on sea ice

Abstract. Melt ponds occupy a large part of the Arctic sea ice in summer and strongly affect the radiative budget of the atmosphere–ice–ocean system. In this study, the melt pond reflectance is considered in the framework of radiative transfer theory. The melt pond is modeled as a plane-parallel layer of pure water upon a layer of sea ice (the pond bottom). We consider pond reflection as comprising Fresnel reflection by the water surface and multiple reflections between the pond surface and its bottom, which is assumed to be Lambertian. In order to give a description of how to find the pond bottom albedo, we investigate the inherent optical properties of sea ice. Using the Wentzel–Kramers–Brillouin approximation approach to light scattering by non-spherical particles (brine inclusions) and Mie solution for spherical particles (air bubbles), we conclude that the transport scattering coefficient in sea ice is a spectrally independent value. Then, within the two-stream approximation of the radiative transfer theory, we show that the under-pond ice spectral albedo is determined by two independent scalar values: the transport scattering coefficient and ice layer thickness. Given the pond depth and bottom albedo values, the bidirectional reflectance factor (BRF) and albedo of a pond can be calculated with analytical formulas. Thus, the main reflective properties of the melt pond, including their spectral dependence, are determined by only three independent parameters: pond depth z, ice layer thickness H, and transport scattering coefficient of ice σt.The effects of the incident conditions and the atmosphere state are examined. It is clearly shown that atmospheric correction is necessary even for in situ measurements. The atmospheric correction procedure has been used in the model verification. The optical model developed is verified with data from in situ measurements made during three field campaigns performed on landfast and pack ice in the Arctic. The measured pond albedo spectra were fitted with the modeled spectra by varying the pond parameters (z, H, and σt). The coincidence of the measured and fitted spectra demonstrates good performance of the model: it is able to reproduce the albedo spectrum in the visible range with RMSD that does not exceed 1.5 % for a wide variety of melt pond types observed in the Arctic.

Simple and Sawtooth Waves in a Resonance Layer with Quadratic Elastic Nonlinearity

We study the excitation of simple and sawtooth discontinuous waves in a nonlinear acoustic resonator representing a plane-parallel layer located in an outer medium and irradiated by a normally incident plane-longitudinal harmonic wave. The amplitudes of the wave at the fundamental frequency and its harmonics, which are emitted by the layer to the outer medium, are determined. Expressions are obtained for the linear and nonlinear Q-factors of such a resonator. The way to determine the nonlinearity parameter of the medium in the layer is discussed on the basis of measuring the amplitude of the second harmonic emitted by the layer to the outer medium in the forward and backward directions relative to the incident wave.

A plane wave model for direct simulation of reflection and transmission by discretely inhomogeneous plane parallel media

A formulation is developed for numerically solving the frequency domain Maxwell’s equations in plane parallel layers of inhomogeneous media. As was done in a recent work [1], the plane parallel layer is modeled as an infinite square lattice of W × W × H unit cells, with W being a sample width of the layer and H the layer thickness. As opposed to the 3D volume integral/discrete dipole formulation, the derivation begins with a Fourier expansion of the electric field amplitude in the lateral plane, and leads to a coupled system of 1D ordinary differential equations in the depth direction of the layer. A 1D dyadic Green’s function is derived for this system and used to construct a set of coupled 1D integral equations for the field expansion coefficients. The resulting mathematical formulation is considerably simpler and more compact than that derived, for the same system, using the discrete dipole approximation applied to the periodic plane lattice. Furthermore, the fundamental property variable appearing in the formulation is the Fourier transformed complex permittivity distribution in the unit cell, and the method obviates any need to define or calculate a dipole polarizability. Although designed primarily for random media calculations, the method is also capable of predicting the single scattering properties of individual particles; comparisons are presented to demonstrate that the method can accurately reproduce, at scattering angles not too close to 90°, the polarimetric scattering properties of single and multiple spheres. The derivation of the dyadic Green’s function allows for an analytical preconditioning of the equations, and it is shown that this can result in significantly accelerated solution times when applied to densely-packed systems of particles. Calculation results demonstrate that the method, when applied to inhomogeneous media, can predict coherent backscattering and polarization opposition effects.

The Method for Calculation of the Coefficient of Reflection of an Electromagnetic Wave from an Inhomogeneous Layer Having a Small Phase Thickness

Analytical expressions for the coefficient of reflection of an electromagnetic wave from a planeparallel layer with an arbitrary profile of the permittivity are obtained. It is shown that the electromagnetic model of a layer with a small phase thickness can be obtained with the help of the perturbation theory method. A method is proposed for the calculation of the reflection coefficient. The method is based on the combination of formulas of the perturbation theory and the formulas describing reflection from a homogeneous layer. The obtained expressions are compared with the numerical solutions of the electromagnetic equations. It is determined that the combined formulas describe the angular dependence of the reflection coefficient better than the formulas obtained only with the help of the perturbation theory.

Spectral model for clear sky atmospheric longwave radiation

An efficient spectrally resolved radiative model is used to calculate surface downwelling longwave (DLW) radiation (0 ∼ 2500 cm−1) under clear sky (cloud free) conditions at the ground level. The wavenumber spectral resolution of the model is 0.01 cm−1 and the atmosphere is represented by 18 non-uniform plane-parallel layers with pressure in each layer determined on a pressure-based coordinate system. The model utilizes the most up-to-date (2016) HITRAN molecular spectral data for 7 atmospheric gases: H2O, CO2, O3, CH4, N2O, O2 and N2. The MT_CKD model is used to calculate water vapor and CO2 continuum absorption coefficients. Longwave absorption and scattering coefficients for aerosols are modeled using Mie theory. For the non-scattering atmosphere (aerosol free), the surface DLW agrees within 2.91% with mean values from the InterComparison of Radiation Codes in Climate Models (ICRCCM) program, with spectral deviations below 0.035 W cm m−2. For a scattering atmosphere with typical aerosol loading, the DLW calculated by the proposed model agrees within 3.08% relative error when compared to measured values at 7 climatologically diverse SURFRAD stations. This relative error is smaller than a calibrated parametric model regressed from data for those same 7 stations, and within the uncertainty (+/− 5 W m−2) of pyrgeometers commonly used for meteorological and climatological applications. The DLW increases by 1.86 ∼ 6.57 W m−2 when compared with aerosol-free conditions, and this increment decreases with increased water vapor content due to overlap with water vapor bands. As expected, the water vapor content at the layers closest to the surface contributes the most to the surface DLW, especially in the spectral region 0 ∼ 700 cm−1. Additional water vapor content (mostly from the lowest 1 km of the atmosphere) contributes to the spectral range of 400 ∼ 650 cm−1. Low altitude aerosols ( ∼ 3.46 km or less) contribute to the surface value of DLW mostly in the spectral range 750 ∼ 1400 cm−1.

On the propagation of charge carriers fluxes in the thin layer of a plane-parallel solid-state structure with scattering at the boundaries of the layer taken into account

The composition of the thin layer of a plane-parallel solid-state structure affects the propagation of differential charge carriers fluxes in the thickness of the layer and through it. Scattering of these fluxes at the boundaries of the thin layer affects also the distribution function of charge carriers. This scattering is correctly taken into account in integrated boundary conditions for the kinetic equation. For a plane-parallel layer, the kinetic equation (in the approximation of the relaxation time) is reduced to a convenient form, which describes the propagation of differential fluxes in the thickness of the layer. The solution for thick and thin layers of different types (metal, insulator, semiconductor) is analyzed. Practically important problems, in which the obtained solutions can be effectively used, are specified.

Tonian to early Cryogenian synorogenic basin of the São Gabriel Terrane, Dom Feliciano Belt, southernmost Brazil

ABSTRACTA provenance and stratigraphic study of the Neoproterozoic Pontas do Salso Complex (PSC), western portion of the Dom Feliciano Belt (DFB), was conducted with U–Pb zircon geochronological analysis of the metasediments and the host rocks. The U–Pb isotopic data from detrital zircon of the metasediments indicate the source from the latest Middle Tonian to Late Cryogenian (between 897 and 684 Ma) and maximum depositional age of 685 ± 18 Ma in an arc-related basin setting adjacent in the Sao Gabriel Arc. The metasediments of the PSC form an elongated body in the N35°E direction and occur in the central portion of the São Gabriel Terrane (SGT), which is constituted by ophiolitic complexes and arc-related rocks, generated probably during the final consolidation of Rodinia supercontinent, although this question is still open. Low- to medium-K calc-alkaline, metaluminous affinity, and trace-element geochemistry suggest that the chemical composition of the protoliths was generated from metasomatized mantle sources in subduction zones. The PSC is composed of meta-arkoses, with subordinate metaconglomerates and metapelites. The meta-arkoses are disposed in plane-parallel layers, which also internally feature small-scale cross-bedding structures. The matrix has a blastopsammitic, poorly selected, fine to coarse texture, and hexagonal quartz and plagioclase porphyroclasts with superimposed thermal metamorphism. The polymict metaconglomerates are matrix-supported, with 15–55% of clasts of metavolcanic rocks, metasediments, undeformed granites, and quartz veins. The metapelites comprise mainly muscovite phyllites with syn-tectonic garnet and chloritoid porphyroblasts. The PSC represents a sedimentary succession deposited on an arc-related basin formed during the collapse and uplift of the SGT.

Enhancement and inversion of an alternating-current electric field in a finely dispersed dielectric

It has been found that a sinusoidal electric field is enhanced by a factor of more than 103 in two plane-parallel layers of different dielectrics placed between plates of a parallel-plate capacitor. The implementation of the enhancement of the electric field requires that the following two conditions should be satisfied: (1) one of the two layers should consist of finely dispersed dielectric particles with ionized donor centers formed on their surface and free electrons in their bulk, and (2) the dielectric permittivity of the powder should have a negative value. It has also been found that, in the powder layer, the enhancement of the electric field occurs simultaneously with its inversion.

Radiative transfer equation and direct simulation prediction of reflection and absorption by particle deposits

Two methods for computing the normal incidence absorptance and hemispherical reflectance from plane parallel layers of wavelength–sized spherical particles are presented. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a system of randomly–positioned spherical particles excited by an incident plane wave. The second method is based upon the scalar radiative transport equation (RTE) applied to a plane parallel medium. Comparisons are made using five values of particle refractive index, sphere size parameters ranging from 1 to 4, and particle volume concentrations ranging from 0.05 to 0.4. The results indicate that the multiple sphere T matrix method (MSTM) and RTE predictions of hemispherical reflectance and absorptance converge when particle volume fraction becomes small. At higher volume fractions the RTE can yield results for hemispherical reflectance that, depending on the particle size and refractive index, significantly depart from the exact predictions. On the other hand, RTE and MSTM predictions of absorptance have a much closer agreement which is largely independent of the sphere optical properties and volume concentration.

Van de Hulst Essay: The DDA, the RTE, and the computation of scattering by plane parallel layers of particles

A formulation and computational algorithm, based on the discrete dipole approximation (DDA), is presented for directly simulating the electromagnetic wave reflection, transmission, and absorption properties of plane parallel layers of random particulate media. The method is intended for situations in which the characteristic size of the particles is comparable to the radiation wavelength, yet no restriction is made regarding the concentration of the particles. In particular, the application is specifically intended for high particle concentrations characteristic of regolith, pigment layers, functional thin films, and so on. Strategies for reducing the memory and time requirements of the computations are developed. Test calculations show that the method can reproduce direct simulation predictions of hemispherical reflectance from layers of spherical particles as calculated by multiple sphere superposition solution. The method also correctly asymptotes to the radiative transport regime in the limit of small particle volume fraction. The connection of the formulation to those for discrete particle scattering, and the radiative transport equation (RTE), is discussed.