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The single-phase Stefan problem is solved by the methods of numerical design for the semitransparent gray crystalline medium with consideration of bulk isotropic scattering. Dependence of radiation scattering albedo on boundary reflection coefficient is shown. The conditions of phase process, obtained through solving the problem, allow the development of both efficient materials for heat protection and better methods of melting for the semitransparent materials, depending on the optical properties of boundaries.

A modified version of the UN method is used to solve the critical slab problem in the case of a combination of forward and backward scattering with isotropic scattering in a uniform finite slab. The Marshak boundary condition is used for the calculation of the critical slab thicknesses and it is shown that the method gives accurate results in one-dimensional geometry and converges rapidly with easily executable equations. The presented numerical results are compared with the results available in literature.

This paper deals with the real-space small-angle scattering (SAS) structure functions and with the isotropic scattering intensity of the isolated single cells of the tessellation of a `dead leaves' model (DLM). The DLM is produced by spherical primary grains of constant diameterd. The cells possess a random shape like the pieces of a puzzle. The maximum diameter of the different pieces isd.

In this paper we demonstrated the effectiveness of imaging in a tissue phantom with isotropic scattering using polarization discrimination combined with the time gating method. This simple polarization discrimination technique was shown ineffective when it was applied to filamentous tissues. In this situation, we utilized the time-gated degree of polarization (DOP) imaging technique to show that the DOP measurement was quite effective for high-quality imaging of objects in filamentous tissues. We also applied this technique to the characterization of myocardial tissues and showed the difference between normal and abnormal tissues. In addition, we demonstrated a novel method for target depth determination in a turbid medium based on co-polarized light measurements. This method relied on the strong dependence of transmitted co-polarized intensity on target depth.

Our recent measurements of the viscosity of spin polarized liquid 3 He revealed that, below 100 mK, the relative enhancement of the viscosity is pressure independent and quadratic in polarization m up to m = 70% . This simple behavior is remarkably close to that expected for a gas (i.e. isotropic scattering). For the dense liquid 3 He, the so-called s-p approximation is believed to give a more realistic description of scattering. Using the formalism developed by Anderson, Pethick and Quader, we have computed the expected polarization dependence in this case, assuming polarization independent collision probabilities. Surprisingly, this leads to an initial linear decrease of the viscosity with polarization, which is not observed experimentally. This may imply that the present description of transport in liquid 3 He is not complete.

Based on the analysis of an isotropic point source in an infinite, isotropically scattering turbid medium, we suggest several modifications to the well-known diffusion theory. Compared with standard diffusion theory these modifications, which require very little extra mathematics, lead to a substantially better approximation of the exact expressions. The improved expression gives reasons to reconsider the basic concept of time-resolved diffusion theory.

The discrete-ordinates method is used to develop a solution to a basic polarization problem in radiative transfer. In particular, a solution for the coupled I and Q components of the Stokes vector is developed for a polarization model based on a mixture of Rayleigh and isotropic scattering. The solution is evaluated for the case of a finite plane-parallel layer that has a polarized beam incident on one surface and which has Lambertian reflection on the other surface.

A Cartesian-based method is proposed for combustion-radiation problems in gray enclosures having one ordinate symmetry and containing absorbing-emitting media with isotropic scattering. This method collapses the 3-D radiative information of the problem into its 2-D solution plane and is shown to be applicable for all ranges of optical thicknesses, including the optically very thin case, while maintaining near-analytic accuracy over most of this range. To accomplish this task, the collapsed dimension method makes use of effective intensity rays, each of which contains the information of the conglomerate of all the conventional intensity rays focused on the same point and contained in a plane that is both inclined at the same angle as the ray and is also normal to the solution plane. This novel procedure thus eliminates the use of solid angles and reduces both the complexity and the computational expense involved in the solution of such problems. The method is shown to be applicable to gray wall problems en...

An exact analytic solution is found for the problem of enhancement of backscattering of a short pulse signal from a slab of finite thickness with isotropic scattering centers.

An approximate form for theH-function for isotropic scattering developed by Karanjai and Sen (1971) has been extended to the case of four-term scattering indicatrix.

Tureci, RG/0000-0001-6309-6300; gulecyuz, mustafa cetin/0000-0002-8838-7400 WOS: 000242562100015 The H-N method, which is developed recently, is used to solve the half-space albedo and the half-space constant source problems for both isotropic and extremely anisotropic scattering kernels. It has been shown that the method solves the problems in a concise manner and leads to fast converging numerical results as shown in tables. (c) 2006 Elsevier Ltd. All rights reserved.

9th International Conference on Advanced Computational Methods in Heat Transfer -- JUL, 2006 -- -- Ashurst, ENGLAND, WOS: 000239953800011, The SKN, (Synthetic Kernel) approximation is applied to a two-dimensional homogeneous cylindrical participating medium with isotropic scattering. The SKN equations are tested against benchmark problems consisting of cold homogeneous participating medium. The solutions are compared with those obtained by various methods available in the literature. The SK3 approximation results for geometries of very large and very small aspect ratios are in excellent agreement with those of benchmark solutions. The SK3 solutions with moderate aspect ratios are accurate within several percent., Wessex Inst Technol, Lund Univ Technol, Dev Heat Transfer Book Series

The classical correction to the velocity auto-correlation function of non-interacting particles due to memory effects, which are beyond the Boltzmann equation, is calculated both analytically and numerically for the case of isotropic scattering in two dimensions., 14 pages, 8 figures

We present a method to determine the back reflected radiance from an isotropically scattering halfspace with matched boundary. The bonus of this method lies in the fact that it is capable, in principle, to handle the case of narrow beams, something which, to our knowledge, no other analytic method can do. Essentially, the method derives from a mathematical criterion that effectively forbids the existence of solutions to the transport equation which grown exponentially as one moves away from the surface and deeper into the medium. Preliminary calculations for infinitely wide beams yield results which agree well with what is found in literature.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We have investigated density heterogeneity of linear low density polyethylene (LLDPE) in the order of submicron scale with 2 dimensional ultra small angle X-ray scattering (2D USAXS). We found that power-law behaviour in small q- region of isotropic scattering patterns of LLDPE studied here, indicating that the density heterogeneity obeys mass fractal. Under stretching, isotropic 2D USAXS patterns of some LLDPE samples were transformed into butterfly patterns caused by heterogeneous deformation.

This paper describes the first research prototype of color in-plane electrophoretic display. Characteristic of optical performance is improved by incorporating an anisotropic scattering layer instead of an isotropic scattering layer. The reflectance of a white state is 35% at an illumination angle of 30° and a detector angle of 0° to the surface normal. The color coordinate does not change very much differently from the reflective LCD while changing an illumination angle from 70° to 30°.

The author describes the correlational properties of the complex envelope of a non-isotropically scattered mobile radio signal specified by Clarke's model. The scattering probability density function of the arriving waves is chosen to describe directional propagation that would occur in an urban environment.

Although it has been known for quite some time that individual leaves display non-Lambertian scattering at wavelengths of strong absorption in the visible part of the spectrum, while displaying near-Lambertian behaviour at wavelengths of little absorption in the near-infrared, this is widely ignored in geobotanical remote sensing investigations. Preliminary data show that non-Lambertian behaviour may have a significant effect on the ratio of infrared/red reflectance with changing illumination and observation angles, but little or no efTect on the location of the steep rise in reflectance from the red to the infrared (‘red edge’). These results indicate the need for a complete assessment of directional scattering from different vegetation and canopy types, and strongly suggest the need for caution in interpretation of observational data taken without regard for illumination and observation angles.

An approximate form for the H -function for isotropic scattering developed by Karanjai and Sen has been extended to anisotropic scatering with a characteristic function of the form ψ ( μ ) = w 1 + w 2 μ 2 + w 3 μ 4 . Our method is applicable to w (1 + x cos θ ), Rayleigh's phase function, 1 + x 1 P 1 (cos θ ) + w 2 P 2 (cos θ ), and similar phase functions.

It is shown that anisotropic scattering with a strong forward peak can give reasonable agreement with angular reflectance data for snow. As a result of the forward peak, solar radiation penetrates deeper into the medium, when measured in terms of photon mean free paths, than it does for isotropic scattering. The radiation transmitted directly through finite slabs can be seen to an optical depth of seven, and decreases much more rapidly with optical depth than does the diffusely transmitted (scattered) radiation.

Two-constant Kubelka—Munk (KM) theory with experimentally fitted values accounts quite well for the total reflectance of opaque mixtures of paints, but systematic errors indicate the need for better theory. No simple satisfactory alternative exists, however. Errors from the Saunderson correction for surface reflections are comparable to errors from KM theory, and opinions differ on the best values for the diffuse internal reflection coefficient. Since the surface corrections can be applied separately from diffuser theory, an extra variable is available. Even for isotropic scattering, theory shows that the internal surface reflectance ranges from 0.57 when the diffuser reflectance is high to 0.65 when it is low, while the corresponding Saunderson coefficient ranges from 0.52 to 0.65. For anisotropic scattering, the coefficient is virtually independent of the phase function for single scatter when the reflectance is high, but critically dependent when it is low. Values of around 0.4 are predicted for the absorption band, unless the particles are very small.

The variation of the critical slab thickness from backward to forward scattering is studied for specified isotropic scattering. Numerical results are obtained from the zeroth and first-order approximate analytical expressions, derived using the method of elementary solutions. It is shown that the critical slab thickness increases monotonically with increasing forward anisotropy.

THE problem of the radiation field in a plane-parallel multilayer system, whose outer boundary is irradiated by parallel rays, is considered. The case of non-isotropic radiation is studied. A formal solution of the problem is given, and using this, the spatial-angular distribution function of the intensity of the diffused radiation is constructed by applying the method of discrete ordinates. Consider a multilayer plane-parallel system, consisting of N layers in contact with one another which are irradiated by a parallel pencil of rays incident at some angle to the outward normal of the system. We assume that the boundaries of the layers are known and that the source functions are defined differently in each layer. It is required to determine the radiative field in any region of the system and find the law of the angular distribution of the outgoing radiation.

The integral equation for the isotropic scattering of radiation in a medium bounded laterally by planes ±y0 is solved as a series in powers of exp (−y0). This series is certainly convergent for y0 large enough, and rapidly convergent for most practical purposes.

The heat transfer in a conducting, absorbing, emitting, scattering and heat generating medium has been considered. The specific problem of a plane parallel system with isotropic scattering was chosen. For this system, it is shown that the effects of scattering are small.

Radiation from arbitrary directions incident on a thick, homogeneous, conservative atmosphere with isotropic scattering is mostly diffusely reflected. A smaller part diffuses through the atmosphere and emerges at the other side. Sobolev's equations, which give the asymptotic forms of the reflection and transmission functions for large thickness,b, in terms of the functionH(μ) known from the theory of semi-infinite atmospheres, are newly derived. It is shown by two examples that knowledge of these asymptotic forms makes it possible accurately to interpolate any quantity dependent onbbetweenb = 1 andb = ∞.

The reflectance of a semi-infinite atmosphere with nonconservative isotropic scattering is evaluated for single-scattering albedos = 0.1, 0.7, and 1.0 and compared with Minneart's law for μ and μ0 in the range 0.4–1.0. The reflectance for = 1.0 is well represented by Minneart's law with k = 1., whereas for small the reflectance is better represented by μR = R0[μμ0/(μ + μ0)]k, where k increases from 1.0 for = 0.0 to 1.08 for = 0.5.

A six-flux theory is derived for the diffuse reflectance and fluorescence of mixed powder samples of various shades of gray. One component of the powder is assumed to be fluorescent, with nonoverlapping excitation and emission bands. For symmetrical normal illumination and isotropic scattering, the six-flux reflectance reduces exactly to the Kubelka-Munk (two-flux) expression. Measurements of the fluorescence of a series of silica-silicon carbide-calcium tungstate mixed powder samples, which were found to vary over a range of 60:1, correlate well with the six-flux theory over the full range, whereas a two-flux theory is satisfactory only at high sample reflectances.

In this paper X- and V-functions which occur in the solution of transfer problems in atmospheres of finite optical thicknesses and scattering radiation isotropically with an albedo ϖ 0 ≤ 1 for single scattering are tabulated. The values of the albedo, ϖ 0 , and optical thickness, τ, for which solutions are tabulated are: ϖ 0 = 1, 0,95,0,9,0,8,0,5, and τ = 0,05,0,10,0.15,0,20,0,25,0,5, and 1.