Radiative transfer in stochastically inhomogeneous media

New radiative transfer theory is developed for stochastically inhomogeneous scattering media. The three-dimensional shapes and large scale (compared to the mean free path) structures of the media are modeled by stochastic interfaces separating regions of different scattering properties. The small scale fluctuations are characterized by a pair-correlation function. The radiative transfer equation is extended to include individual scattering and propagation probabilities of a ray for each subregion as well as the probability for a ray to cross the interface between two subregions. The propagation probability is found to depend on the entire preceding path of the ray; the present formulation accounts for the two previous scatterings. A new adding/doubling algorithm is developed to solve this problem numerically. Transmission through a cloud layer and backward scattering seem to be particularly sensitive to inhomogeneities.     

Spectropolarised ray-tracing simulations in densely packed particulate medium

Light scattering from particulate medium is simulated using the Monte Carlo ray-tracing technique. The medium is modelled as a randomly packed medium of ellipsoidal grains with stochastically rough surfaces, with an optional thin coating. Optical properties are modelled using a wavelength-dependent complex refractive index and taking Fresnelian reflections and refractions from the interfaces. The size and shape of the grains are assumed to be large and smooth enough for geometric optics to apply reasonably well.The ray-tracing technique uses parallel, weighted rays for computing simultaneously over a wide wavelength spectrum and a small roughness range, and scaling to obtain a large range of sizes and absorbities simultaneously. Polarisation is fully accounted for. The multiobservation technique is effectively used at each scattering point. The scattering from thinner sample layers is also received as a subresult.Simulations are run for a set of model samples to study the effects and sensitivities regarding the values of certain parameters. It has been found that the size and composition of the grains affect the scattering in a unique and invertible way. The shape of the grain causes similar significant effects that must certainly be taken into account if any accuracy is required, although inverting for the shape is difficult without further constraints. The packing density has a small but observable effect. Polarisation can be used to study the composition of low-albedo objects.     

Finite Degree Holomorphic Covers of Compact Riemann Surfaces

A conjecture of Ehrenpreis states that any two compact Riemann surfaces of genus at least two have finite degree unbranched holomorphic covers that are arbitrarily close to each other in moduli space. Here we prove a weaker result where certain branched covers associated with arithmetic Riemann surfaces are allowed, and investigate the connection of our result with the original conjecture.     

Two isomers of Pd2(S2NC7H4)4

The dichloromethane solvates of the isomers tetrakis(μ‐1,3‐benzothiazole‐2‐thiolato)‐κ⁴N:S;κ⁴S:N‐dipalladium(II)(Pd—Pd), (I), and tetrakis(μ‐1,3‐benzothiazole‐2‐thiolato)‐κ⁶N:S;κ²S:N‐dipalladium(II)(Pd—Pd), (II), both [Pd₂(C₇H₄NS₂)₄]·CH₂Cl₂, have been synthesized in the presence of (o‐isopropylphenyl)diphenylphosphane and (o‐methylphenyl)diphenylphosphane. Both isomers form a lantern‐type structure, where isomer (I) displays a regular and symmetric coordination and isomer (II) an asymmetric and distorted structure. In (I), sitting on an centre of inversion, two 1,3‐benzothiazole‐2‐thiolate units are bonded by a Pd—N bond to one Pd atom and by a Pd—S bond to the other Pd atom, and the other two benzothiazolethiolate units are bonded to the same Pd atoms by, respectively, a Pd—S and a Pd—N bond. In (II), three benzothiazolethiolate units are bonded by a Pd—N bond to one Pd atom and by a Pd—S bond to the other Pd atom, and the fourth benzothiazolethiolate unit is bonded to the same Pd atoms by, respectively, a Pd—S bond and a Pd—N bond.     

The analysis of chromium, cobalt, iron, nickel, niobium, tantalum, titanium and zinc in cemented tungsten carbides with cobalt as a binder by inductively coupled plasma atomic emission spectrometry

 Inductively coupled plasma atomic emission spectrometry (ICP-AES) was applied as a rapid routine method for the analysis of cemented tungsten carbides. Chromium, cobalt, iron, nickel, niobium, tantalum, titanium and zinc were selected as major, minor and trace constituents in the material investigated. In the first step, the sample was treated with hydrochloric and orthophosphoric acid. The second step consisted of the simultaneous addition of hydrofluoric and nitric acids. Cemented tungsten carbides dissolved completely, leaving only minor quantities of carbon in the solution. Multiple linear regression proved to be very effective in the search for interfering elements. Using simple acid based standards, all the elements investigated could be determined individually from the complicated matrix using an appropriate method of calculation. The method described was successfully applied to real type commercial samples. The advantages of the ICP-AES method in comparison with the XRF-method are discussed. Received: 15 February 1996/Revised: 22 April 1996/Accepted: 2 May 1996     

On Strictly Convex Subsets in Negatively Curved Manifolds

In a complete simply connected Riemannian manifold X of pinched negative curvature, we give a sharp criterion for a subset C to be the ??-neighbourhood of some convex subset of X, in terms of the extrinsic curvatures of the boundary of C.     

The role of MFC/NFC swelling in the rheological behavior and dewatering of high consistency furnishes

The influence of swelling on the rheological and dewatering properties of high consistency nanocellulose based furnishes is considered. Different consistencies of suspensions (1–4 %) and furnishes (5–15 %) were prepared made of two distinctly different grades of nanocellulose containing, micro fibrillated (MFC) and nanofibrillated (NFC) cellulose, and systematic comparison between the rheological and dewatering parameters was conducted. The characterization of the rheological and dewatering properties was performed with a stress controlled rheometer combined with an immobilization cell in parallel plate geometry, as well as with an independent gravimetric dewatering device. The surface charge of nanofibrillated cellulose was found to influence the rheological and dewatering properties of the evaluated suspensions and furnishes due to its impact on swelling and effectively bound water. Due to the complex behavior of the novel materials, the immobilization times were difficult to determine from the changes in the damping factor, as often used for coating colors. Instead, we propose a modified method for determination of immobilization times based on a rheological analysis adopting the rate of change in viscoelastic loss factor over time, d(tan δ = G′′/G′)/dt, describing the critical point(s) in the ratio of the viscous to elastic stress response moduli. With this approach we show that it is possible to characterize immobilization of these materials incorporating the concept of the combined physical interactions of the components and the non-removable bound water, without requiring a direct measure of the nanocellulose surface swelling. Based on the results, we hypothesize that fibrillar swelling impacts the dewatering of MFC and NFC suspensions, and furnishes containing them, by an interfiber pore connectivity blocking/sealing mechanism, which effectively defines the immobilization of the material matrix at the end point of free water extraction caused by the physical blocking imposed by the remaining bound water.     

An original approach for Raman spectroscopy analysis of radioactive materials and its application to americium‐containing samples

An approach for Raman measurements of highly radioactive samples is presented here. The innovative part of this approach lies in the fact that no single part of the Raman equipment is in direct contact with the radioactive sample, as the sample is sealed in an alpha‐tight capsule. Raman analysis is effectively performed through the optical‐grade quartz window closing the capsule. This allows performing micro‐Raman measurements on radioactive samples with no limitations on the laser source wavelength, polarisation mode, spectrometer mode and microscope mode (provided the focal length of the microscope objective is greater than the thickness of the quartz window and with sub mg samples). Some example results are shown and discussed. In particular, some spectral features of americium‐containing oxide nuclear fuel specimens are presented. Raman spectra clearly reveal in these specimens the presence of abundant oxygen defects induced in the fcc fluorite lattice by trivalent americium. In order to complete the analysis the Raman spectrum of pure americium dioxide was also measured with a lower energy excitation source compared with previous research. The current results seem to be consistent with the possible occurrence of a photolysis process induced by the Raman laser, resulting in the formation of hyperstoichiometric americium sesquioxide Am₂O_{3 + z}. Such a photolytic process is deemed to be unavoidable when visible lasers are used as excitation sources for the Raman analysis of americium dioxide. © 2015 The Authors Journal of Raman Spectroscopy Published by John Wiley & Sons, Ltd.