Intermittency of energy in rapid granular shear flows

Hard-disk simulations are used for two-dimensional rapid granular shear flows of circular disks between two rotating cylinders. The intermittency effects associated with the rate of the energy dissipation of collisions are studied. The statistics of intermittent signals of energy dissipation reveals that a power law governs the dynamics of rapid shear granular flows. A dynamical system approach based on the Gledzer-Ohkitani-Yamada shell model of turbulence is employed to reproduce signals for energy dissipation that are statistically consistent with those from simulations. The results suggest that rapid granular flows can be analyzed by appropriate turbulent models.     

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.     

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.     

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.     

The determination of certain major and minor elements in geological samples by inductively coupled plasma atomic emission spectrometry. Some interference problems with the analysis of geological standard reference materials and nutrition supplements

Direct ICP-AES measurements of the digested geological standard reference material samples yielded the wrong information about their composition. The differences between certified and measured concentrations of the samples were due to the complicated sample matrix. The measured concentrations can be successfully corrected by using a multiple linear regression technique. The correction is based on the multiple regression line calculated from the analytical results at synthetic mixtures of matrix elements, where concentrations varied on five levels. There were no significant (P = 0.05) differences between certified and measured concentrations in standard reference materials after the correction. The same method was used in the analysis of nutrition supplements. Received: 25 January 2000 / Revised: 15 March 2000 / Accepted: 31 March 2000     

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     

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.     

Linear differential equations with coefficients in weighted Bergman and Hardy spaces

Complex linear differential equations of the form

with coefficients in weighted Bergman or Hardy spaces are studied. It is shown, for example, that if the coefficient of belongs to the weighted Bergman space , where , for all , then all solutions are of order of growth at most , measured according to the Nevanlinna characteristic. In the case when all solutions are shown to be not only of order of growth zero, but of bounded characteristic. Conversely, if all solutions are of order of growth at most , then the coefficient is shown to belong to for all and .

Analogous results, when the coefficients belong to certain weighted Hardy spaces, are obtained. The non-homogeneous equation associated to is also briefly discussed.

     

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.     

Categoricity in homogeneous complete metric spaces

We introduce a new approach to the model theory of metric structures by defining the notion of a metric abstract elementary class (MAEC) closely resembling the notion of an abstract elementary class. Further we define the framework of a homogeneous MAEC were we additionally assume the existence of arbitrarily large models, joint embedding, amalgamation, homogeneity and a property which we call the perturbation property. We also assume that the Löwenheim-Skolem number, which in this setting refers to the density character of the set instead of the cardinality, is ${\aleph_0}$ . In these settings we prove an analogue of Morley’s categoricity transfer theorem. We also give concrete examples of homogeneous MAECs.