Mathematical modeling of flows through inelastic porous solids

We propose a framework, based on classical mixture theory, to describe the isothermal flow of an incompressible fluid through a deformable inelastic porous solid. The modeling of the behavior of the inelastic solid takes into account changes in the elastic response due to evolution in the microstructure of the material. We apply the model to a compression layer problem. The mathematical problem generated by the model is a free boundary problem.     

Broadband frequency-domain electromagnetic analysis and automatic extraction of Spice-compatible equivalent circuits

A very simple and effective algorithm able to predict the frequency response of a multiport device over a wide band, starting from the electromagnetic analysis at some spot frequencies, is derived. Data obtained by the proposed procedure are further processed to extract a Foster's type, lumped element, equivalent circuit, suitable for use as a Spice model of the device.     

On the derivation of coupled-line models from EM simulators and application to MoM analysis

This paper addresses the problem of deriving an actual coupled-line model from the "spot frequency" characteristics of transmission media derived by means of a numerical electromagnetic simulator. For a given set of coupled lines, possibly asymmetric and lossy, one of the main issues is to recover a model whose parameters are physically and practically meaningful. In order to satisfy the requirements, the model ought to basically yield a natural generalization of the well-known even/odd and c//spl pi/ modes for couples of lines, and collapse to a set of uncoupled lines when coupling is negligible. Hence, part of this study is devoted to discussing and evaluating models that satisfy such requirements. The end result is a Weissfloch-type equivalent circuit made up of uncoupled lines and input and output ideal transformers. The algorithm is then applied to the network parameters of coupled lines. The latter are evaluated by a full-wave method of moments approach, and a subsequent short-open calibration (SOC) procedure. Finally, a new algorithm is introduced that is able to evaluate and remove the contribution of the naked discontinuity due to ports, usually not directly available from the SOC routine.     

Über den Einfluß der Struktur stickstoffhaltiger Substanzen bei der Mikrobestimmung von Kohlenstoff und Wasserstoff mit Außenabsorption der Stickoxide

Zusammenfassung Bei der C-H-Bestimmung mit Außenabsorption der Stickoxide wurden bei einer Serie stickstoffhaltiger Substanzen zu hohe Wasserstoffwerte erhalten, während sich bei einer zweiten Serie, mit gleichen Atomgruppen, richtige Werte ergaben. Um dieses verschiedene Verhalten erklären zu können, wurden weitere Substanzen dieser Art dargestellt und analysiert. Dabei konnte beobachtet werden, daß Substanzen mit der Atomgruppe bei der Analyse im allgemeinen zu hohe Wasserstoffwerte geben, während die Anwesenheit von Phenylringen oder OH-Gruppen, in und Stellung wieder zu regelmäßigen Wasserstoffwerten führen.Die Darstellung neuer Verbindungen dieser Art wurde beschrieben. In den Verbindungen, die bei der C-H-Bestimmung zu hohe Wasserstoffwerte gaben, wurden zur Identifizierung einerseits der Stickstoff, anderseits C und H nach einer Methode bestimmt, die die Reduktion der Stickoxide vorsieht. Diese wird beschrieben.

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Summary Too high hydrogen values were obtained in the C-H-determinations, with external absorption of the nitrogen oxides, in a series of nitrogenous substances, whereas a second series with the same atom groups gave correct results. To explain these divergent behaviors, additional substances were prepared and analyzed. It was then observed that substances with the group yielded too high hydrogen values in general, while the presence of phenyl rings or OH-groups in the and-position led again to uniform hydrogen values. The preparation of the new compounds of this kind is described. In the case of the compounds that gave too high hydrogen values in the C-H-determination, identification was made on one hand by determining the nitrogen, on the other hand by determining the carbon and hydrogen by another method that provides for the reduction of the nitrogen oxides. The latter is described.

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Herrn Univ.-Prof. Dr.Hans Lieb zum 80. Geburtstag gewidmet.     

High-pressure dissociation of crystalline para-diiodobenzene: optical experiments and Car-Parrinello calculations

We have investigated the high-pressure properties of the molecular crystal para-diiodobenzene, by combining optical absorption, reflectance, and Raman experiments with Car-Parrinello simulations. The optical absorption edge exhibits a large red shift from 4 eV at ambient conditions to about 2 eV near 30 GPa. Reflectance measurements up to 80 GPa indicate a redistribution of oscillator strength toward the near-infrared. The calculations, which describe correctly the two known molecular crystal phases at ambient pressure, predict a nonmolecular metallic phase, stable at high pressure. This high-density phase is characterized by an extended three-dimensional network, in which chemically bound iodine atoms form layers connected by hydrocarbon bridges. Experimentally, Raman spectra of samples recovered after compression show vibrational modes of elemental solid iodine. This result points to a pressure-induced molecular dissociation process which leads to the formation of domains of iodine and disordered carbon.     

High-pressure structure of Li2CO3

The high-pressure behavior of Li₂CO₃ is studied up to 25 GPa with synchrotron angle-dispersive powder X-ray diffraction in diamond anvil cells and synthesis using a multi-anvil apparatus. A new non-quenchable hexagonal polymorph (P6₃/mcm, Z=2) occurs above 10 GPa with carbonate groups in a staggered configuration along the c-axis—a=4.4568(2) Å and c=5.1254(6) Å at 10 GPa. Two columns of face-shared distorted octahedra around the Li atoms are linked through octahedral edges. The oxygen atoms are coordinated to one carbon atom and four lithium atoms to form a distorted square pyramid. Splittings of X-ray reflections for the new polymorph observed above about 22 GPa under non-hydrostatic conditions arise from orthorhombic or monoclinic distortions of the hexagonal lattice. The results of this study are discussed in relation to the structural features found in other Me₂CO₃ carbonates (Me: Na, K, Rb, Cs) at atmospheric conditions.     

Scattering theory,cross sections,and the lattice of propositions

The asymptotic conditions for the nonrelativistic quantum scattering of a particle by a center of force are derived in terms of a metric on the space of states on a complete orthocomplemented lattice. The flux of particles scattered into a coneC per unit incident flux, averaged over all displacements of the center of force at right angles to the axis of the incident beam, is expressed in terms of the differential cross sectiond/d when the motion is classical, and in terms of the scattering amplitudef when the motion is quantum mechanical. This enables the usual identificationd/d=|f|² to be made.     

Sorption of divalent metal ions on CrPO4

The divalent metal ion sorption (Cu(2+), Cd(2+), Ni(2+), and Pb(2+)) on chromium phosphate (CrPO(4)) was studied as a function of pH, temperature, and concentration of metal ions. The sorption of metal ions is observed to increase with the increase in pH, temperature, and concentration of metal ions in solution. The mechanism of sorption is found to be the exchange of the hydrolyzed metal cations with the protons from solid at high temperature. The sorption at low temperature is found to be accompanied by the precipitation of the corresponding metal phosphates such as Pb(3)(PO(4))(2).     

Tartaglia-Pascal’s triangle: a historical perspective with applications

The aim of this paper is to provide a historical perspective of Tartaglia-Pascal’s triangle with its relations to physics, finance, and statistical signal processing. We start by introducing Tartaglia’s triangle and its numerous properties. We then consider its relationship with a number of topics: the Newton binomial, probability theory (in particular with the Gaussian probability density function, pdf), the Fibonacci sequence, the heat equation, the Schrödinger equation, the Black–Scholes equation of mathematical finance and stochastic filtering theory. Thus, the main contribution of this paper is to present a systematic review of the triangle properties, its connection to statistical theory, and its numerous applications. The paper has mostly a scientific-educational character and is addressed to a wide circle of readers. Sections 7 and 8 are more technical; thus, they may be of interest to more expert readers.     

Experimental evaluation of epithermal neutron self-shielding for 96Zr and 98Mo

In a previous work we experimentally tested some neutron self-shielding calculations methods for thermal absorbers, from which the semi-empirical “sigmoid method” gave the most accurate results. In this work we aim at evaluating the accuracy of this method on the epithermal self-shielding phenomena as compared to the analytical “MatSSF method”. Metallic foils of Zr and Mo were compactly stacked together into small cylinders (or disks) of different thickness, allowing for up to 20 % epithermal self-shielding when irradiated on two channels of the BR1 reactor. A 2 % relative difference between calculated and experimental self-shielding factors was obtained from the MatSSF method when a perpendicular source-sample axial configuration was assumed, while the isotropic or the co-axial configuration alternatives gave up to 10 % relative differences. On the other hand, the sigmoid method gave relative differences of up to 6 % that can be reduced to just 2 % by applying the “effective” epithermal absorption cross-sections for ⁹⁸Mo and ⁹⁶Zr proposed in this work.