Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients

In this short note, we present a new technique to accelerate the convergence of a FFT-based solver for numerical homogenization of complex periodic media proposed by Moulinec and Suquet [1]. The approach proceeds from discretization of the governing integral equation by the trigonometric collocation method due to Vainikko [2], to give a linear system which can be efficiently solved by conjugate gradient methods. Computational experiments confirm robustness of the algorithm with respect to its internal parameters and demonstrate significant increase of the convergence rate for problems with high-contrast coefficients at a low overhead per iteration.     

Possibilities of applying the Piloyan method of determination of decomposition activation energies in the differential thermal analysis of polynitroaromatic compounds and their derivatives

The Piloyan activation energiesE, as well as the initial exotherm temperaturesT _D, are determined for sixN-monoalkyl- and fiveN,N-dialkyl-2,4,6-trinitroanilines. By comparison withR _f-factors, orR _M-functions of paper chromatography, the molecular-structural dependences ofE andT _D are studied for these compounds. Relationships are also found between the termE · T _D ^–1 and theR _M-functions. The effects are discussed of the introduction of the 6-nitro group into the TV-substituted 2,4-dinitroanilines, and of the introduction of the 4-nitro group into the 2,6-dinitro analogues, upon the thermal stabilities of the resulting 2,4,6-trinitroanilines.

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Zusammenfassung Die AktivierungsenergienE nach Piloyan und die Anfangswerte der ExothermenT _D der sechsN-monoalkyl- und fünfN,N-Dialkyl-2,4,6-trinitroaniline wurden bestimmt. Unter Berücksichtigung des Vergleichs mitR _f-Faktoren oderR _M-Funktionen der Papierchromatographie wurden die molekularstrukturellen AbhÄngigkeiten der WerteE undT _D dieser Verbindungen untersucht. ZusammenhÄnge wurden auch zwischen dem AusdruckE · Tw _D ^–1 und denR _M-Funktionen gefunden. Der Einfluss der Einführung der 6-Nitrogruppe in dieN-substituierten 2,4-Dinitroaniline, sowie der Einfluss der Einführung der 4-Nitrogruppe in 2,6-Nitroanaloge auf die ThermostabilitÄt der resultierenden 2,4,6-Trinitroaniline werden erörtert.

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Résumé On a déterminé les énergies d'activation par la méthode de Piloyan ainsi que les températures initialesT _D de l'effet exothermique de sixN-monoalcoyl- et cinqN,N-dialcoyl-2,4,6-trinitroanilines. En se référant aux facteursR _F ou aux valeurs des fonctionsR _M en Chromatographie sur papier, on a étudié la dépendance entre les valeurs deE et deT _D sur les caractéristiques moléculaires-structurales de ces composés.On a également trouvé des rapports entre le termeE · T _D ^–1 et les fonctionsR _M. On discute l'influence de l'introduction du groupe 6-nitro dans les 2,4-dinitroanilinesN-substituées ainsi que l'influence de l'introduction du groupe 4-nitro dans les 2,6-dinitro analogues sur la stabilité thermique des 2,4,6-trinitroanilines qui en résultent.

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N-- N,N--2,4,6- E , T _D. R _f,- R _M — , - E T _D. E.T _D ^–1 R _M-. 6N- 2,4- 4 2,6- 2,4,6- .

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The authors would like to thank Mrs. Anna Colláková for careful DTA measurements, and Dr. Ladislav Smolka for help in the treatment of the measured results with the Wang 600 computer.     

A treatment of the tμ +D2 reaction by the methods of quantum reactive scattering

In this article, we describe how we are applying the methods of chemically reactive scattering to the key resonant reaction in muon catalysed fusion. Preliminary results are presented for cross-sections. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermogravimetric Analysis of Polynitro Arenes

Attention was paid to seventeen samples of polynitro arenes. Stability of these nitrocompounds was specified by means of non-isothermal thermogravimetric analysis (TG). Linear relationships were specified between the positions of TG-onsets and the mass of the samples. The relation of slopes of the mentioned relationships to the rate constants of the thermal decomposition under condition of Russian manometric method (SMM) was confirmed and solved for studied polynitro arenes. These arene derivatives were classified into several groups in the sense of this relation. The classification was interpreted by dominating influence of intermolecular interaction factors on the corresponding TG-onsets positions. The found relations can be used for the TG results conversion to the parameters, which are comparable with SMM outputs. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-isothermal differential thermal analysis in the study of the initial state of the thermal decomposition of polynitroaromatic compounds in the condensed state

The activation energies, E, of the decomposition of picramide and its N-methyl-,N-ethyl-,N-n-propyl- and N-n-butyl-derivatives are determined by means of non-isothermal DTA, in its simple form, as well as by the Piloyan method. A relationship is found between the E values of the above-mentioned compounds and the published values of the moments of inertia of the corresponding n-alkyl groups. Taking into account data published previously, which were obtained by application of the Piloyan method in the DTA of polynitroaromates, it is concluded that by suitable selection of DTA measurement conditions, it is possible to record the early part of the exothermal decomposition of the above-mentioned compounds were no autocatalytic influence exists. Attention is also paid to the thermostability of the polynitroaromates due to their contact with the construction materials employed in the course of thermolysis.     

A new principle of activation-analysis separations-X Substoichiometric determination of traces of gallium

A rapid method for the substoichiometric determination of gallium by neutron-activation analysis has been developed. After irradiation and dissolution of the test sample, gallium carrier is added and two preliminary separation steps are performed: the extraction into chloroform of cupferrates from 7N sulphuric acid and of diethyldithiocarbamates from 2-3N sulphuric acid. The pH of the remaining aqueous phase is then adjusted to 5.5, the solution extracted with a substoichiometric amount of 8-hydroxyquinoline in chloroform and the activity of the gallium hydroxyquinolate extract measured. A simultaneously irradiated gallium standard is treated in exactly the same way. From the activities of these two substoichiometric extracts the amount of gallium originally present in the test sample can be calculated. The method has been applied to the determination of 10(-6) to 10(-3)% of gallium in metallic aluminium and transistor-grade silicon.     

HNC/HCN ratio in acetonitrile, formamide, and BrCN discharge

Time-resolved Fourier transform (FT) spectrometry was used to study the dynamics of radical reactions forming the HCN and HNC isomers in pulsed glow discharges through vapors of BrCN, acetonitrile (CH(3)CN), and formamide (HCONH(2)). Stable gaseous products of discharge chemistry were analyzed by selected ion flow tube mass spectrometry (SIFT-MS). Ratios of concentrations of the HNC/HCN isomers obtained using known transition dipole moments of rovibrational cold bands v(1) were found to be in the range 2.2-3%. A kinetic model was used to assess the roles the radical chemistry and ion chemistry play in the formation of these two isomers. Exclusion of the radical reactions from the model resulted in a value of the HNC/HCN ratio 2 orders of magnitude lower than the experimental results, thus confirming their dominant role. The major process responsible for the formation of the HNC isomer is the reaction of the HCN isomer with the H atoms. The rate constant determined using the kinetic model from the present data for this reaction is 1.13 (±0.2) × 10(-13) cm(3) s(-1).     

Modelling of rotating shafts with flexible disks

This paper deals with the methodology of the modelling of rotating shafts with flexible disks. Rotating shafts are modelled as a one dimensional continuum on the basis of the Bernouli-Euler theory, which assumes that the shaft cross section remains a flat plane and is perpendicular to the centerline during vibration. Disks are modelled as a three dimensional continuum by means of the finite element method. The presented approach allows to introduce centrifugal and gyroscopic effects. The special coupling matrix is used for the connecting a rotating shaft and a mounted flexible disk. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)