Runge–Kutta convolution quadrature methods for well-posed equations with memory

Runge–Kutta based convolution quadrature methods for abstract, well-posed, linear, and homogeneous Volterra equations, non necessarily of sectorial type, are developed. A general representation of the numerical solution in terms of the continuous one is given. The error and stability analysis is based on this representation, which, for the particular case of the backward Euler method, also shows that the numerical solution inherits some interesting qualitative properties, such as positivity, of the exact solution. Numerical illustrations are provided.     

Microperforated insertion units: An alternative strategy to design microperforated panels

Microperforated panels (MPPs) coupled to a rigid wall have been proposed recently as an alternative to porous absorbers in situations having concerns with bacterial contamination and small particles discharge, like food, pharmaceutical and microelectronic industries. There exists also an increasing interest for MPP absorbers in the transportation industry and civil engineering. In general, an optimally designed MPP with good broadband absorption requires many submillimetric holes distributed over a panel of also submillimetric thickness. Such thin plates or foils become so fragile that they need to be protected from mechanical damage. In this paper, an alternative strategy is investigated which allows the design of MPPs with panels of millimetric thickness while maintaining their acoustic performance. These absorbers, named microperforated insertion units (MIUs), avoid the structural problems of the classical MPPs. An assessment of the sound absorption properties of these structures is presented. Comparisons between calculations and measurements are also made under two experimental conditions: plane waves at normal incidence (impedance tube) and free field (anechoic room).     

Monitoring powder blending by NIR spectroscopy

A strategy is proposed for the monitoring of powder blending. Samples are taken throughout the blender vessel and scanned by diffuse reflectance spectroscopy in the NIR range. The NIR spectra are first subjected to the Standard Normal Variate transformation (SNV). The first approach consists of overlaying the transformed spectra taken from different locations at each time. To quantify the differences between the spectra, the standard deviation spectrum at each time is calculated and the mean standard deviation value is plotted as a function of time. This plot indicates the time at which the blend is most homogeneous. Each individual spectrum can be compared with the mixture spectrum, which is an approximation of the spectrum of a true homogeneous sample. For that purpose several approaches, i.e. determination of the dissimilarity, Principal Component Analysis, are proposed. As an alternative approach to monitoring the blending the use of SIMPLISMA is recommended.Dedicated to Professor Dr. h.c. mult. J.F.K. Huber on the occasion of his 70th birthday     

Short stereocontrolled synthesis of trans and cis-tetrahydro-pyrazinoisoquinolinediones

Addition of aldehyde dimethyl acetals (here acetaldehyde) to unisolated O-trimethylsilyl derivatives of 1-acetyl-3-arylmethylpiperazine-2,5-diones (here 2,5-dimethoxyphenyl), in the presence of TMSOTf as the catalyst, gave nearly quantitatively the corresponding N-methoxyalkyl derivatives which, under acidic treatment, gave in very good yield through a Pictet-Spengler-type reaction involving N-acyliminium cations (6S*,11aR*)-2-acetyl-6-alkyl-3,6,11,11a-tetrahydro-2H-pyrazino[1,2-b]isoquinoline-1,4-diones. Epimerization of the 11a-stereocentre was accomplished by radical bromination, spontaneous hydrobromide elimination and catalytic hydrogenation, to give the (6S*,11aS*)-isomers. We propose these compounds as precursors of tetrahydroisoquinoline antitumour antibiotics.     

Ligand adsorption on an activated carbon for the removal of chromate ions from aqueous solutions

The results presented in this work are related to the design of a guideline to develop specific properties at the surface of an activated carbon (AC). For this, two model aromatic compounds have been synthesized and their electrolytic behavior in aqueous solutions was studied by a potentiometric method. The textural characteristics of the activated carbon were determined by porosimetry methods. The nature of oxygen-carrying functions and the acid-base behavior of the AC surface were characterized by TPD and potentiometric titration methods, respectively. The adsorption and desorption equilibria of the aromatic compounds on activated carbon were measured in aqueous solutions, and the hysteresis between adsorption and desorption, which reveals irreversible adsorption, was discussed on the basis of the frontier orbital theory. HOMO and LUMO orbitals of the adsorbent and adsorbates were calculated, and irreversible adsorption was attributed to the small energy difference between HOMO and LUMO of the aromatic adsorbates and the adsorbent. Adsorption equilibria of K2CrO4 in aqueous solution on the AC alone and on the AC-aromatic ligand adsorbents, respectively, prove the efficient development of specific chemical functions at the carbon surface provided by the adsorbed aromatic compounds.     

Reactivity of molybdenum and rhenium hydroxo-carbonyl complexes toward organic electrophiles

The hydroxo compounds [Re(OH)(CO)(3)(N-N)] (N-N=bipy, 2 a; Me(2)-bipy, 2 b) were prepared in a biphasic H(2)O/CH(2)Cl(2) medium by reaction of [Re(OTf)(CO)(3)(N-N)] with KOH. In contrast, when anhydrous CH(2)Cl(2) was used, the binuclear hydroxo-bridged compound [[Re(CO)(3)(bipy)](2)(mu-OH)]OTf (3-OTf) was obtained. Compound [Re(OH)(CO)(3)(Me(2)-bipy)] (2 b) reacted with phenyl acetate or vinyl acetate to afford [Re(OAc)(CO)(3)(Me(2)-bipy)] (4) and phenol or acetaldehyde, respectively. The reactions of [Mo(OH)(eta(3)-C(3)H(4)-Me-2)(CO)(2)(phen)] (1), 2 a, and 2 b toward several unsaturated organic electrophiles were studied. The reaction of 1 with (p-tolyl)isocyanate afforded an adduct of N,N'-di(p-tolyl)urea and the carbonato-bridged compound [[Mo(eta(3)-C(3)H(4)-Me-2)(CO)(2)(phen)](2)(mu-eta(1)(O),eta(1)(O)-CO(3))] (5). In contrast, the reaction of 2 a with phenylisocyanate afforded [Re(OC(O)NHPh)(CO)(3)(bipy)] (6); this results from formal PhNCO insertion into the O-H bond. On the other hand, compounds [Mo[SC(O)NH(p-tolyl)](eta(3)-C(3)H(4)-Me-2)(CO)(2)(phen)] (7), [Re[SC(O)NH(p-tolyl)](CO)(3)(Me(2)-bipy)] (8 a), and [Re[SC(O)NHEt](CO)(3)(Me(2)-bipy)] (8 b) were obtained by reaction of 1 or 2 b with the corresponding alkyl or aryl isothiocyanates. In those cases, RNCS was inserted into the M-O bond. The reactions of 1, 2 a, and 2 b with dimethylacetylenedicarboxylate (DMAD) gave the complexes [Mo[C(OH)-C(CO(2)Me)C(CO(2)Me)-O](eta(3)-C(3)H(4)-Me-2)(CO)(phen)] (9) and [Re[C(OH)C(CO(2)Me)C(CO(2)Me)O](CO)(2)(N-N)] (N-N=bipy, 10 a; Me(2)-bipy, 10 b). The molecules of these compounds contain five-membered metallacycles that are the result of coupling between the hydroxo ligand, DMAD, and one of the CO ligands. The new compounds were characterized by a combination of IR and NMR spectroscopy, and for [[Re(CO)(3)(bipy)(2)(mu-OH)]BF(4) (3-BF(4)), 4, 5, 6, 7, 8 b, 9, and 10 b, also by means of single-crystal X-ray diffraction.     

Theoretical study on the structures and electronic spectra of TCNE2-.

Investigations into the charge-separated states and electron-transfer transitions in tetracyanoethylene (TCNE) complexes have recently generated much interest. In this work we present theoretical calculations showing that the most stable structure of the dianion TCNE2- has D2d symmetry in vacuum as well as in the solvents dichloromethane and acetonitrile. By means of the coupled cluster linear response, we compute the vertical electronic spectrum in both the gas phase and solution. The theoretical results are compared to the experimental data and good agreement is achieved.     

Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates

The phase diagram of a polydisperse mixture of uniaxial rodlike and platelike hard parallelepipeds is determined for aspect ratios kappa=5 and 15. All particles have equal volume, and polydispersity is introduced in a highly symmetric way. The corresponding binary mixture is known to have a biaxial phase for kappa=15, but to be unstable against demixing into two uniaxial nematics for kappa=5. The phase diagram for kappa=15 is qualitatively similar to that of the binary mixture, regardless of the amount of polydispersity, while for kappa=5 a sufficient amount of polydispersity stabilizes the biaxial phase. This provides clues for designing an experiment to observe this long searched biaxial phase.     

Overcomplete Free Energy Functional for D = 1 Particle Systems with Next Neighbor Interactions

We deduce an overcomplete free energy functional for D=1 particle systems with next neighbor interactions, where the set of redundant variables are the local block densities _i of i interacting particles. The idea is to analyze the decomposition of a given pure system into blocks of i interacting particles by means of a mapping onto a hard rod mixture. This mapping uses the local activity of component i of the mixture to control the local association of i particles of the pure system. Thus it identifies the local particle density of component i of the mixture with the local block density _i of the given system. Consequently, our overcomplete free energy functional takes on the hard rod mixture form with the set of block densities _i representing the sequence of partition functions of the local aggregates of particle numbers i. The system of equations for the local particle density of the original system is closed via a subsidiary condition for the block densities in terms of . Analoguous to the uniform isothermal-isobaric technique, all our results are expressible in terms of effective pressures. We illustrate the theory with two standard examples, the adhesive interaction and the square-well potential. For the uniform case, our proof of such an overcomplete format is based on the exponential boundedness of the number of partitions of a positive integer (Hardy-Ramanujan formula) and on Varadhan's theorem on the asymptotics of a class of integrals.