A new regularized method for two dimensional nonhomogeneous backward heat problem

We consider the problem of finding, from the final data u(x,y,T)=g(x,y), the initial data u(x,y,0) of the temperature function u(x,y,t),(x,y)I=(0,π)×(0,π),t[0,T] satisfying the following system

The problem is severely ill-posed. In this paper a simple and convenient new regularization method for solving this problem is considered. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively.     

On dynamic finite element analysis of viscoplastic thin-walled structures with non-local damage

In this article we propose a non-local damage model for dynamic finite element computation of viscoplastic thin-shell structures. To take void nucleation and growth into account, the free energy function is enhanced phenomenologically in terms of a non-local damage variable and its gradient on the mid-surface of shell structures. The dynamic thin-shell elastic theory including large rotations proposed by Simo and Tarnow (1994) is used to capture finite deformation. Local constitutive laws considering viscoplastic behaviour, isotropic hardening and isotropic ductile damage leading to softening in Velde et al. (2009) are employed. The performance of the proposed approach is demonstrated through the preliminary numerical simulations of shock-wave loaded structures, which are validated by comparision with the experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Klaus Krickeberg und Vietnam. Erinnerungen

Ohne Zusammenfassung

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Original Russian Text ? X.X.Nguyen, 2009, published in Izvestiya NAN Armenii. Matematika, 2009, No. 1, pp. 26–31.     

Control of interchain contacts, solid-state fluorescence quantum yield, and charge transport of cationic conjugated polyelectrolytes by choice of anion

Simple procedures are provided for exchanging charge-compensating ions in conjugated polyelectrolytes by progressive dilution of the original species and for determining the degree of ion exchange by using X-ray photoelectron spectroscopy. By using these methods, the bromide ions in poly[(9,9-bis(6'-N,N,N-trimethylammoniumbromide)hexyl)fluorene-co-alt-4,7-(2,1,3-benzothiadiazole)]were exchanged with BF4-, CF3SO3-, PF6-, BPh4-, and B(3,5-(CF3)2C6H3)4- (BArF4-). Absorption, photoluminescence (PL), and PL quantum yields (Phi) were measured in different solvents and in solid films cast from methanol. Examination of the resulting trends, together with the spectral bandshapes in different solvents, suggests that increasing the counteranion (CA) size decreases interchain contacts and aggregation and leads to a substantial increase of Phi in the bulk. Size analysis of polymers containing Br- and BArF4- in water by dynamic light scattering techniques indicates suppression of aggregation by BArF4-. Nanoscale current-voltage measurements of films using conducting atomic force microscopy show that hole mobilities and, more significantly, charge injection barriers are CA dependent. These results show that it is possible to significantly modify the optoelectronic properties of conjugated polyelectrolytes by choosing different counterions. A parent conjugated backbone can thus be fine-tuned for specific applications.     

Performances under representative pressure and temperature conditions of the gas chromatography-mass spectrometry space experiment to investigate Titan's atmospheric composition

In the frame of the calibration of the aerosol collector and pyrolyser, and gas chromatography-mass spectrometry experiments of the Huygens probe arrived at Titan, systematic experimental studies were led to estimate the influence of the operating conditions on the analyses that should have been achieved in the Titan's atmosphere. The primary objective of this study was to estimate the influence of operating conditions variations induced by (i) instrumental modifications made shortly before the probe launch which can have changed the operating pressures; (ii) the change of the probe environmental conditions (pressure, temperature) during its descent in the atmosphere; (iii) a possible deviation of pressure and temperature regulations from their nominal values because of the long journey of the instrument in space, or of other external events. The secondary objective of this work was to create an analytical database that can be used as a reference to treat the chromatograms obtained in situ, and help to identify chromatographically the analyzed species, complementary to mass spectrometry. Beyond the application to a specific instrument, this work was also useful to experimentally estimate the fundamental evolution of the separation as a function of the changes of operating conditions with time. The obtained results show (i) the significant influence of inlet and outlet pressure variation on the time of analysis, but not on the separation power. It thus enables to significantly shorten the analysis duration, and thus to analyze more compounds within the fixed time of analysis of the instrument; (ii) the significant influence of temperature on the retention. In this frame, the enthalpies of exchange between the gas phase and the stationary phase of the species were determined to be used to retrieve the analyzed species in case of deviation of the operating temperature; (iii) that the possible aging of the columns does not have influence on the columns efficiency and separation power; (iv) the analytical capabilities of the gas chromatography-mass spectrometry experiment within operating conditions representative of those encountered in situ. Finally, in spite of possible operating condition changes, it is shown that results coming from the gas chromatograph-mass spectrometer experiment, which are currently under analysis, could bring important information on the Titan's atmosphere and its history.     

Total synthesis of oxyfagaronine, phenolic benzo[c]phenanthridine and general synthetic way of 2,3,7,8- and 2,3,8,9-tetrasubstituted benzo[c]phenanthridine alkaloids

Benzo[c]phenanthridine alkaloids such as oxynitidine, oxysanguinarine, oxyavicine and phenolic oxyfagaronine were synthesized from easily available starting benzonitriles 5 and toluamides 6 using a lithiated toluamide-benzonitrile cycloaddition reaction. The coupling reaction provided 3-arylisoquinolinones that were transformed to the benzo[c]phenanthridones. This method is highly efficient and could be useful for preparing diverse substituted aromatic benzo[c]phenanthridine compounds on a multi gram scale.     

Sodium zinc hydroxide sulfite with a novel Zn3OH geometry

The synthesis and crystal structure of a new sodium zinc hydroxide sulfite, Na[(Zn(OH)]3(SO3)2, with novel structural features and bonding geometry are reported. In Na[(Zn(OH)]3(SO3)2, Zn2+ and O2- alternate to form an interesting corrugated hexagonal sheet with rings consisting of (ZnO)3. Another rare occurrence is the bonding geometry of one-third of the O sites within the sheet. These O sites form a planar Zn3O unit, unlike other known compounds, in which Zn3O is pyramidal.     

A method for simultaneously determining the zeta potentials of the channel surface and the tracer particles using microparticle image velocimetry technique

The zeta potentials of channel surfaces and tracer particles are of importance to the design of electrokinetic microfluidic devices, the characterization of channel materials, and the quantification of the microparticle image velocimetry (microPIV) measurement of EOFs. A method is proposed to simultaneously measure the zeta potentials of the channel surface and the tracer particles in aqueous solutions using the microPIV technique. Through the measurement of the steady velocity distributions of the tracer particles in both open- and closed-end rectangular microchannels under the same water chemistry condition, the electrophoretic velocity of the tracer particles and the EOF field of the microchannel are determined using the expressions derived in this study for the velocity distributions of charged tracer particles in the open- and closed-end rectangular microchannels. Thus, the zeta potentials of the tracer particles and the channel surfaces are simultaneously obtained using the least-square method to fit the microPIV measured velocity distribution of the tracer particles. Measurements were carried out with a microPIV system to determine the zeta potentials of the channel wall and the fluorescent tracer particles in deionized water and sodium chloride and boric acid solutions of various concentrations.     

Long-Time Stability of Multi-Dimensional Noncharacteristic Viscous Boundary Layers

We establish long-time stability of multi-dimensional noncharacteristic boundary layers of a class of hyperbolic–parabolic systems including the compressible Navier–Stokes equations with inflow [outflow] boundary conditions, under the assumption of strong spectral, or uniform Evans, stability. Evans stability has been verified for small-amplitude layers by Guès, Métivier, Williams, and Zumbrun. For large-amplitude layers, it may be efficiently checked numerically, as done in the one-dimensional case by Costanzino, Humpherys, Nguyen, and Zumbrun.     

POLAR project: Numerical modeling of the accretion column

In this paper we study the formation and evolution of radiative accretion shocks in the context of accretion columns in magnetic cataclysmic variables. The phenomenon induces extreme regimes of matter and the radiation emitted by those region dominates the observed emission from polars. A 2D hydrodynamical code, HYDRO-COOL, has been developed in order to deal with high-Mach number flows and is currently improved to produce a numerical model of the accretion column. This code is the hydrodynamical part of the HADES code which aims at modeling radiative hydrodynamical systems. The final goal of this model is to improve our understanding of observational results. First numerical results are reported here, as well as a discussion about the time-dependent evolution of the column.