A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Viscoelastic properties of nanostructured natural rubber/polystyrene interpenetrating polymer networks

The effects of the blend ratio and initiating system on the viscoelastic properties of nanostructured natural rubber/polystyrene‐based interpenetrating polymer networks (IPNs) were investigated in the temperature range of ?80 to 150 °C. The studies were carried out at different frequencies (100, 50, 10, 1, and 0.1 Hz), and their effects on the damping and storage and loss moduli were analyzed. In all cases, tan δ and the storage and loss moduli showed two distinct transitions corresponding to natural rubber and polystyrene phases, which indicated that the system was not miscible on the molecular level. However, a slight inward shift was observed in the IPNs, with respect to the glass‐transition temperatures (T_g's) of the virgin polymers, showing a certain degree of miscibility or intermixing between the two phases. When the frequency increased from 0.1 to 100 Hz, the T_g values showed a positive shift in all cases. In a comparison of the three initiating systems (dicumyl peroxide, benzoyl peroxide, and azobisisobutyronitrile), the dicumyl peroxide system showed the highest modulus. The morphology of the IPNs was analyzed with transmission electron microscopy. The micrographs indicated that the system was nanostructured. An attempt was made to relate the viscoelastic behavior to the morphology of the IPNs. Various models, such as the series, parallel, Halpin–Tsai, Kerner, Coran, Takayanagi, and Davies models, were used to model the viscoelastic data. The area under the linear loss modulus curve was larger than that obtained by group contribution analysis; this showed that the damping was influenced by the phase morphology, dual‐phase continuity, and crosslinking of the phases. Finally, the homogeneity of the system was further evaluated with Cole–Cole analysis. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1680–1696, 2003     

RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 μm atmospheric window

The absorption spectrum of natural water vapour around 1.5 μm has been recorded with a typical sensitivity of 5 × 10⁻¹⁰ cm⁻¹ by using a CW-cavity ring down spectroscopy set up based on fibred DFB lasers. A series of 31 DFB lasers has allowed a full coverage of the 6130.8-6748.5 cm⁻¹ (1.63-1.48 μm) region corresponding to the H transparency band of the atmosphere. The line parameters (wavenumber and intensity) of a total of 5190 lines, including 4247 lines of water vapor, were derived by a one by one fit of the lines to a Voigt profile. Different isotopologues of water (H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, and HD¹⁶O) present in natural abundance in the sample contribute to the spectrum. For the main isotopologue, H₂¹⁶O, 2130 lines were measured with line intensities as weak as 10⁻²⁹ cm/molecule while only 926 lines (including a proportion of 30% inaccurate calculated lines) with a minimum intensity of 3 × 10⁻²⁷ cm/molecule are provided by the HITRAN and GEISA databases. Our comparison in the whole 5750-7965 cm⁻¹ region, has also evidenced that an error in the process of conversion of the intensity units from cm⁻²/atm to cm⁻¹/(molecule × cm⁻²) at 296 K, has led to H₂¹⁶O line intensities values listed in the HITRAN-2000 database, systematically 8 % below the original FTS values. The rovibrational assignment was performed on the basis of the ab initio calculations by Schwenke and Partridge with a subsequent refinement and validation using the Ritz combination principle together with all previously measured water transitions relevant to this study. This procedure allowed determining 172, 139, 71, and 115 new energy levels for the H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, and HD¹⁶O isotopologues, respectively. The results are compared with the available databases and discussed in regard of previous investigations by Fourier transform spectroscopy. The spectrum analysis has showed that most of the transitions which cannot be assigned to water are very weak and are due to impurities such as carbon dioxide and ammonia, leaving only about 3% of the observed transitions unassigned. The interest of a detailed knowledge of water absorption for trace detectors developed in the 1.5 μm range is underlined: for instance HDO contributes significantly to the considered spectrum while no HDO line parameters are provided by the HITRAN database.     

On the number of curves of genus 2 over a finite field

In this paper we compute the number of curves of genus 2 defined over a finite field k of odd characteristic up to isomorphisms defined over k; the even characteristic case is treated in an ongoing work (G. Cardona, E. Nart, J. Pujolàs, Curves of genus 2 over field of even characteristic, 2003, submitted for publication). To this end, we first give a parametrization of all points in , the moduli variety that classifies genus 2 curves up to isomorphism, defined over an arbitrary perfect field (of zero or odd characteristic) and corresponding to curves with non-trivial reduced group of automorphisms; we also give an explicit representative defined over that field for each of these points. Then, we use cohomological methods to compute the number of k-isomorphism classes for each point in .     

2-Dimension from the Topological Viewpoint

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset.      

Large area bolometers for millimeter-wave power calibration

An accurate monolithic power meter has been developed for millimeter-wave applications. The detector is a large-area Bismuth bolometer, integrated on a fused-Quartz substrate. It simply measures the temperature change caused by the absorption of millimeter-wave radiation. The power meter is simple to fabricate, inexpensive, and can be easily calibrated using a low-frequency network. The measured responsivity for a 50 bolometer, with an area of 1×1cm, at a bias of 1V. and a video modulation of 100Hz, is 1mV/W. The noise spectrum exhibits a 1/f rolloff till 1KHz, and is limited by the Johnson noise for higher frequencies. The NEP of the detector is 3WHz^–1/2 at a video modulation of 1KHz. It is possible to decrease the current NEP by fabricating bolometers with higher responsivities. Possible application areas are absolute power calibration and localized power density measurements at millimeter and submillimeter wavelengths.     

Comparative preparations of homoleptic hydridic anions of iron and ruthenium using solution-based organometal hydrogenation techniques

A study of the preparations of the complex hydridic anions [MH(6)](4)(-) (M = Fe and Ru) reveals a number of distinctive features. Here a soluble homoleptic ruthenium hydride has been prepared for the first time. For example, both FeX(2) and [Ru(eta(4)-1,5-COD)X(2)], X = Cl and Br, react with PhMgBr solutions under hydrogen to produce the title compounds. The benzene liberated in these reactions is more readily hydrogenated in the case of a homogeneous room temperature ruthenium hydride preparation to both cyclohexane and cyclohexene. The (1)H NMR spectroscopic data show that the two complex anions have hydride absorptions in the low-frequency region, delta -20.3 and -14.7, respectively. Further, (1)H spin-lattice relaxation times (T(1)) for M-H are longer in the case of Ru vs Fe.     

(Benzylthio)- und (Arylthio)-substituierte Nitril-ylide: Thermische Erzeugung und Reaktionen

Thermal Generation and Reactions of (Benzylthio)-and (Arylthio)-Substituted Nitrile Ylides Thermolysis of 4-(benzylthio)- and 4-(arylthio)-1,3-oxazol-5(2H)-ones 6 , at 110–155° in the presence of dipolarophiles with activated C≡C, C?C, C?O, C?S, and N?N bonds, led to 5-membered cyclo-adducts and CO² (cf. Schemes 3, 5-7). Heating 6a and 6c in the presence of ethyl propiolate yielded ethyl quinoline-3-carboxylate ( 19 ) and ethyl pyridine-3-carboxylate( 22 ), respectively (cf. Scheme 8). These results are rationalized on the basis of the intermediate formation of thio-substituted nitrile ylides of type 7 (cf. Scheme 2), which undergo regioselective 1,3-dipolar cycloadditions with reactive dipolarophiles. In the absence of such a dipolarophile, the nitrile ylides isomerize via a [1,4]-H shift to give 2-aza-1,3-butadienes of type 20 . The latter are trapped in a Diels-Alder reaction with ethyl propiolate (cf. Scheme 8).     

Jet cooled NO2 intra cavity laser absorption spectroscopy (ICLAS) between 11200 and 16150 cm

We have combined the high sensitivity of the ICLAS technique with the rotational cooling effect of a slit jet expansion in order to observe and to understand the visible and near infrared NO₂ spectrum. By this way, an equivalent absorption pathlength of several kilometers through rotationally cooled molecules has been achieved. Due to the vibronic interaction between the two lowest electronic states, ²A₁ and à ²B₂, this spectrum is vibronically dense and complex. Moreover, the dense room temperature rotational structure is perturbed by additional rovibronic interactions. In contrast, the rotational analysis of our jet cooled spectrum is straightforward. The NO₂ absorption spectrum is vanishing to the IR but, owing to the high sensitivity of the ICLAS technique, we have been able to record the NO₂ spectrum down to 11200 cm⁻¹ with a new Ti:sapphire ICLAS spectrometer. As a result 249 ²B₂ vibronic bands have been observed (175 cold bands and 74 hot bands) in the 11200–16150 cm⁻¹ energy range. Due to the cooling effect of the slit jet we have reduced the rotational temperature down to about 12 K and at this temperature the K = 0 subbands are dominant. Consequently, we have analysed only the K = 0 manifold for N 7 of each vibronic band. The dynamical range of the band intensities is about one thousand. Due to the strong vibronic interaction between the ²A₁ and à ²B₂ electronic states, we observed not only the a₁ vibrational levels of the à ²B₂ state but also the b₂ vibrational levels of the ²A₁ state interacting with the previous ones. By comparison with the calculated density of states, we conclude that we have observed about 65% of the total number of ²B₂ vibronic levels located in the studied range. However, there are more missing levels in the IR because of the weakness of the spectrum in this range. The correlation properties of this set of vibronic levels have been analysed calculating the power spectrum of the absorption stick spectrum which displays periodic motions: the dominant period, at 714 ± 20 cm⁻¹, corresponds to the bending motion of the à ²B₂ state. The other observed periods remain unassigned. In contrast the next neighbor spacing distribution (NNSD) shows a strong level repulsion, i.e. a manifestation of quantum chaos. These two observations, apparently contradictory, can be rationalized as follows: the short time dynamics, for t < 10⁻¹² s, is “regular” while for longer times the dynamics becomes “chaotic”. We suggest that this behavior may be observed directly with a pump and probe fs laser experiment.