Rigid sets and nonexpansive mappings

We introduce a new class of normed spaces (not necessarily finite dimensional), which contains the finite dimensional normed spaces with polyhedral norm. We study the properties of rigid sets of the spaces of this class and we apply the results to limit sets of the sequences of iterates of nonexpansive maps.

     

Structure-energy relationship in barbituric acid: a calorimetric, computational, and crystallographic study

This paper reports the value of the standard (p(o) = 0.1 MPa) molar enthalpy of formation in the gas phase at T = 298.15 K for barbituric acid. The enthalpies of combustion and sublimation were measured by static bomb combustion calorimetry and transference (transpiration) method in a saturated N2 stream and a gas-phase enthalpy of formation value of -(534.3 +/- 1.7) kJ x mol(-1) was determined at T = 298.15 K. G3-calculated enthalpies of formation are in very good agreement with the experimental value. The behavior of the sample as a function of the temperature was studied by differential scanning calorimetry, and a new polymorph of barbituric acid at high temperature was found. In the solid state, two anhydrous forms are known displaying two out of the six hydrogen-bonding patterns observed in the alkyl/alkenyl derivatives retrieved from the Cambridge Crystallographic Database. The stability of these motifs has been analyzed by theoretical calculations. X-ray powder diffraction technique was used to establish to which polymorphic form corresponds to the commercial sample used in this study and to characterize the new form at high temperature.     

Rheological properties of microfibrillar suspension of TEMPO-oxidized pulp

The rheology of cellulose microfibril suspensions from TEMPO-oxidized pulp was investigated. The suspension showed a pseudo-plastic and thixotropic behavior, slowly evolving with time under a given shear rate. The viscosity was proportional to the concentration up to the critical concentration of 0.23%. Above it, the viscosity followed a power law with exponents from 2 to 6 depending on the shear rate, and the system showed shear thinning behavior and behaved gel-like. Below this concentration, the system was more Newtonian. Birefringence measurement of 0.44% and 0.78% suspension showed that microfibrils alignment saturated at a small shear rate with a Herman’s orientation parameter below 0.65 probably due to the interconnection of microfibrils.     

Gadolinium chelate coated gold nanoparticles as contrast agents for both X-ray computed tomography and magnetic resonance imaging

Functionalized gold nanoparticles were applied as contrast agents for both in vivo X-ray and magnetic resonance imaging. These particles were obtained by encapsulating gold cores within a multilayered organic shell which is composed of gadolinium chelates bound to each other through disulfide bonds. The contrast enhancement in MRI stems from the presence of gadolinium ions which are entrapped in the organic shell, whereas the gold core provides a strong X-ray absorption. This study revealed that these particles suited for dual modality imaging freely circulate in the blood vessels without undesirable accumulation in the lungs, spleen, and liver.     

Simulating electron spin resonance spectra of nitroxide spin labels from molecular dynamics and stochastic trajectories

Simulating electron spin resonance spectra of nitroxide spin labels from motional models is necessary for the quantitative analysis of experimental spectra. We present a framework for modeling the spin label dynamics by using trajectories such as those from molecular dynamics (MD) simulations combined with stochastic treatment of the global protein tumbling. This is achieved in the time domain after two efficient numerical integrators are developed: One for the quantal dynamics of the spins and the other for the classical rotational diffusion. For the quantal dynamics, we propagate the relevant part of the spin density matrix in Hilbert space. For the diffusional tumbling, we work with quaternions, which enables the treatment of anisotropic diffusion in a potential expanded as a sum of spherical harmonics. Time-averaging arguments are invoked to bridge the gap between the smaller time step of the MD trajectories and the larger time steps appropriate for the rotational diffusion and/or quantal spin dynamics.     

Lamellar-to-nematic phase transition in a lipid-surfactant mixture

A lyotropic system, consisting of a lecithin (DMPC) and a non-ionic surfactant (C₁₂E₅) in water was studied. The system exhibits a lamellar-to-nematic phase transition. The nematic phase appears as the temperature is decreased and only exists in a very limited temperature and concentration range, for specific lipid-to-surfactant ratios. While a lamellar phase is found at higher temperatures in both mixed and pure C₁₂E₅ systems, the transition to the nematic phase at lower temperatures coincides with a micellar phase in the pure C₁₂E₅ system. The transition appears to be driven by the strong temperature dependence of the surfactant film spontaneous curvature. The structural properties of the lamellar phase close to the lamellar-to-nematic boundary have been studied by polarised light microscopy and small-angle neutron and X-ray scattering experiments. The signature of a helical defect with Burgers vector of magnitude 2 is apparent in our data, close to the lamellar-to-nematic phase transition. The proliferation of screw dislocations in the lamellar phase might be a plausible mechanism for driving this transition. Received 6 July 1999 and Received in final form 17 April 2000     

Undulation instability under shear: A model to explain the different orientations of a lamellar phase under shear?

We study the effects of a dilation on a sheared smectic A phase. Through a linear analysis, we show that undulation may grow in the direction of the flow and of the vorticity as found in previous works. At higher shear rates, we evidence that the undulation along the flow disappears whereas it persists in the vorticity direction. We determine the stable or unstable zone as a function of the shear rate and of the lamellar spacing. This allows us to draw a theoretical shear diagram of the instability. Finally we compare our results with the orientations found experimentally in a lyotropic lamellar phase under shear. Our diagram describes qualitatively and quantitatively the transition observed at high shear rate. Received 18 October 1999