Titan Based Hybrid Organic-Inorganic Gels Comprising Carbohydrate Moiety

Abstract

A series of titanium based gels comprising carbohydrate moieties was synthesized. The sugars used include a specific hydrazide group as complex forming agent. Additionally, this group forms stable hydrates which allow further slow water release. As a result, the compounds used in this study form transparent and stable gels with titanium alkoxide without addition of external water. Interpretation of the IR-spectra reveals that some compounds form monodentate ligands and other bidentate ligands. Further Tian-Calvet calorimetric measurements confirmed our IR-based conclusions. This strategy of synthesis gives a new opportunity to obtain hybrid materials by addition of natural chelating ligands to slow down the hydrolysis/condensation reactions that occur during the sol-gel process. Therefore, carbohydrate moieties have been incorporated in the gels obtained and different type of Ti coordination was proposed based on the IR spectroscopy studies. SEM investigations show the influence of the ligand on the morphology of the xerogel.

GRAPHICAL ABSTRACT      

Quantum Hall Phases and Plasma Analogy in Rotating Trapped Bose Gases

A bosonic analogue of the fractional quantum Hall effect occurs in rapidly rotating trapped Bose gases: There is a transition from uncorrelated Hartree states to strongly correlated states such as the Laughlin wave function. This physics may be described by effective Hamiltonians with delta interactions acting on a bosonic N-body Bargmann space of analytic functions. In a previous paper (Rougerie et al. in Phys. Rev. A 87:023618, 2013) we studied the case of a quadratic plus quartic trapping potential and derived conditions on the parameters of the model for its ground state to be asymptotically strongly correlated. This relied essentially on energy upper bounds using quantum Hall trial states, incorporating the correlations of the Bose-Laughlin state in addition to a multiply quantized vortex pinned at the origin. In this paper we investigate in more details the density of these trial states, thereby substantiating further the physical picture described in (Rougerie et al. in Phys. Rev. A 87:023618, 2013), improving our energy estimates and allowing to consider more general trapping potentials. Our analysis is based on the interpretation of the densities of quantum Hall trial states as Gibbs measures of classical 2D Coulomb gases (plasma analogy). New estimates on the mean-field limit of such systems are presented.     

A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators

In the limit of a nonlinear diffusion model involving the fractional Laplacian we get a “mean field” equation arising in superconductivity and superfluidity. For this equation, we obtain uniqueness, universal bounds and regularity results. We also show that solutions with finite second moment and radial solutions admit an asymptotic large time limiting profile which is a special self-similar solution: the “elementary vortex patch”.     

3D Gabor analysis of transient waves propagating along an AT cut quartz disk

Laser detection methods allow the investigation of ultrasonic transient phenomena in both space and time dimensions. Used for the experimental investigation of surface wave propagation along a 2D surface, laser ultrasonic leads to three dimensional (3D) space-time signal collections. The classical high resolution signal processing methods or 3D Fourier Transforms can be used in order to extract the wave propagation information, however these methods are not adapted for identifying where and when the waves are generated. In order to quantify these transient aspects in the space-time-wave number-frequency domains, the 3D Gabor transform is introduced. The 3D Gabor transform properties are presented. The potential of the 3D Gabor for the identification of the local and transient complex wave numbers is illustrated on the propagation of surface waves on a piezoelectric quartz (AT cut, 6 MHz). In this experimental study, the quartz is excited by a voltage pulse and the quartz surface is scanned by a laser vibrometer. The 3D Gabor analysis shows that the circular electrodes borders generate anti-phase surface waves that propagates outside the electrodes, with a strong energy contribution in the low frequency domain (<1 MHz). The transient analysis also points out, for higher frequencies, where the surface waves are generated and how they propagate with respect of both to the geometry of the electrodes and the crystallographic axis of the quartz. These results confirm the theoretical modal analysis and provide new knowledge about the key role played by the electrodes border. This will allow the optimization of the electrodes shape in order to design low frequency Lamb wave sensors.     

Laser ultrasonic analysis of normal modes generated by a voltage pulse on an AT quartz sensor

Laser ultrasonic detection is a versatile and highly sensitive tool for the observation of surface waves. In the following study, laser ultrasonic detection is used for the experimental study of spurious normal vibration modes of a disk quartz sensor excited by a voltage pulse. The AT cut crystal (cut of the crystal relative to the the main crystallographic axis is 35.25 degrees) is optimal for generating mainly thickness-shear vibrations (central frequency 6 MHz) on the quartz surface. However, resulting from shear-to-longitudinal and shear-to-surface mode conversion, and from the weak coupling with the other crystallographic axes, other modes (thickness-compressional and bending modes) are always present in the plate response. Since the laser vibrometer is sensitive to normal displacements, the laser investigation shows waves that can be considered as unwanted for the AT quartz used as a shear sensor. The scanned three dimensional (3D) amplitude-space-time signals are carefully analysed using their representation in three dual Fourier domains (space-time, wave number-frequency). Results on the transient analysis of the waves, the normal bending modes and the dispersion curves are shown.