Collisions between type II two-dimensional quadratic solitons

We report experimental and numerical results that describe collisions between two-dimensional type II quadratic solitons excited in a KTP crystal by fundamental waves of orthogonal polarization. Our results provide experimental evidence of the possibility of both inelastic collision (when two quadratic solitons merge at input into a single soliton at output) and quasi-elastic collision.     

Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity Calculation∗

ABSTRACT

The semi-analytical method of design sensitivity analysis that is widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements is studied in this paper. It is shown that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Errors are shown to be associated with an incompatibility of the sensitivity field with the structure. An error index is developed to test the accuracy of the semi-analytical method. It characterizes the difference in errors between a general finite difference method and the semi-analytical method. A method for improving the accuracy of the semi-analytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.     

How topological rearrangements and liquid fraction control liquid foam stability

The stability of foam is investigated experimentally through coalescence events. Instability (coalescence) occurs when the system is submitted to external perturbations (T1) and when the liquid amount in the film network is below a critical value. Microscopically, transient thick films are observed during film rearrangements. Film rupture, with coalescence and eventual collapse of the foam, occurs when the available local liquid amount is too small for transient films to be formed. Similar experiments and results are shown in the two-bubble case.     

Quadrupolar interaction study of various cations confined in porous charged polymer film of sPI ionomers

The structure of a sulfonated polyimide (sPI) ionomer membranes was investigated via the transport properties of various confined cations (7Li+, 23Na+, 87Rb+, 133Cs+). Their NMR spectra show large residual quadrupolar splitting depending on the orientation of the film in the static magnetic field B0. This behavior is the fingerprint of a macroscopic nematic ordering of charged interfaces. This is also confirmed by the anisotropy of the self-diffusion tensor measured by 1H and 7Li PGSE experiments on N(CH3)4+ and Li+ cations, respectively.     

Ferromagnetic and antiferromagnetic intermolecular interactions in a new family of Mn4 complexes with an energy barrier to magnetization reversal

A new family of tetranuclear Mn complexes [Mn4X4L4] (H2L = salicylidene-2-ethanolamine; X = Cl (1) or Br (2)) and [Mn4Cl4(L')4] (H2L' = 4-tert-butyl-salicylidene-2-ethanolamine, (3)) has been synthesized and studied. Complexes 1-3 possess a square-shaped core with ferromagnetic exchange interactions between the four Mn(III) centers resulting in an S = 8 spin ground state. Magnetochemical studies and high-frequency EPR spectroscopy reveal an axial magnetoanisotropy with D values in the range -0.10 to -0.20 cm(-1) for complexes 2 and 3 and for differently solvated forms of 1. As a result, these species possess an anisotropy-induced energy barrier to magnetization reversal and display slow relaxation of the magnetization, which is observed as hysteresis for 1 and 3 and frequency-dependent peaks in out-of-phase AC susceptibility measurements for 3. The effective energy barrier was determined to be 7.7 and 7.9 K for 1 and 3, respectively, and evidence for quantum tunneling of the magnetization was observed. Detailed magnetochemical studies, including measurements at ultralow temperatures, have revealed that complexes 1 and 2 possess solvation-dependent antiferromagnetic intermolecular interactions. Complex 3 displays ferromagnetic intermolecular interactions and approaches a ferromagnetic phase transition with a critical temperature of approximately 1 K, which is coincident with the onset of slow relaxation of the magnetization due to the molecular anisotropy barrier to magnetization reversal. It was found that the intermolecular interactions have a significant effect on the manifestation of slow relaxation of the magnetization, and thereby, these complexes represent a new family of "exchange-biased single-molecule magnets", where the exchange bias is controlled by chemical and structural modifications.     

Estimation of conditional laws given an extreme component

Let (X,Y) be a bivariate random vector. The estimation of a probability of the form P(Y ≤ y |X > t) is challenging when t is large, and a fruitful approach consists in studying, if it exists, the limiting conditional distribution of the random vector (X,Y), suitably normalized, given that X is large. There already exists a wide literature on bivariate models for which this limiting distribution exists. In this paper, a statistical analysis of this problem is done. Estimators of the limiting distribution (which is assumed to exist) and the normalizing functions are provided, as well as an estimator of the conditional quantile function when the conditioning event is extreme. Consistency of the estimators is proved and a functional central limit theorem for the estimator of the limiting distribution is obtained. The small sample behavior of the estimator of the conditional quantile function is illustrated through simulations. Some real data are analysed.     

Bayesian model averaging for multivariate extremes

The main framework of multivariate extreme value theory is well-known in terms of probability, but inference and model choice remain an active research field. Theoretically, an angular measure on the positive quadrant of the unit sphere can describe the dependence among very high values, but no parametric form can entirely capture it. The practitioner often makes an assertive choice and arbitrarily fits a specific parametric angular measure on the data. Another statistician could come up with another model and a completely different estimate. This leads to the problem of how to merge the two different fitted angular measures. One natural way around this issue is to weigh them according to the marginal model likelihoods. This strategy, the so-called Bayesian Model Averaging (BMA), has been extensively studied in various context, but (to our knowledge) it has never been adapted to angular measures. The main goal of this article is to determine if the BMA approach can offer an added value when analyzing extreme values.     

Local structure of Mn4+ and Fe3+ spin probes in layered LiAlO2 oxide by modelling of zero-field splitting parameters

The zero-field splitting parameters (ZFS) of Mn(4+) and Fe(3+) ions in LiAlO(2) with a layered structure are analyzed experimentally and theoretically by using high-frequency electron paramagnetic resonance spectroscopy, Neuman superposition model (NSM), DFT and multiconfigurational calculations. The interpretation of ZFS is based on the comparison of the experimentally determined values with the calculated ones. This approach allows assessing the performance of different methods for computation of ZFS of Fe(3+) and Mn(4+) in layered oxide matrices. DFT and multiconfigurational calculations are used to analyze the effect of oxygen, aluminium, and lithium neighbours on ZFS of Fe(3+) and Mn(4+). These calculations are based on a cluster comprising Fe(3+) or Mn(4+) ions in a trigonally compressed octahedron with 6 metal ions (Al(3+) or Co(3+)) as first metal neighbours and 6 O(2-) and 2 Li(+) (above and below the layer) as second neighbours. A satisfactory agreement with the experimental data is achieved when the local structure of Mn(4+) and Fe(3+) deviates from the trigonal host-site geometry. The local structure of Fe(3+) comprises an axial distortion, while trigonal environment with reduced extent of distortion appears around Mn(4+).     

Effective boundary condition at a rough surface starting from a slip condition

We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength ?. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit ε=0 is always no-slip. We give in this paper error estimates for this homogenized no-slip condition, and provide a more accurate effective boundary condition, of Navier type. Our result extends those obtained in Basson and Gérard-Varet (2008) [6] and Gerard-Varet and Masmoudi (2010) [13], in which the special case of a Dirichlet condition at the rough boundary was examined.     

Adsorption of multilamellar tubes with a temperature tunable diameter at the air/water interface

The ethanolamine salt of 12-hydroxy stearic acid is known to form tubes having a temperature tunable diameter. Here, we study the behavior of those tubes at the air/water interface by using Neutron Reflectivity. We observed that tubes indeed adsorbed at this interface below a fatty acid monolayer and exhibit the same temperature behavior as in bulk. There is however a peculiar behavior at around 50 °C for which the increase of the diameter of the tubes at the interface yields an unfolding of those tubes into a multilamellar layer. Upon further heating, the tubes re-fold and their diameter re-decreases after which they melt into micelles as observed in the bulk. All structural transitions at the interface are nevertheless reversible. This provides to the system a high interest for its interfacial properties because the structure at the air/water interface can be tuned easily by the temperature.