Well-posedness of the spatially homogeneous Landau equation for soft potentials

We consider the spatially homogeneous Landau equation of kinetic theory, and provide a differential inequality for the Wasserstein distance with quadratic cost between two solutions. We deduce some well-posedness results. The main difficulty is that this equation presents a singularity for small relative velocities. Our uniqueness result is the first one in the important case of soft potentials. Furthermore, it is almost optimal for a class of moderately soft potentials, that is for a moderate singularity. Indeed, in such a case, our result applies for initial conditions with finite mass, energy, and entropy. For the other moderately soft potentials, we assume additionally some moment conditions on the initial data. For very soft potentials, we obtain only a local (in time) well-posedness result, under some integrability conditions. Our proof is probabilistic, and uses a stochastic version of the Landau equation, in the spirit of Tanaka [H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Z. Wahrsch. Verw. Geb. 46 (1) (1978-1979) 67-105].     

Effects of an anisotropic parabolic potential and Coulomb’s impurity potential on the energy characteristics of asymmetrical semi-exponential CsI quantum wells

Because of its unique optoelectronic properties,people have studied the characteristics of polarons in various quantum well(QW)models.Among them,the asymmetrical semiexponential QW(ASEQW)is a new model for studying the structure of QWs in recent years.It is of great significance to study the influences of the impurity and anisotropic parabolic confinement potential(APCP)on the crystal’s properties,because some of the impurities,usually regarded as Coulomb’s impurity potential(CIP),will exist in the crystal more or less,and the APCP has flexible adjustment parameters.However,the energy characteristics of the ASEQW under the combined actions of impurities and APCP have not been studied,which is the motivation of this paper.Using the linear combination operation and Lee-Low-Pines unitary transformation methods,we investigate the vibrational frequency and the ground state energy of the strong coupling polaron in an ASEQW with the influences of the CIP at the origin of coordinates and APCP,and make a comparison between our results and previous literature’s.Our numerical results about the energy properties in the ASEQW influenced by the CIP and APCP may have important significances for experimental design and device preparation.     

Experimental characterization of dynamic behaviour of gelatin-based material using DIC

In this paper, the dynamic response of gelatin-based soft material under impact loading is investigated. The dynamic tests are principally performed by the classical SHPB (Split Hopkinson Pressure Bars) technique. However, due to the very low mechanical impedance of the specimen compared with the Hopkinson bars, the feeble impact forces are measured by highly sensitive piezoelectric polyvinylidene fluoride (PVDF) pressure sensors instead of SHPB measurement system. The PVDF pressure sensors are placed on the interfaces between the specimen and the bars. During the impact test, the non-equilibrium stress state and inhomogeneous strain fields are developed in the specimen; a digital image correlation (DIC) technique is proposed to identify the inhomogeneous displacement fields using high speed photography. A non-parametric approach based on the DIC technique is developed to deduce the transient stress fields in the longitudinal and transverse directions from the displacement fields measured by DIC. The validation of the calculated stress fields is performed by comparing them with the stress measurements from the PVDF pressure sensor at the bottom end of the specimen. Furthermore, stress-strain response is carried out using this approach throughout the specimen. It is clearly shown that the average highest strain rate varies with position in the specimen. This lead to multiple stress-strain relations determined at different strain rates by only one impact test. The significant strain rate sensitivity is observed at the tested rate range from 81/s to 269/s. Under compression loading, the axial stress state is developed as a simple compression only in the central part of the specimen due to the friction at the interfaces between the specimen and the bars. According to the calculated results based on movement of “long waves”, the region of the simple compression stress state in the central part of the specimen is localized. It is observed that the axial stress is much more important than the transverse stress in the central part and this confirms the assumption of uni-axial compression stress state in the specimen.     

Mechanically Strong Janus Poly(N-isopropylacrylamide)/Graphene Oxide Hydrogels as Thermo-responsive Soft Robots

Simple preparation of stimuli-responsive hydrogels with good mechanical properties and mild stimuliresponsiveness is essential for their applications as smart soft robots.Mechanically strong Janus poly(Nisopropylacrylamide)/graphene oxide (PNIPAM/GO) nanocomposite hydrogels with stimuli-responsive bending behaviors are prepared through a simple one-step method by using molds made of a Teflon plate and a glass plate.Residual oxygen in the air bubbles on the Teflon plate surface affects the polymerization and hence the cross-linking density,leading to the different swelling/deswelling rates of the two sides of the gels.Therefore,the hydrogels exhibit bending/unbending behaviors upon heating/cooling in water.The incorporation of GO nanosheets dramatically enhances the mechanical properties of Janus hydrogels.Meanwhile,the photo-responsive property of the GO nanosheets also imparts the hydrogels with remotecontrollable deformation under IR irradiation.The application of the Janus PNIPAM/GO hydrogels as thermo-responsive grippers is demonstrated.     

Confining effect on the bearing capacity of circular footings on a purely cohesive soilEffet du confinement sur la capacité portante d'une fondation circulaire sur un sol purement cohérent

The bearing capacity of axially symmetrical footings acting on a purely cohesive soil foundation contained by a rigid wall at a finite distance is investigated within the framework of the Yield design theory. Following the same tracks as in a preceding paper devoted to strip footings, the analysis is performed by referring to already existing results concerning the bearing capacity of a circular footing on a soil layer with limited thickness. It comes out that the bearing capacity factor determined by Eason and Shield for a rough circular footing on an unlimited soil foundation is increased by a correction factor that increases when the diameter of the container decreases. Comparison with the results obtained for strip footings acting on a purely cohesive soil in the same conditions shows that the confining effect is significantly lower for a circular footing than for a strip footing. To cite this article: J. Salençon, C. R. Mecanique 330 (2002) 521–525.     

High-pressure investigations under CO/H2 of rhodium complexes containing hemispherical diphosphites

The two rhodium complexes [Rh(acac)(L(R))] (L(R)=(S,S)-5,11,17,23-tetra-tert-butyl-25,27-di(OR)-26,28-bis(1,1'-binaphthyl-2,2'-dioxyphosphanyloxy)calix[4]arene; 6: R=benzyl, 7: R=fluorenyl), each based on a hemispherical chelator forming a pocket about the metal centre upon chelation, are active in the hydroformylation of 1-octene and styrene. As expected for this family of diphosphanes, both complexes resulted in remarkably high selectivity towards the linear aldehyde in the hydroformylation of 1-octene (l/b≈15 for both complexes). Linear aldehyde selectivity was also observed when using styrene, but surprisingly only 6 displayed a marked preference for the linear product (l/b=12.4 (6) vs. 1.9 (7)). A detailed study of the structure of the complexes under CO or CO/H(2) in toluene was performed by high-pressure NMR (HP NMR) and FT-IR (HP-IR) spectroscopies. The spectroscopic data revealed that treatment of 6 with CO gave [Rh(acac)(CO)(η(1)-L(benzyl))] (8), in which the diphosphite behaves as a unidentate ligand. Subsequent addition of H(2) to the solution resulted in a well-defined chelate complex with the formula [RhH(CO)(2)(L(benzyl))] (9). Unlike 6, treatment of complex 7 with CO only led to ligand dissociation and concomitant formation of [Rh(acac)(CO)(2)], but upon addition of H(2) a chelate complex analogous to 9 was formed quantitatively. In both [RhH(CO)(2)(L(R))] complexes the diphosphite adopts the bis-equatorial coordination mode, a structural feature known to favour the formation of linear aldehydes. As revealed by variable-temperature NMR spectroscopy, these complexes show the typical fluxionality of trigonal bipyramidal [RhH(CO)(2)(diphosphane)] complexes. The lower linear selectivity of 7 versus 6 in the hydroformylation of styrene was assigned to steric effects, due to the pocket in which the catalysis takes place being less adapted to accommodate CO or larger olefins and, therefore, possibly leading to facile ligand decoordination. This interpretation was corroborated by an X-ray structure determination carried out for 7.     

Properties of Ionic Liquid Confined in Porous Silica Matrix

Porous silica matrices of different pore sizes with confined ionic liquid (1‐butyl‐3‐methylimidazolium hexafluorophosphate) [BMIM] [PF₆] were prepared by sol‐gel technique using a tetraethyl orthosilicate (TEOS) precursor with an aim to study the changes in physico‐chemical properties of ionic liquid on confinement. It is found that on confinement 1) melting point decreases, 2) fluorescence spectra shows a red shift and 3) the vibrational bands are affected particularly those of imadazolium ring, which interacts more with the walls of the silica matrix. Preliminary theoretical calculations suggest that SiO₂ matrix interact more with the heterocyclic group of [BMIM] cation than the tail alkyl chain end group resulting in significant changes in the aromatic vibrations.     

Micro-patterning of vapor-phase polymerized poly(3,4-ethylenedioxythiophene) (PEDOT) using ink-jet printing/soft lithography

Highly conductive and transparent poly(3,4-ethylenedioxythiophene) (PEDOT) thin films can be prepared effectively via vapor-phase polymerization (VPP) with the addition of imidazole (Im) based derivatives. The addition of Im that has one and/or two alkyl substituents significantly improved the electrical conductivity of PEDOT thin films. In an effort to develop a facile PEDOT micro-patterning method, we investigated ink-jet printing and soft lithography. The procedure of oxidant patterning with a weak base followed by VPP of a 3,4-ethylenedioxythiophene (EDOT) monomer provides an effective and simple method for micro-patterning of an intrinsic conductive polymer (ICP).