Smoothing Effect for the Regularized Schrödinger Equation with Non-Controlled Orbits

We prove that the geometric control condition is not necessary to obtain the smoothing effect and the uniform stabilization for the strongly dissipative Schrödinger equation.     

Synthesis and crystal structure of [3,5-(CH3)2C6H3NH3]4P4O12·3H2O

Chemical preparation and crystal structure are given for a new cyclotetraphosphate: [3,5-(CH₃)₂C₆H₃NH₃]₄P₄O₁₂·3H₂O. This compound is triclinic P with the following unit-cell parameters: a=8.298(3), b=8.299(3), c=17.242(7)Å, α=97.13(3), β=102.72(3), γ=64.55(3)°, Z=1 and V=1045.2(8)ų. The crystal structure has been solved and refined to R=0.040 using 6086 independent reflections. The atomic arrangement can be described as layers organization. Layers built by P₄O₁₂ ring anions, ammonium groups and water molecules parallel to the plan (001), between which the organic groups are located. Characterization by X-ray diffraction, IR absorption, and thermal analysis are described.     

Synthesis and resolution of a new helically chiral azahelicene

Helically chiral azahexahelicene 3 was prepared in four steps using the Mizoroki-Heck coupling followed by classical oxidative photodehydrocyclisation. Resolution of this new chiral system was achieved through separation by HPLC providing (−)- and (+)-3 in high optical purity. The absolute configurations of (−)- and (+)-3 were assigned as M and P, respectively, by means of circular dichroism. Each of the hexacyclic systems (M)-(−)- and (P)-(+)-3 was reacted with boron tribromide to provide the corresponding helical pyridophenols in good yields.     

Non-parametric identification of the non-homogeneous stress in high strain-rate uni-axial experiments

Stress and strain homogeneity, in tested samples, is a crucial assumption during a dynamic test. Whenever this assumption is true, the conventional recovery of the mean strain and stress is valid. However, when the stress and strain fields in the sample are not homogeneous, more sophisticated treatment must be considered. Inverse problem techniques are then proposed. Nevertheless, they may yield a non-physical result. In this paper, a non-parametric solution to the problem of non-homogeneity in dynamic tests is presented. The stress field is deduced from the displacement field measured via a Digital Speckle Photography (DSP) technique and a force boundary condition.     

Theoretical and numerical study of Couette-Taylor flow with an axial flow using lattice Boltzmann method

In this study, the numerical models for swirling flows developed by Li et al and Zhou for lattice Boltzmann method (LBM) are chosen. These models were firstly validated using the Couette-Taylor flow between two concentric cylinders simulations. Numerical results showed the efficiency of the Zhou's model. Numerical simulation results using LBM are in good agreement for the steady and unsteady regimes compared to the literature review. In a second step, the Zhou model was then adopted to our study to determine the Couette-Taylor instabilities with an axial flow. Two protocols are tested. The first one (direct protocol) starts with an azimuthal flow without any axial flow (Re = 0). Once the regime is established, an axial flow is then superposed to the Couette-Taylor flow (with a sudden or a progressive manner). The second protocol (inverse protocol) starts with an axial flow at a given Reynolds number (Poiseuille flow). Once the regime is established, an azimuthal flow is the executed (with a sudden or a progressive manner). The effect of various parameters controlling the physical situation is also discussed. The increase of the azimuthal velocity mainly led to the emergence and development of Taylor vortices. Its influence decreases when the axial Reynolds number increases. The relevant result for this study is the change of the critical axial Reynolds number Re_c (total disappearance of instabilities) with both protocols and both manners.     

Helically chiral functionalized [6]helicene: Synthesis,optical resolution,and photophysical properties

A short and efficient synthetic pathway leading to a new chiral π-conjugated system is reported. The X-ray structure of the target compound was determined and showed a helical conformation. Its resolution was successfully accomplished, leading to two enantiomers in high optical purity, and their chiroptical properties were examined experimentally. The photophysical properties of the organic material were also evaluated, showing an emission in the visible region, and HOMO and LUMO levels have been estimated experimentally, demonstrating an electrochemical band gap of 2.37 eV.     

Synthesis and characterization of new heptacyclic helicenes

New helically chiral substituted heptacyclic systems have been prepared from a simple phenanthrene building block in good yields and purity, via a four-step sequence involving palladium-catalysed Heck coupling and oxidative photocyclization. X-ray crystal structure analysis indicated that the conformation resembled that of the unsubstituted heptahelicene. The optical properties of these heptacyclic helicenes were investigated and show interesting behaviour.     

Synthesis and characterization of a new hexacyclic helicene

A new helically chiral hexacyclic system, bearing an acetoxymethyl group, was prepared from a simple naphthalene building block in good yield and purity, via a four-step sequence involving palladium-catalysed Heck couplings and oxidative photocyclizations. Suitable crystals of the latter indicate that its conformation closely resembles that of unsubstituted [6]helicene, whose idealized symmetry is C₂. The optical properties of the hexacyclic helicene were investigated and show interesting behaviour.