Strong ergodicity of the regime-switching diffusion processes

We provide criteria for the strong ergodicity of regime-switching diffusion processes. Our conditions are imposed on the coefficients of the processes. Particularly, we show that for regime-switching diffusions on the half line, if the corresponding diffusion on each fixed environment is strongly ergodic, then the regime-switching diffusion is strongly ergodic as well, which does not depend on the changing rate of the environment. Moreover, the converse is not always true, which is shown by an example. For transience, recurrence and positive recurrence, there is no such good consistency [R. Pinsky and M. Scheutzow, Some remarks and examples concerning the transience and recurrence of random diffusions, Ann. Inst. Henri. Poincaré 28 (1992) 519–536].     

Orientation and conformation of two [6]carbohelicenes in stretched polystyrene and a thermoresponsive polyaspartate

Two functionalized [6]carbohelicenes, one of which was also available in its two enantiomeric pure forms, were oriented in stretched polystyrene in CDCl₃, and in a recently introduced chiral thermoresponsive lyotropic polyaspartate (poly(benzyl)_0.5(phenethyl)_0.5-L-aspartate) in C₂D₂Cl₄. From the resulting ¹H,¹³C residual dipolar couplings, the helical pitch of a methylated [6]carbohelicene was determined and found to be in agreement with theoretical predictions and existing crystal structures (d(C2,C2′) ≈ 4.3 Å). For a second [6]carbohelicene with para-methoxyphenyl substituents, a clear conformational preference of the substituents was observed. The orientational properties of the two helicene enantiomers in the chiral polyaspartate are very similar, but both drastically change around 306 K. We suggest this behavior is due to an unusual phase transition in the liquid crystal.     

The stabilizability of heat equations with time-dependent coefficients

In this paper, we study the stabilizability of heat equations with time-dependent coefficients. The instability of the systems is illustrated by special solutions. The boundary feedback stabilization results are established by the backstepping method where the growth order of the kernel function depends on time.     

On a hidden symmetry of quantum harmonic oscillators

We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal kinematical invariance group on the standard solutions. In addition, the phase space oscillations of the electron position and linear momentum probability distributions are computer animated and some possible applications are briefly discussed. A visualization of the Heisenberg uncertainty principle is presented.     

Intermolecular spin–spin coupling constants between P atoms

This paper reports the study by NMR spectroscopy and ab initio methods of the structure of 3,4-dimethyl-1-cyanophosphole and its dimer. The dimer presents a P···P interaction of the pnictogen type due to the presence of σ-holes. NMR of the monomer was recorded in CDCl₃ solution while NMR of the dimer corresponds to the solid state (CPMAS) experiments. The ^2pJ_PP spin–spin coupling constant has not been measured, but calculated at the B3LYP level. AIM, NBO and ELF methodologies have been used to describe the electronic structure of the dimer.     

Filler effects on the thermomechanical response of stretched rubbers

This paper deals with the calorimetric analysis of deformation processes in filled styrene-butadiene rubbers. More especially, the study focuses on the effects of the addition of carbon black fillers on the calorimetric response of “demullinized” SBR. Temperature variations are measured by infrared thermography during cyclic uniaxial tensile tests at ambient temperature. Heat sources¹ produced or absorbed by the material due to deformation processes are deduced from temperature fields by using the heat diffusion equation. First, the results show that no mechanical (intrinsic) dissipation is detected for weakly filled SBR, meaning that the heat produced and absorbed over one mechanical cycle is the same whatever the stretch ratio reached. Second, the mechanical dissipation in highly filled SBR is significant. The quantitative analysis carried out highlights the fact that it increases quasi-linearly with the stretch ratio. Finally, a simplified framework is proposed to discuss the identification of the heat sources, in particular the mechanical dissipation.