Aspect ratio effects on three-dimensional incompressible flow in a two-sided non-facing lid-driven parallelepiped cavity

A numerical study of the three-dimensional fluid flow has been carried out to determine the effects of the transverse aspect ratio, Ay, on the flow structure in two-sided non-facing lid-driven cavities. The flow is complex, unstable and can undergo bifurcation. The numerical method is based on the finite volume method and multigrid acceleration. Computations have been investigated for several Reynolds numbers and various aspect ratio values. At a fixed Reynolds number, Re=500, the three-dimensional flow characteristics are analyzed considering four transverse aspect ratios, Ay=1,0.75,0.5 and 0.25. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. An analysis of the flow evolution shows that, at Ay=0.75, the flow bifurcates to a periodic regime at (Re=600) with a frequency f=0.093 less than the predicted value in the cubical cavity. A correlation is established when Ay=0.5 and gives the critical Reynolds number value. At Ay=0.25, the periodic regime occurs at high Re value beyond 3500, after which the flow becomes chaotic. It is shown that, when increasing Ay over the unit, the flow in the cavity exhibits a complex behavior. The kinetic energy transmission from the driven walls to the cavity center is reduced at low Ay values.     

Ab initio investigation of the electronic and vibrational properties for the (CaLi)+ ionic molecule

A wide adiabatic study has been performed for numerous electronic states of CaLi⁺ molecular ion. The adiabatic potential energy curves and their spectroscopic constants (R_e, D_e, ω_e and T_e) have been calculated using an ab initio approach including a nonempirical pseudo-potential for the Ca and Li cores with the core polarisation potentials operator through full configuration interaction (FCI). Thereafter, the energies of vibrational levels and their spacing for all these states have been reported. In addition, the electric dipole moment curves have been investigated for the (1-19) Σ, (1-12) Π and (1-8) Δ electric states. Moreover it lets us check the extreme transition dipole moments (TDM). These behaviours of TDM are more accustomed to estimate the radiative lifetimes for all vibrational levels in 2¹Σ⁺ and 3¹Σ⁺ states. Also, the bound-bound and the bound-free contribution have been calculated precisely and by employing a Franck–Condon (FC) approximation.     

Optical Detection and Spectroscopy of Single Molecules

The optical study of single molecules opens new paths in molecular spectroscopy, solid state physics and quantum optics. And recent experiments at room temperature hold great promise for chemistry and biology as well     

Homogenization of a three-phase flow model in porous media

We give homogenization results for an immiscible and incompressible three-phase flow model in a heterogeneous petroleum reservoir with periodic structure, including capillary effects. We consider a model which leads to a coupled system of partial differential equations which includes an elliptic equation and two nonlinear degenerate parabolic equations of convection–diffusion types. Using two-scale convergence, we get an homogenized model which governs the global behavior of the flow. The determination of effective properties require the numerical resolution of local problems in a standard cell.     

A comparative study of cationic distribution in the systems Li1+5XM1−XO3 and Li1+XM1−XM′ XO3 (M=Nb,M′=Ti; M=Ta,M′=Ti,Zr, Sn)

Abstract

A comparative ferroelectric and NMR studies of the systems Li_1+5X M_1?XO₃ and Li_1+XM_1?XM^′ _XO₃ (M=Nb, M′=Ti M = Ta; M′=Ti, Zr, Sn) have indicated that plot of T_C versus composition can be qualitatively explained on the basis of cationic distribution. The strong drop of T_C has been found in systems with all cations in octahedral sites, whereas little change of T_C was observed along the solid solutions with Li-ions in interstitial tetrahedral sites.     

Stochastic optimal multi-modes switching with a viscosity solution approach

We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary (_gij(t,x)≥0$g_{ij}(t,x)\ge 0$). We show existence of the optimal strategy, via a verification theorem. Finally, when the state of the system is a Markov process, we show that the vector of value functions of the optimal problem is the unique viscosity solution to the system of m$m$ variational partial differential inequalities with inter-connected obstacles.     

Crystal structures of two allotropic forms of Na2CoP2O7

Na₂CoP₂O₇ may be prepared in two allotropie forms:I, rose,M _r =278.85, triclinic, P1,a=9.735(2),b=10.940(3),c=12.289(4) Å,=148.78,=121.76(1), =68.38(2)°,V=566.8(2) ų,Z=4,D _meas=3.28(5) g cm^–3,D _calc=3.267 g cm^–3, (MoK)=0.71069 Å,=37.12 cm^–1, F(000)=540,T=298 K,R=5.4% for 2911 observed reflections; andII, blue,M _r =278.85, orthorhombic, P2₁cn,a=7.713(2) Å,b=10.271(4),c=15.378(6)°,V=1218.2(8) ų,Z=8,D _meas=3.06(5) g cm^–3,D _calc=3.040 g cm^–1, (MoK ) Å,=34.55 cm^–1, F(000)=1080,T=298 K,R=9.9% for 1450 observed reflections. Cobalt displays octahedral coordination to six oxygen atoms in the rose form whereas the metal coordination is tetrahedral in the blue form.