Theoretical Studies on Dihedral Angle-Bending Isomers of M2Pt20/-Clusters

The structures and electronic properties of the gaseous M\begin{document}$ _2 $\end{document}Pt\begin{document}$ _2 $\end{document}\begin{document}$ ^{0/-} $\end{document} clusters (M represents the alkaline earth metal) were investigated using the density functional theory (B3LYP and PBE0) and wave function theory (SCS-MP2, CCSD and CCSD (T)). The results indicate that the D\begin{document}$ _{2{h}} $\end{document} isomers with the planar structures are more stable than the C\begin{document}$ _{2v} $\end{document} isomers with smaller dihedral angles and shorter Pt-Pt bond lengths. The mutual competition of M(s, p)-Pt(5d) interaction and Pt-Pt covalent bonding contributes to the different stabilizations of the two kinds of isomers. The M(s, p)-Pt(5d) interaction favors the planar isomers with D\begin{document}$ _{2h} $\end{document} symmetry, while the Pt-Pt covalent bonding leads to the C\begin{document}$ _{2v} $\end{document} isomers with bending structures. Two different crossing points are determined in the potential energy curves of Be\begin{document}$ _2 $\end{document}Pt\begin{document}$ _2 $\end{document} with the singlet and triplet states. But there is just one crossing point in potential energy curves of Ra\begin{document}$ _2 $\end{document}Pt\begin{document}$ _2 $\end{document} and Ca\begin{document}$ _2 $\end{document}Pt\begin{document}$ _2 $\end{document}\begin{document}$ ^- $\end{document} because of flatter potential energy curves of Ra\begin{document}$ _2 $\end{document}Pt\begin{document}$ _2 $\end{document} with the triplet state or Ca\begin{document}$ _2 $\end{document}Pt\begin{document}$ _2 $\end{document}\begin{document}$ ^- $\end{document} with quartet state. The results reveal a unique example of dihedral angle-bending isomers with the smallest number of atoms and may help the understanding of the bonding properties of other potential angle-bending isomers.     

The potential energy surface and chaos in 2D Hamiltonian systems

We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion.     

Numerical rheometry of bulk materials using a power law fluid and the lattice Boltzmann method

In the present study, the flow of bulk materials is characterised as a non-Newtonian fluid and modelled using the lattice Boltzmann method. A power law and a Bingham model is implemented in the LBM, which is hydrodynamically coupled to the discrete element method (DEM) for structural interaction. The performance of both non-Newtonian models is assessed, both qualitatively and quantitatively, in benchmark problems. The validated, non-Newtonian LBM–DEM framework is then applied to the geometry of a cylindrical Couette rheometer to numerically determine the constitutive response of a sample of Leighton Buzzard sand. The numerical results, which employ the power law, are compared with experimental data, and a number of other synthetic soil samples are defined using the presented process of numerical rheometry. Finally, the numerical stress–strain rate response of the synthetic soil samples is interpreted within the context of a regularised Bingham model, and the similarities discussed.     

Manage Pension Deficit with Heterogeneous Insurance

This paper considers a positive and increasing pension deficit of a certain pay-as-you-go (PAYG) pension system, and tries to make up for this deficit by using heterogeneous insurance. The positive pension deficit is formulated as a mathematical function in continuous time. The surplus of an appropriate heterogeneous insurance is described by diffusion approximation of a Cramér-Lundberg process. The system of extended Hamilton-Jacobi-Bellman equations under mean-variance criterion is established. The closed-form solution and optimal surplus-multiplier of heterogenous insurance are obtained. Some interpretations further explain the theoretical values of the results.

     

Numerical simulation on tunnel splitting of Bose-Einstein condensate in multi-well potentials

The low-energy-level macroscopic wave functions of the Bose-Einstein condensate (BEC) trapped in a symmetric double-well and a periodic potential are obtained by solving the Gross-Pitaevskii equation numerically. The ground state tunnel splitting is evaluated in terms of the even and odd wave functions corresponding to the global ground and excited states respectively. We show that the numerical result is in good agreement with the analytic level splitting obtained by means of the periodic instanton method.     

Homomorphisms between JC＊-algebras and Lie C＊-algebras

It is shown that every almost ＊-homomorphism h ： A→B of a unital JC＊-algebra A to a unital JC＊-algebra B is a ＊-homomorphism when h（rx） = rh（x） （r 〉 1） for all x∈A, and that every almost linear mapping h ： A→B is a ＊-homomorphism when h（2^nu o y） - h（2^nu） o h（y）, h（3^nu o y） - h（3^nu） o h（y） or h（q^nu o y） = h（q^nu） o h（y） for all unitaries u ∈A, all y ∈A, and n = 0, 1,.... Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings. We prove that every almost ＊-homomorphism h ： A→B of a unital Lie C＊-algebra A to a unital Lie C＊-algebra B is a ＊-homomorphism when h（rx） = rh（x） （r 〉 1） for all x ∈A.     

Coherence phenomena in the phase-sensitive optical parametric amplification inside a cavity

We theoretically and experimentally demonstrate coherence phenomena in optical parametric amplification inside a cavity. The mode splitting in the transmission spectra of a phase-sensitive optical parametric amplifier is observed. Especially, we show that a very narrow dip and peak, which are the shape of a delta function, appear in the transmission profile. The origin of the coherence phenomenon in this system is the interference between the harmonic pump field and the subharmonic seed field in cooperation with dissipation of the cavity.     

Controlled shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system

The dependence of the shift of an optical bistability hysteresis curve on the nonlinear phase shift induced by a controlling light is observed in a four-level atomic system of 87 Rb inside an optical ring cavity. In the process the intensity of the coupling beam keeps constant and the atomic system is operated at near conditions of coherent population trapping due to atomic coherence. The refractive and absorptive chi3 nonlinearities enhanced by atomic coherence provide the physical mechanism of the phenomena. Based on the effects, all-optical flip-flop and storage of optical pulse signals with a low peak power of several tens of microwatts are implemented.     

Effect of nonlinear gradient terms on pulsating,erupting and creeping solitons

The effect of nonlinear gradient terms on the pulsating, erupting and creeping solitons, respectively, of the cubic–quintic complex Ginzburg–Landau equation is investigated. It is found that the nonlinear gradient terms result in dramatic changes in the soliton behavior. They eliminate the periodicity of the pulsating and erupting solitons and transform them into fixed-shape solitons. This is important for potential use, such as to realize experimentally the undistorted transmission of femtosecond pulses in optical fibers. However, the nonlinear gradient terms cause the creeping soliton to breathe periodically at different frequencies on one side and spread rapidly on the other side. PACS 47.20.Ky; 05.70.Ln; 03.40.Gc; 42.65.Tg