GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION

In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].

Dirac reduction of binary asteroid systems with symmetry and stability of relative equilibria

In this paper, we study symmetry reduction for a binary asteroid system modeled by a rigid body and a particle. In particular, we demonstrate how translational and rotational symmetry reduction appeared in the binary asteroid system can be carried out in the context of Dirac reduction by stages and with the associated reduction of implicit Hamiltonian systems. Then we investigate Stability of relative equilibria of the asteroid pair and show stability regions by using the energy-momentum method. Lastly, we illustrate some numerical simulations for stable and unstable orbits near from relative equilibria of the Collinear and T configurations.C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1301311]

Coexisting State of Surge and Rotating Stall in a Two-Stage Axial Flow Com-pressor using a Double-Phase-Locked Averaging Technique

The interaction between surge and rotating stall in an axial flow compressor was investigated from the viewpoint of an unsteady inner flow structure. The aim of this study was to identify the key factor that determines the switching phenomenon of a surge cycle. The main feature of the tested compressor is a shock tube connected in series to the compressor outlet through a diaphragm, slits, and a concentric duplex pipe: this system allows surge and rotating stall to be generated by connecting the shock tube with the compressor, or enables the compression plane wave injection. The unsteady characteristics and the internal flow velocity fluctuations were measured in detail, and the stall cell structure was averaged and visualized along the movement of the operation point under a coexisting state of surge. A coefficient of the cell scale fluctuation was calculated using the result of the averaging, and it confirmed that the processes of inner flow structure change differed from each other according to the next cycle of the surge. The result suggests that the key factor that determines the next cycle is the transformation of the internal flow structure, particularly between the stall cell and the entire circumferential stall, in both the recovering and stalling processes.

Unsteady Behavior of Leading-edge Vortex and Diffuser Stall in a Centrifugal Compressor with Vaned Diffuser

The characteristics of a rotating stall of an impeller and diffuser and the evolution of a vortex generated at the diffuser leading-edge(i.e., the leading-edge vortex(LEV)) in a centrifugal compressor were investigated by experiments and numerical analysis. The results of the experiments revealed that both the impeller and diffuser rotating stalls occurred at 55 and 25 Hz during off-design flow operation. For both, stall cells existed only on the shroud side of the flow passages, which is very close to the source location of the LEV. According to the CFD results, the LEV is made up of multiple vortices. The LEV is a combination of a separated vortex near the leading-edge and a longitudinal vortex generated by the extended tip-leakage flow from the impeller. Therefore, the LEV is generated by the accumulation of vorticity caused by the velocity gradient of the impeller discharge flow. In partial-flow operation, the spanwise extent and the position of the LEV origin are temporarily transmuted. The LEV develops with a drop in the velocity in the diffuser passage and forms a significant blockage within the diffuser passage. Therefore, the LEV may be regarded as being one of the causes of a diffuser stall in a centrifugal compressor.

Unsteady Behavior and Control of Vortices in Centrifugal Compressor

Two examples of the use of vortex control to reduce noise and enhance the stable operating range of a centrifugal compressor are presented in this paper.In the case of high-flow operation of a centrifugal compressor with a vaned diffuser,a discrete frequency noise induced by interaction between the impeller-discharge flow and the diffuser vane,which appears most notably in the power spectra of the radiated noise,can be reduced using a tapered diffuser vane(TDV) without affecting the performance of the compressor.Twin longitudinal vortices produced by leakage flow passing through the tapered portion of the diffuser vane induce secondary flow in the direction of the blade surface and prevent flow separation from the leading edge of the diffuser.The use of a TDV can effectively reduce both the discrete frequency noise generated by the interaction between the impeller-discharge flow and the diffuser surface and the broadband turbulent noise component.In the case of low-flow operation,a leading-edge vortex(LEV) that forms on the shroud side of the suction surface near the leading edge of the diffuser increases significantly in size and blocks flow in the diffuser passage.The formation of an LEV may adversely affect the performance of the compressor and may cause the diffuser to stall.Using a one-side tapered diffuser vane to suppress the evolution of an LEV,the stable operating range of the compressor can be increased by more than 12 percent,and the pressure-rise characteristics of the compressor can be improved.The results of a supplementary examination of the structure and unsteady behavior of LEVs,conducted by means of detailed numerical simulations,are also presented.

A SIMPLE DISCRETE-TIME ANALOGUE PRESERVING THE GLOBAL STABILITY OF A CONTINUOUS SIRS EPIDEMIC MODEL

In this paper, we consider the backward Euler discretization derived from a continuous SIRS epidemic model, which contains a remaining problem that our discrete model has two solutions for infected population; one is positive and the other is negative. Under an additional positiveness condition on infected population, we show that the backward Euler discretization is one of simple discrete-time analogue which preserves the global asymptotic stability of equilibria of the corresponding continuous model.