Bifurcations of limit cycles from a quintic Hamiltonian system with a heteroclinic cycle

In this paper,we consider Li′enard systems of the form dx/dt=y,dy/dt=x+bx3-x5+ε(α+βx2+γx4)y,where b∈R,0|ε|1,(α,β,γ)∈D∈R3 and D is bounded.We prove that for |b|1(b0) the least upper bound of the number of isolated zeros of the related Abelian integrals I(h)=∮Γh(α+βx2+γx4)ydx is 2(counting the multiplicity) and this upper bound is a sharp one.     

A boundary integral equation method for Navier-Stokes equations—application to flow in annulus of eccentric cylinders

A novel Navier-Stokes solver based on the boundary integral equation method is presented. The solver can be used to obtain flow solutions in arbitrary 2D geometries with modest computational effort. The vorticity transport equation is modelled as a modified Helmholtz equation with the wave number dependent on the flow Reynolds number. The non-linear inertial terms partly manifest themselves as volume vorticity sources which are computed iteratively by tracking flow trajectories. The integral equation representations of the Helmholtz equation for vorticity and Poisson equation for streamfunction are solved directly for the unknown vorticity boundary conditions. Rapid computation of the flow and vorticity field in the volume at each iteration level is achieved by precomputing the influence coefficient matrices. The pressure field can be extracted from the converged streamfunction and vorticity fields. The solver is validated by considering flow in a converging channel (Hamel flow). The solver is then applied to flow in the annulus of eccentric cylinders. Results are presented for various Reynolds numbers and compared with the literature.     

Probing the Lipid Annular Belt by Gas‐Phase Dissociation of Membrane Proteins in Nanodiscs

Interactions between membrane proteins and lipids are often crucial for structure and function yet difficult to define because of their dynamic and heterogeneous nature. Here, we use mass spectrometry to demonstrate that membrane protein oligomers ejected from nanodiscs in the gas phase retain large numbers of lipid interactions. The complex mass spectra that result from gas‐phase dissociation were assigned using a Bayesian deconvolution algorithm together with mass defect analysis, allowing us to count individual lipid molecules bound to membrane proteins. Comparison of the lipid distributions measured by mass spectrometry with molecular dynamics simulations reveals that the distributions correspond to distinct lipid shells that vary according to the type of protein–lipid interactions. Our results demonstrate that nanodiscs offer the potential for native mass spectrometry to probe interactions between membrane proteins and the wider lipid environment.     

Rotational properties of annulus dusty plasma in a strong magnetic field

The collective dynamics of an annulus dusty plasma formed between a co-centric conducting (non-conducting) disk and ring configuration is studied in a strongly magnetized radiofrequency (rf) discharge. A superconducting electromagnet is used to introduce a homogeneous magnetic field to the dusty plasma medium. In the absence of the magnetic field, the dust grains exhibit thermal motion around their equilibrium position. The dust grains start to rotate in the anticlockwise direction with increasing magnetic field (B > 0.02 T ), and the constant value of the angular frequency at various strengths of the magnetic field confirms the rigid body rotation. The angular frequency of dust grains linearly increases up to a threshold magnetic field (B > 0.6 T ) and after that its value remains nearly constant in a certain range of magnetic field. Further increase in magnetic field (B > 1 T ) lowers the angular frequency. Low value of the angular frequency is expected by reducing the width of the annulus dusty plasma or the input rf power. The azimuthal ion drag force due to the magnetic field is assumed to be the energy source which drives the rotational motion. The resultant radial electric field in the presence of a magnetic field determines the direction of rotation. The variation of floating (plasma) potential across the annular region at given magnetic field explains the rotational properties of the annulus dusty plasma in the presence of a magnetic field.     

环空大挠度钻柱力学分析的动坐标迭代法及其简化应用

应用动坐标迭代法分析环空钻柱的边界待定问题与几何非线性受力变形问题。将摩擦引入平衡计算中，导出了三维分析模型。计算说明该方法和模型简便可靠，实际应用可以简化计算。     

A Class of Planar Surfaces in Surface×I

Ｗｅｒｅｓｔｒｉｃｔｏｕｒｃｏｎｓｉｄｅｒａｔｉｏｎｔｏｏｒｉｅｎｔａｂｌｅａｎｄｃｏｍｐａｃｔｃａｔｅｇｏｒｙ .Ｆｏｒｄｅｆｉｎｉｔｉｏｎｓａｎｄｔｅｒｍｉｎｏｌｏｇｙ ,ｓｅｅｆｏｒｅｘａｍｐｌｅ ,[1 ]ａｎｄ [2 ].　ＬｅｔＳｂｅａｃｌｏｓｅｄｏｒｉｅｎｔａｂｌｅｓｕｒｆａｃｅｗｉｔｈｐｏｓｉｔｉｖｅｇｅｎｕｓ .Ｉｎｔｈｉｓｐａｐｅｒ ,ＭａｌｗａｙｓｄｅｎｏｔｅｓＳ×Ｉ ,ａｎｄＳ0 =Ｓ× 0 ,Ｓ1=Ｓ× 1 .ＡｎａｎｎｕｌｕｓＡｉｎＭｗｉｔｈｉｔｓｔｗｏｂｏｕｎｄａｒｉｅｓｌｙｉｎｇｉｎＳ0ａｎｄＳ1ｒ…     

圆内开缝圆自然对流的Ruelle-Takens混沌道路

使用热格子Boltzmann方法针对圆内开缝圆自然对流的流动与换热进行数值模拟,通过相空间、功率谱等进行非线性动力学特性分析,研究其流动与换热的稳定性.结果表明：随着瑞利数Ra的增加,流场的相图从开始稳定的平衡点经历Hopf分岔后转变为极限环,表明流场进入一个倍周期性振荡状态;随着瑞利数进一步增加,稳定的极限环分岔为二维环面,系统相空间结构复杂化;当瑞利数Ra大于某一临界值时,二维环面分岔突变进入混沌状态,系统在相空间中出现非常复杂的轨线结构.总体上,通过系统不同瑞利数所对应的非线性动力学特性的表现形式,表明系统经过Ruelle-Takens道路到达混沌,展现出自然对流从稳定的流动和换热发展到非线性运动特征的混沌历程.     

Experimental studies on natural convection boiling of water in a vertical annulus of a closed-loop thermo-siphon

Experimental studies on natural convection boiling of water in an internally heated narrow vertical annulus, with the liquid circulating through a cold leg forming a closed-loop thermo-siphon, have been carried out. The radius and aspect ratios of the annulus are 1.184 and 352, respectively. The experimental data, which consist of wall and liquid temperatures, liquid and vapor flow rates, and differential pressure across the test section, are recorded on a data logging system. The experiments have been performed for a constant heat flux of 15–35 kW/m² from the startup period until the steady state to study the transient behavior of the system. The boiling and non-boiling zones in the annulus have been identified and presented graphically through the liquid and wall temperatures for the steady state. They have been also verified through the visual photographs of the flow patterns in the annulus. The flow is found to be oscillatory in nature with no particular trend. Although the experimental data seems to be scattered, but when analyzed for a short duration, they are found well within the ±3σ (three sigma). This confirms the quasi-steady-state condition of the system. The steady-state values of Reynolds number and liquid circulation rate come out to be 133.1–453.5 and 7.0–23.87 g/s, respectively, while the Nusselt number and heat transfer coefficient are 7.98–13.57 and 1433.57–2435.35 W/m²K, respectively. Mathematical correlations for liquid mass flow rates, heat transfer coefficient, Reynolds number, and Nusselt number have been developed and compared with the existing correlations, which are in good agreement.     

Drag reduction by an elastic rubber band?

The influence on the friction behaviour caused by a rubber band held fixed at one end of a circular tube containing a fully developed turbulent flow was investigated. The drag was slightly higher under these conditions with the drag approaching the Prandtl-Karman law at high Reynolds numbers. The results are in contrast to the behaviour of a polymer thread in heterogeneous drag reduction.