A study of the effect of step excrescences and free‐stream disturbances on boundary layer stability

In this work, a study of the mechanism by which free‐stream acoustic and vorticity disturbances interact with a boundary layer flow developing over a flat plate featuring a step excrescence located at a certain distance from a blunt leading edge is included. The numerical tool is a high‐fidelity implicit numerical algorithm solving for the unsteady, compressible form of the Navier–Stokes equations in a body‐fitted curvilinear coordinates and employing high‐accurate compact differencing schemes with Pade‐type filters. Acoustic and vorticity waves are generated using a source term in the momentum and energy equations, as opposed to using inflow boundary conditions, to avoid spurious waves that may propagate from boundaries. The results show that the receptivity to surface step excrescences is largely the result of an overall adverse pressure gradient posed by the step, and that the free‐stream disturbances accelerate the generation of instabilities in the downstream. As expected, it is found that the acoustic disturbance interacting with the surface imperfection is more efficient in exciting the Tollmien–Schlichting waves than the vorticity disturbance. The latter generates Tollmien–Schlichting waves that are grouped in wave packets consistent with the wavelength of the free‐stream disturbance. Copyright © 2015 John Wiley & Sons, Ltd.     

On the oscillons in the signum-Gordon model

New periodic solutions of signum-Gordon equation are presented. We first find solutions φ₀(x, t) defined for (x, t) ∈ ? × [0, T ] and satisfying the condition φ₀(x, 0) = φ₀(x, T ) = 0. Then these solutions are extended to the whole spacetime by using (2.4).     

Extension of the Wilson-NRF Gibbs Energy Model in Correlating Vapor-Liquid and Liquid-Liquid Phase Behavior of Polymer-Polymer Aqueous Two-Phase Systems

In this work, the proposed model by Pazuki et al. based on the Local Composition Concept (LCC), has been used in correlating the vapor-liquid phase behavior of polymer solutions and the liquid-liquid phase behavior of aqueous two-phase systems. The Flory-Huggins model has been used as the combinatorial part of the proposed model, as well as the model proposed by Pazuki et al. was considered as the residual term. The proposed model has been used in correlating the vapor-liquid phase behavior for a number of PEG-Water systems at constant temperature. The results obtained from the proposed model have been compared with those obtained from the Poly-NRTL and the Poly-Wilson models. The results showed that the proposed model can accurately correlate the VLE data for PEG-Water systems. Also, the proposed model has been used to obtain phase behavior of aqueous two-phase systems for PEG-DEX-Water systems. The results obtained from the proposed model have been compared with those obtained from the UNIQUAC and the UNIQUAC-NRF models. The results showed that the proposed model can accurately correlate liquid-liquid phase behavior of aqueous two-phase systems than the UNIQUAC and the UNIQUAC-NRF models.     

Investigation on the Tribological Properties of POM Modified by Nano-PTFE

The tribological properties of polyoxymethylene (POM) modified by nano-polytetrafluorethylene (nano-PTFE) were investigated by a block-on-ring wear tester. For comparison, modified POM with micro-polytetrafluoroethylene (micro-PTFE) was also studied. The modified POM with a much lower concentration of nano-PTFE showed the similar tribological properties compared with POM modified by micro-PTFE. The friction coefficient decreased with the increase of nano-PTFE, while the wear rate showed the lowest value when the concentration of nano-PTFE was 2%. Scanning electron microscope (SEM) micrographs revealed that transfer films played an important role in the friction process. The transfer films decreased and stabilized the friction coefficient. Comparing to POM/2%nano-PTFE, when the concentration of nano-PTFE reached 4%, the mechanical properties decreased significantly, possibly due to poor dispersion of nano-PTFE.     

A Petrov-Galerkin method for equal width equation

The equal width equation is solved numerically by Petrov-Galerkin method using linear hat function and quadratic B-spline function as trial and test functions respectively. Product approximation has been used in this method. A linear stability analysis of the scheme is shown to be conditionally stable. Test problems including the single soliton and the interaction of solitons are used to validate the suggested method, which is found to be accurate and efficient. The Maxwellian initial condition pulse and the development of an undular bore are also studied.     

一类二阶多点边值问题正解的存在性

利用锥上不动点定理讨论了二阶常微分方程组多点边值问题正解的存在性，所得结论推广了最近的一些结果．     

Exact Analytical Solution to Equations of Perihelion Advance in General Relativity

Previously the perihelion advance in binary system was computed approximately. We will present an exact analytical solution to nonlinear differential equation of perihelion advance by method of Jacobian elliptic function and the advanced angle between successive perihelions. Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars from Ministry of Education, China (Grant No. [2004]527) and the Natural Science Foundation of Hunan Province, China (Grant No. 06JJ2026)