A survey of surface tension,molar volume and density for Sn–Ag–Cu–Bi–Sb quinary alloys as lead-free solders

ABSTRACT

By applying the geometric models and the theoretical equation, the surface tension, the molar volume and the density were studied. The empirical calculations were carried out in temperature range 623?K?≤?T?≤?1123?K. Only few thermophysical properties were estimated for eight quinary alloys: Sn3.55Ag0.5Cu3Bi3Sb, Sn3.48Ag0.5Cu3Bi5Sb, Sn3.48 Ag0.5Cu5Bi3Sb, Sn3.40 Ag0.5Cu5Bi5Sb, Sn3.53Ag1Cu3Bi3Sb, Sn3.46Ag1Cu3Bi5Sb, Sn3.46Ag1Cu5Bi3Sb, Sn3.38Ag1Cu5Bi5Sb. The results show that surface tension and density have a linear appearance for all temperatures. We have also studied the influence of the composition and temperature in the studied alloys. The obtained theoretical results are compared with the experimental ones and with the conventional Pb–Sn welds.     

Exact controllability for some degenerate wave equations

In this paper, we study one-dimensional linear degenerate wave equations with a distributed controller. We establish observability inequalities for degenerate wave equation by multiplier method. We also deduce the exact controllability for degenerate wave equation by Hilbert uniqueness method when the control acts on the nondegenerate boundary. Moreover, an explicit expression for the controllability time is given.     

Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrödinger Equation

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.     

基于耦合Ginzburg-Landau方程的石墨烯锁模光纤激光器的暗暗孤子解及其稳定性

以耦合Ginzburg-Landau方程为模型,对石墨烯锁模光纤激光器中脉冲的动力学行为进行了详细地研究.首先,采用拟解法推导了该方程组的啁啾类暗暗孤子对解;其次,对啁啾类暗暗孤子对的传输特性及稳定性进行了数值研究.结果表明:合理选择系统参数,不仅可以得到啁啾类暗暗孤子对的精确解,而且该精确解还可以在一定的扰动下稳定传输.相关结果将为设计和改善石墨烯锁模光纤激光器的性能提供一定的理论依据.     

General non local boundary value problem for second order elliptic equation

In this paper we study a class of second order coefficient operators differential equation with general (possibly non local) boundary conditions. We obtain new results extending those given in a previous paper 1 . Existence, uniqueness and optimal regularity of the strict solution are proved in UMD spaces, using the well‐known Dore–Venni theorem.     

A class of time‐fractional reaction‐diffusion equation with nonlocal boundary condition

The purpose of the study is to analyze the time‐fractional reaction‐diffusion equation with nonlocal boundary condition. The proposed model is used to predict the invasion of tumor and its growth. Further, we establish the existence and uniqueness of a weak solution of the proposed model using the Faedo‐Galerkin method and compactness arguments.     

Screening gas-phase chemical kinetic models: Collision limit compliance and ultrafast timescales

Detailed gas-phase chemical kinetic models are widely used in combustion research, and many new mechanisms for different fuels and reacting conditions are developed each year. Recent works have highlighted the need for error checking when preparing such models, but a useful community tool to perform such analysis is missing. In this work, we present a simple online tool to screen chemical kinetic mechanisms for bimolecular reactions exceeding collision limits. The tool is implemented on a user-friendly website, cloudflame.kaust.edu.sa, and checks three different classes of bimolecular reactions; (ie, pressure independent, pressure-dependent falloff, and pressure-dependent PLOG). In addition, two other online modules are provided to check thermodynamic properties and transport parameters to help kinetic model developers determine the sources of errors for reactions that are not collision limit compliant. Furthermore, issues related to unphysically fast timescales can remain an issue even if all bimolecular reactions are within collision limits. Therefore, we also present a procedure to screen ultrafast reaction timescales using computational singular perturbation. For demonstration purposes only, three versions of the rigorously developed AramcoMech are screened for collision limit compliance and ultrafast timescales, and recommendations are made for improving the models. Larger models for biodiesel surrogates, tetrahydropyran, and gasoline surrogates are also analyzed for exemplary purposes. Numerical simulations with updated kinetic parameters are presented to show improvements in wall-clock time when resolving ultrafast timescales.     

Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation

Previously, master equation (ME) simulations using semiclassical transition state theory (SCTST) and high-accuracy extrapolated ab initio thermochemistry (HEAT) predicted rate constants in excellent agreement with published experimental data over a wide range of pressure and temperatures ≳250 K, but the agreement was not as good at lower temperatures. Possible reasons for this reduced performance are investigated by (a) critically evaluating the published experimental data and by investigating; (b) three distinct ME treatments of angular momentum, including one that is exact at the zero- and infinite-pressure limits; (c) a hindered-rotor model for HOCO that implicitly includes the cis- and trans-conformers; (d) possible empirical adjustments of the thermochemistry; (e) possible empirical adjustments to an imaginary frequency controlling tunneling; (f) including or neglecting the prereaction complex PRC1; and (g) its possible bimolecular reactions. Improvements include better approximations to factors in SCTST and using the Hill and van Vleck treatment of angular momentum coupling. Evaluation of literature data does not reveal any specific shortcomings, but the stated uncertainties may be underestimated. All ME treatments give excellent fits to experimental data at T ≥ 250 K, but the discrepancy at T < 250 K persists. Note that each ME model requires individual empirical energy transfer parameters. Thermochemical adjustments were unable to match the experimental H/D kinetic isotope effects. Adjusting an imaginary frequency can achieve good fits, but the adjustments are unacceptably large. Whether PRC1 and its possible bimolecular reactions are included had little effect. We conclude that none of the adjustments is an improvement over the unadjusted theory. Note that only one set of experimental data exists in the regime of the discrepancy with theory, and data for DO + CO are scanty.     

An Uzawa-type algorithm for the coupled Stokes equations

An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method. The velocity solved by the presented algorithm is weakly divergence-free, which is different from the one solved by the common Uzawa method. Besides, an optimal relaxation parameter of the presented algorithm is provided.