A stable three-level finite difference scheme for solving the parabolic two-step model in a 3D micro-sphere heated by ultrashort-pulsed lasers

Ultrashort-pulsed lasers with pulse durations of the order of sub-picosecond to femtosecond domain possess exclusive capabilities in limiting the undesirable spread of the thermal process zone in the heated sample. Parabolic two-step micro heat transport equations have been widely applied for thermal analysis of thin metal films exposed to picosecond thermal pulses. In this study, we develop a three level finite difference scheme for solving the heat transport equations in a three-dimensional micro-sphere heated by ultrashort-pulsed lasers. It is shown that the scheme is unconditionally stable. The method is illustrated by numerical examples.     

左消半群M与幂单半群B的Schǔzenberger积

本文讨论了每个元都有幂等元作为右单位元的左消半群与幂单半群N的Schuzenberger积M◇N的ρ类，证明了这种半群M与N的Schuzenberger积M◇N的ρ类是右E一半适合半群和弱E-headged半群．     

Time-resolved chemiluminescence technique for the microdetermination of proteins based on their complexation with copper(II).

Based on the complexation between proteins and Cu(II) coupled with the time-resolved chemiluminescence (CL) technique, a highly sensitive and quantitative assay for measuring proteins in solution is described. The complexes of proteins with Cu(II) have a strongly catalytic effect on the luminol-H2O2 CL reaction. Because the CL emission produced by the complexes is much more long-lived than that by Cu(II), the CL signals originating from proteins can be easily identified and measured with a time-resolved technique. On this basis, bovine albumin fraction V (BAF V) can be quantitatively determined in the range of 0.01 - 5.0 microg/ml with a detection limit of 5.8 ng/ml. The results show that the proposed assay exhibits a small variation in the response values for the same amount of different proteins, as compared to the Lowry as well as Bradford assays. The CL assay has also been studied for the detection of immobilized proteins.     

Fully-developed pipe and planar flows of multimode viscoelastic fluids

Two solutions are presented for fully-developed pipe and planar flows of multimode viscoelastic models. The fluids have a Newtonian solvent contribution and the polymer modes are described by the Phan-Thien—Tanner (PTT), the FENE-P or the Giesekus equation. The first solution is exact and can handle any number of modes, but is only semi-analytical. The second solution, which is presented only for the PTT model with a linear stress coefficient and the FENE-P model, can also handle any number of modes. It is based on a truncated series expansion and is completely analytical, but provides only an approximated solution. The complexity of the multimode solutions is investigated first with the exact semi-analytical method and it is shown that at high Deborah number flows the high-order stresses can become as important as the stress of the first mode. It is also under these conditions that the approximated analytical solution deviates from the exact semi-analytical solution. A criterion for the accurate use of the approximated solution is presented. Fortran codes are provided to obtain these solutions at the internet address at the end.     

Nonlinear transient analysis of moderately thick laminated composite sector plates

This study presents a simple formulation for the nonlinear dynamic analysis of shear-deformable laminated sector plates made up of cylindrically orthotropic layers. The non-axisymmetric formulation in cylindrical coordinates is discretized in space domain using two-dimensional Chebyshev polynomials. Houbolt time marching is used for temporal discretization. Quadratic extrapolation is used for linearization along with fixed-point iteration for obtaining the results. Several combinations of simply supported, clamped and free edge conditions are considered. Convergence study has been carried out and the results are compared with the results of square plates. Effects of boundary conditions, moduli ratio, lamination scheme, sector angle and annularity on the transient deflection response are plotted graphically. Transient responses are compared for step, saw-tooth and sinusoidal loadings.     

One-dimensional global attractor for strongly damped wave equations

We consider the dynamical behavior of the strongly damped wave equations under homogeneous Neumann boundary condition. By the property of limit set of asymptotic autonomous differential equations, we prove that in certain parameter region, the system has a one-dimensional global attractor, which is a periodic horizontal curve.     

Influence of swirl on the stability of a rod in annular leakage flow

The influence of swirl (flow rotation) on the stability of a rod in annular leakage flow is investigated. Under the assumption of laminar flow and plane vibrations (no whirling), it is shown that the swirl acts, in effect, as an elastic foundation with negative foundation stiffness, the magnitude being proportional to the mean circumferential flow rate squared. Consequently, swirl always lowers the critical axial flow speed in case of divergence instability of a rod of finite length. Numerical analysis is needed to predict the effect of swirl in case of flutter instability of a finite rod; this is not performed here. However, for the flutter-like instability of travelling waves in an infinite rod-channel system, it is shown analytically that swirl again always lowers the critical axial flow speed. Finally, it is found that by circumferential flow alone, the travelling waves are extinguished at a certain flow rate, followed by a divergence-like instability.     

A class of subgrid-scale models preserving the symmetry group of Navier–Stokes equations

Navier–Stokes equations (NS) admit transformations which transform a solution to another solution (galilean transformation, scaling transformation, …). They also admit viscosity dependent transformations which transform a solution to a solution of another NS with different viscosity. These particular transformations are called symmetries of NS. Each of them has a physical role (such as conservation laws, …). A consistent turbulence model should then remain invariant under these symmetry transformations. Unfortunately, this is not the case of several models.In this article, a class of subgrid-scale models preserving the symmetries of NS is built. This class is then refined such that the models respect the second law of thermodynamics. One of the simplest models of the class is tested to the flow in a ventilated room. Better results than those provided by Smagorinsky and dynamic models are obtained.