Mixed convection heat transfer in the boundary layers on an exponentially stretching surface with magnetic field

An analysis has been carried out to describe mixed convection heat transfer in the boundary layers on an exponentially stretching continuous surface with an exponential temperature distribution in the presence of magnetic field, viscous dissipation and internal heat generation/absorption. Approximate analytical similarity solutions of the highly non-linear momentum and energy equations are obtained. The present results are found to be in excellent agreement with previously published work on various special cases of the problem. Numerical results for temperature distribution and the local Nusselt number have been obtained for different values of the governing parameters. The numerical solutions are obtained by considering an exponential dependent stretching velocity and prescribed boundary temperature on the flow directional coordinate. The effects of various physical parameters like Prandtl number, Hartman number, Grashof number on dimensionless heat transfer characteristics are discussed in detail. In particular, it has been found that increase in Prandtl number decreases the skin-friction coefficient at the stretching surface, while increase in the strength of the magnetic field leads to increase in the local Nusselt number.     

Temporal boundary value problems in interfacial fluid dynamics

We study problems in interfacial fluid dynamics which do not have well-posed initial value problems. We prove existence of solutions for these problems by considering instead boundary value problems, where boundary data is specified at two different times. We develop a general framework, for problems on the real line and for problems which are spatially periodic. A variety of boundary conditions are considered, including Dirichlet, Neumann and mixed conditions. The framework is applied to two specific problems from interfacial fluid dynamics: a family of generalizations of the Boussinesq equations developed by Bona, Chen and Saut, and the vortex sheet.     

Fundamental relationships between deformation-induced surface roughness,critical strain localisation and failure in AA5754-O

This research employs two approaches to characterise the apparent structure observed in localised strain maps constructed from surface topography data acquired from AA5754-O sheet stock that was deformed in three in-plane stretching modes. The first uses a conventional two-point autocorrelation function (ACF), while the second uses the combination of the eigenvalue spectrum associated with each map and information theory. The results from the ACF analysis are inconclusive, implying that this technique lacks the sensitivity necessary to quantify the relationships between multi-point clustering and strain localisation. The information theory-based approach reveals that the relative spectral entropy increases monotonically, attains a maximum and then decreases sharply to the failure strain. This behaviour occurs in all three strain modes and results from two competing processes: one where the formation of structure is favourable and one where it is not. The crossover point is a clear indicator of the onset of critical strain localisation and, therefore, can be regarded as a precursor to failure because once the dominant process shifts, additional strain results in the precipitate formation of a critical strain localisation event.     

Heat transfer in boundary layer stagnation-point flow towards a shrinking sheet with non-uniform heat flux

In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types: direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations (PDEs) are transformed into non linear self-similar ordinary differential equations (ODEs) by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Raman spectroscopy of proteins: a review

In this work, 26 proteins of different structure, function and properties are investigated by Raman spectroscopy with 488, 532 and 1064 nm laser lines. The excitation lines were chosen in NIR and Vis range as the most common and to show the difference due to normal and resonance effect, sometimes accompanied by the fluorescence. The selected proteins were divided, according to the Structural Classification of Proteins, into four classes according to their secondary structure, i.e. α‐helical (α), β‐sheet (β), mixed structures (α/β, α + β, s) and others. For all compounds, FT‐Raman and two Vis spectra are presented along with the detailed band assignment. To the best of our knowledge, this is the first review showing the potential of Raman spectroscopy for the measurement and analysis of such a large collection of individual proteins. This work can serve as a comprehensive vibrational spectra library, based on our and previous Raman measurements. Copyright © 2013 John Wiley & Sons, Ltd.     

An Itô Formula of Generalized Functionals and Local Time for Fractional Brownian Sheet

Abstract

By using the white noise theory for a fractional Brownian sheet, we derive an Itô formula for the generalized functionals for the fractional Brownian sheet with arbitrary Hurst parameters H ₁, H ₂ ∈ (0,1). As an application, we give the integral representations for two versions of local times of a fractional Brownian sheet, respectively.     

1/2波片对机载激光雷达偏振探测影响的研究

利用平面平行板模型和晶体膜层理论定量分析了1/2波片对机载激光雷达回波信号偏振探测的影响。计算结果表明:当入射光波长为532nm时,1/2石英波片对机载激光雷达回波信号平行分量与垂直分量透过率比值的影响幅度为0.82～1.196,1/2方解石波片对机载激光雷达回波信号的平行分量与垂直分量透过率比值的影响幅度为0.86～1.27;若用1/2石英波片测得的k=1.2,当考虑石英波片对五的影响时,则偏振探测两通道k的真实值应在1.003～1.463之间;若用1/2方解石波片测得的k=1.2,当考虑方解石波片对k的影响时,偏振探测两通道k的真实值应在0.945～1.395之间。由于1/2波片对k的影响,使机载激光雷达反演得到卷云等探测目标的退偏振比有较大的系统误差。