Buoyancy-driven algebraic (localised) boundary-layer disturbances

We show that a new class of steady linear eigenmodes exist in the Falkner–Skan boundary layer, associated with an algebraically developing, thermally coupled three-dimensional perturbation that remains localised in the spanwise direction. The dominant mode has a weak temperature difference that decays (algebraically) downstream, but remains sufficient (for favourable pressure gradients that are below a critical level) to drive an algebraically growing disturbance in the velocity field. We determine the critical Prandtl number and pressure gradient parameter required for downstream algebraic growth. We also march the nonlinear boundary-region equations downstream, to demonstrate that growth of these modes eventually gives rise to streak-like structures of order-one aspect ratio in the cross-sectional plane. Furthermore, this downstream flow can ultimately become unstable to a two-dimensional Rayleigh instability at finite amplitudes.

X-type vortex and its effect on beam shaping

In this article we propose a new type of optical vortex, the X-type vortex. This vortex inherits and develops the conventional noncanonical vortex, i.e., it no longer has a constant phase gradient around the center, while the intensity keeps invariant azimuthally. The strongly focusing properties of the Xtype vortex and its effect on the beam shaping in three-dimensional (3D) fields are analyzed. The interesting phenomena, which cannot be seen in canonical vortices, are observed, for instance the `switch effect' which shows that the intensity pattern can switch from one transverse axis to another in the focal plane by controlling the phase gradient parameter. It is shown that by adjusting the phase gradient of this vortex, the focal field can have marvelous patterns, from the doughnut shape to the shapes with different lobes, and the beam along propagation direction will form a twisting shape in 3D space with controllable rotation direction and location. The physical mechanisms underlying the rule of the beam shaping are also discussed, which generally say that the phase gradient of the X-type vortex, the orbital angular momentum, the polarization and the `nongeneric' characteristic contribute differently in shaping fields. This new type of vortex may supply a new freedom for tailoring 3D optical fields, and our work will pave a way for exploration of new vortices and their applications.

Heat transfer and skin-friction in a nonequilibrium adverse pressure gradient

The paper presents the results of an experimental study of influence of a weak and moderate nonequilibrium adverse pressure gradient (APG) on the parameters of the dynamic and thermal boundary layers. The Reynolds number based on the momentum thickness at the beginning of the APG region was Re **=5500. The section of the channel with APG was a slotted channel with an opening angle of the upper wall of 0-14°. The values of the relative (referred to the parameters in a zero pressure gradient flow at the same Re **) friction and heat transfer coefficients, as well as the Reynolds analogy factor depending on the longitudinal pressure gradient, are obtained. The values of the relative friction coefficient decreased to cf/cf0 =0.7 and those of the heat transfer to St/St0=0.9. A maximum value of the Reynolds analogy factor (St/St0)/(cf/cf0 )=1.16 was reached for the pressure gradient parameter β=2.9. The ratio of the heat transfer and drag coefficients of the dimpled to smooth surfaces remained approximately constant regardless of the presence or magnitude of a adverse pressure gradient.

Parametric Stability Analysis of a Spring Attached, Pre-Twisted, Rotating Sandwich Beam with Tip Mass and Viscoelastic Support

This paper inspects the influence of a spring attachment provided on the top elastic layer on the stability of a pre-twisted, rotating sandwich beam having viscoelastic supports at the root under the impact of a periodically varying axial load. The spring is deployed on the beam to achieve more strength to weight ratio without compromising the stability. The beam is exponentially tapered, and a tip mass is at the free end to represent the rotating members in various types of machinery as closely as possible. The ruling equations and inter-related boundary conditions are attained by applying Hamilton’s principle. To obtain the solution, a matrix equation was developed through the assumed-mode variational method. The resulting matrix equation was converted to a coupled Hill’s equation of parametric vibration through the modal matrix corresponding to the free vibration problem. Finally, static and dynamic stability graphs were obtained for several system parameters such as position and length of the attached spring on the top elastic layer, the mass of the spring attachment, stiffness of the spring attachment, angle of pre-twist, tip mass, taper parameter, temperature gradient parameter, setting angle, viscoelastic spring stiffness, etc. to analyze their impact on the system’s stability. Saito and Otomi conditions were used to obtain dynamic stability plots. Greater stability is achieved due to the spring attachment on the top of the top elastic layer.

Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source

The thermal problem of functionally graded materials (FGM) under linear heat source is studied by a hybrid numerical method. The accuracy of the analytical method and the efficiency of the finite element method are taken into account. The volume fraction of FGM in the thickness direction can be changed by changing the gradient parameters. Based on the weighted residual method, the heat conduction equation under the third boundary condition is established. The temperature distribution of FGM under the action of linear heat source is obtained by Fourier transform. The results show that the closer to the heat source it is, the greater the influence of the heat source is and the influence of the heat source is local. The temperature change trend of the observation points is consistent with the heat source, showing a linear change. The results also show that the higher the value of gradient parameter is, the higher the temperature of location point is. The temperature distribution of observation points is positively correlated with gradient parameter. When the gradient parameter value exceeds a certain value, it has a little effect on the temperature change in the model and the heat conduction in the model tends to be pure metal heat conduction, the optimal gradient parameters combined the thermal insulation property of ceramics and the high strength toughness of metals are obtained.

New hyrid conjugate gradient method as a convex combination of HZ and CD methods

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems, the conjugate gradient parameter [Formula: see text] is computed as a convex combination of [Formula: see text] and [Formula: see text]. Under the wolfe line search, we prove the sufficient descent and the global convergence. Numerical results are reported to show the effectiveness of our procedure.

A new conjugate gradient method based on a modified secant condition with its applications in image processing

We propose an effective conjugate gradient method belonging to the class of Dai-Liao methods for solving unconstrained optimization problems. We employ a variant of the modified secant condition, and introduce a new conjugate gradient parameter by solving an optimization problem. Optimization problem combines the well-known features of the linear conjugate gradient method using some penalty functions. This new parameter takes advantage of function information as well as the gradient information to provide the iterations. Our proposed method is globally convergent under mild assumptions. We examine the ability of the method for solving some real world problems from image processing field. Numerical results show that the proposed method is efficient in the sense of PSNR test. We also compare our proposed method with some well-known existing algorithms using a collection of CUTEr problems to show it's efficiency.