Post-buckling of an elastic half-space coated by double layers

We investigate the buckling and post-buckling properties of a hyperelastic half-space coated by two hyperelastic layers when the composite structure is subjected to a uniaxial compression. In the case of a half-space coated with a single layer, it is known that when the shear modulus [Formula: see text] of the layer is larger than the shear modulus [Formula: see text] of the half-space, a linear analysis predicts the existence of a critical stretch and wave number, whereas a weakly nonlinear analysis predicts the existence of a threshold value of the modulus ratio [Formula: see text] below which the buckling is super-critical and above which the buckling is sub-critical. It is shown that when another layer is added, a larger variety of behaviour can be observed. For instance, buckling can occur at a preferred wavenumber super-critically even if both layers are softer than the half-space although the top layer would need to be harder than the bottom layer. When the shear modulus of the bottom layer lies in a certain interval, the super-critical to sub-critical transition can happen a number of times as the shear modulus of the top layer is increased gradually. Thus, an extra layer imparts more flexibility in producing wrinkling patterns with desired properties, and our weakly nonlinear analysis provides a road map on the parameter regimes where this can be achieved.

Throughflow and G-Jitter Effects on Oscillatory Convection in a Rotating Porous Medium

The impact of vertical throughflow and g-jitter effect on rotating porous medium is investigated. A feeble nonlinear stability analysis associate to complex Ginzburg-Landau equation (CGLE) has been studied. This weakly nonlinear analysis performed for a periodic mode of convection and quantified heat transport in terms of the Nusselt number, which is governed by the non-autonomous advanced CGLE. Each idea, rotation and throughflow is used as an external mechanism to the system either to extend or decrease the heat transfer. The results of amplitude and frequency of modulation on heat transport are analyzed and portrayed graphically. Throughflow has dual impact on heat transfer either to increase or decrease heat transfer in the system. Particularly the outflow enhances and inflow diminishes the heat transfer. High centrifugal rates promote heat transfer and low centrifugal rates diminish heat transfer. The streamlines and isotherms area portrayed graphically, the results of rotation and throughflow on isotherms shows convective development.

Weakly Nonlinear Mass Transfer in an Internally Soluted and Modulated Porous Layer

The effect of solutal modulation on a rotating porous media is studied. Using solvability condition, the finite amplitude equation is derived at third order of the system. A weakly nonlinear analysis is applied to investigate mass transfer in a porous medium. In this article, the stationary convection is discussed in the presence of solutal Rayleigh number. The amplitude equation (GLE) is solved numerically. Using this GLE the Sherwood number is evaluated in terms of the various system parameters. The effect of individual parameters on mass transport is discussed in detail. It is found that the mass transfer is more for modulated system than un-modulated case. Further, internal solute number Si enhance or diminishes the mass transfer. Finally it is also found that, solutal modulation can be effectively applied in either enhancing or diminishing the mass transfer.