Abstract: A mechanical wave or vibration propagating through
granular media exhibits a specific signature in time. A coherent
pulse or wavefront arrives first with multiply scattered waves (coda)
arriving later. The coherent pulse is micro-structure independent i.e.
it depends only on the bulk properties of the disordered granular
sample, the sound wave velocity of the granular sample and hence
bulk and shear moduli. The coherent wavefront attenuates (decreases
in amplitude) and broadens with distance from its source. The
pulse attenuation and broadening effects are affected by disorder
(polydispersity; contrast in size of the granules) and have often been
attributed to dispersion and scattering. To study the effect of disorder
and initial amplitude (non-linearity) of the pulse imparted to the
system on the coherent wavefront, numerical simulations have been
carried out on one-dimensional sets of particles (granular chains).
The interaction force between the particles is given by a Hertzian
contact model. The sizes of particles have been selected randomly
from a Gaussian distribution, where the standard deviation of this
distribution is the relevant parameter that quantifies the effect of
disorder on the coherent wavefront. Since, the coherent wavefront is
system configuration independent, ensemble averaging has been used
for improving the signal quality of the coherent pulse and removing
the multiply scattered waves. The results concerning the width of the
coherent wavefront have been formulated in terms of scaling laws. An
experimental set-up of photoelastic particles constituting a granular
chain is proposed to validate the numerical results.
Abstract: The effect of time-periodic oscillations of the Rayleigh- Benard system on the heat transport in dielectric liquids is investigated by weakly nonlinear analysis. We focus on stationary convection using the slow time scale and arrive at the real Ginzburg- Landau equation. Classical fourth order Runge-kutta method is used to solve the Ginzburg-Landau equation which gives the amplitude of convection and this helps in quantifying the heat transfer in dielectric liquids in terms of the Nusselt number. The effect of electrical Rayleigh number and the amplitude of modulation on heat transport is studied.
Abstract: Linear and weakly nonlinear analysis of shallow wake
flows is presented in the present paper. The evolution of the most
unstable linear mode is described by the complex Ginzburg-Landau
equation (CGLE). The coefficients of the CGLE are calculated
numerically from the solution of the corresponding linear stability
problem for a one-parametric family of shallow wake flows. It is
shown that the coefficients of the CGLE are not so sensitive to the
variation of the base flow profile.