Generalized integral transform solution for hydrodynamically developing non-Newtonian flows in circular tubes

ABSTRACT: The Generalized Integral Transform Technique (GITT) is applied to the solution of the momentum equations in a hydrodynamically developing laminar flow of a non-Newtonian power-law fluid inside a circular duct. A primitive variables formulation is adopted in order to avoid the singularity of the auxiliary eigenvalue problem in terms of Bessel functions at the centerline of the duct when the GITT approach is applied. Results for the velocity field and friction factor-Reynolds number product are computed for different power-law indices, which are tabulated and graphically presented as functions of the dimensionless coordinates. Critical comparisons with previous results in the literature are also performed, in order to validate the numerical codes developed in the present work and to demonstrate the consistency of the final results.

Division of labor between M and P visual pathways: different visual pathways minimize joint entropy differently

Visual perception and action are strongly linked with parallel processing channels connecting the retina, the lateral geniculate nucleus, and the input layers of the primary visual cortex. Achromatic vision is provided by at least two of such channels formed by the M and P neurons. These cell pathways are similarly organized in primates having different lifestyles, including species that are diurnal, nocturnal, and which exhibit a variety of color vision phenotypes. We describe the M and P cell properties by 3D Gábor functions and their 3D Fourier transform. The M and P cells occupy different loci in the Gábor information diagram or Fourier Space. This separation allows the M and P pathways to transmit visual signals with distinct 6D joint entropy for space, spatial frequency, time, and temporal frequency. By combining the M and P impacts on the cortical neurons beyond V1 input layers, the cortical pathways are able to process aspects of visual stimuli with a better precision than it would be possible using the M or P pathway alone. This performance fulfils the requirements of different behavioral tasks.