The Chao and Fagbenle’s modification of Merk series has been employed for the analysis of forced convection laminar thermal boundary layer transfer for non-isothermal surfaces. In addition to the Prandtl number (Pr) and the pressure gradient (∧), a third parameter (temperature parameter, γ ) was introduced in the analysis. Solutions of the resulting universal functions for the thermal boundary layer have been obtained for Pr of 0.70, 1.0 and 10.0 and for a range of ∧ . The results obtained for the similarity equations agreed with published results within very close limits for all the ∧’s investigated.

Abstract:
In this paper, the power-law model for a non-Newtonian (pseudo-plastic) flow is investigated numerically. The D2Q9 model of Lattice Boltzmann method is used to simulate the micro-channel flow with expansion geometries. This geometry is made by two squared or trapezoid cavities at the bottom and top of the channel which can simulate an artery with local expansion. The cavities are displaced along the channel and the effects of the displacements are investigated for inline structures and staggered ones (anti-symmetric expansion). The method is validated by a Poiseuille flow of the power-law fluid in a duct. Validation is performed for two cases: The Newtonian fluid and the shear thinning fluid (pseudo-plastic) with n = 0.5. The results are discussed in four parts: 1) Pressure drop; It is shown that the pressure drop along the channel for inline cavities is much more than the pressure drop along the staggered structures. 2) Velocity profiles; the velocity profiles are sketched at the centerline of the cavities. The effects of pseudo-plasticity are discussed. 3) Shear stress distribution; the shear stress is computed and shown in the domain. The Newtonian and non-Newto- nian fluids are discussed and the effect of the power n on shear stress is argued. 4) Generated vortices in the cavities are also presented. The shape of the vortices is depicted for various cases. The results for these cases are talked over and it is found that the vortices will be removed for flows with n smaller than 0.5.

Abstract:
Waves of finite amplitude on a thin layer of non-Newtonian fluid modelled as a power-law fluid are considered. In the long wave approximation, the system of equations taking into account the viscous and nonlinear effects has the hyper- bolic type. For the two-parameter family of periodic waves in the film flow on a vertical wall the modulation equations for nonlinear wave trains are derived and investigated. The stability criterium for roll waves based on the hyperbolicity of the modulation equations is suggested. It is shown that the evolution of stable roll waves can be described by self-similar solutions of the modulation equations.

Abstract:
A simple stochastic mechanism that produces exact and approximate
power-law distributions is presented. The model considers radially symmetric
Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a
radially uniform sampling scheme produces heavy-tailed distributions. For
two-dimensional Gaussians and one-dimensional exponential functions, exact
power-laws with exponent –1 are obtained. In other cases, densities with an
approximate power-law behaviour close to the origin arise. These densities are
analyzed using Padé approximants in order to show the approximate power-law behaviour.
If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities
that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic
situations different from previously considered specialized systems such as
multi-particle systems close to phase transitions, dynamical systems at
bifurcation points or systems displaying self-organized criticality. Thus, the
presented mechanism may serve as an alternative hypothesis in system
identification problems.

Abstract:
This article aims to numerically investigate the flow pattern for Newtonian and power law non-Newtonian fluid in a semi-half circular channel with corrugated walls under the influence of a magnetic field. The results indicate that, presence of a magnetic field affects the flow field in several aspects, especially in the vortex creation and dissipation. In addition, the analysis is carried out for different Reynolds numbers to ascertain the influence of magnetic field on each flow regime. Eventually, the analysis is carried out for a range of power indices including pseudo plastic (shear-thinning) to dilatants (shear-thickening) fluids. The results show that by increasing the power-index, the vortices begin to form and grow gradually so that in the shear-thickening fluid an extra vortex is formed and created nearby the corrugated part of the channel.

Abstract:
The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting non-Newtonian power-law fluid past a non-linearly stretching surface in the presence of a transverse magnetic field is considered. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. These equations are then solved numerically by an implicit finite-difference scheme known as Keller-Box method. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, velocity exponent parameter, temperature exponent parameter, Modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena.

Abstract:
The language of gene expression displays topological symmetry. An important step during gene expression is the binding of transcriptional proteins to DNA promoters adjacent to a gene. Some proteins bind to many promoters in a genome, defining a regulon of genes wherein each promoter might vary in DNA sequence relative to the average consensus. Here we examine the linguistic organization of gene promoter networks, wherein each node in the network represents a promoter and links between nodes represent the extent of base pair-sharing. Prior work revealed a fractal nucleus in several σ-factor regulons from Escherichia coli. We extend these findings to show fractal nuclei in gene promoter networks from three bacterial species, E. coli, Bacillus subtilis, and Pseudomonas aeruginosa. We surveyed several non-σ transcription factors from these species and found that many contain a nucleus that is both visually and numerically fractal. Promoter footprint size scaled as a negative power-law with both information entropy and fractal dimension, while the latter two parameters scaled positively and linearly. The fractal dimension of the diffuse networks (dB = ~1.7) was close to that expected of a diffusion limited aggregation process, confirming prior predictions as to a possible mechanism for development of this structure.

Abstract:
non-newtonian fluids, such as polymer solutions, have been used by the oil industry for many years as fracturing agents and drilling mud. these solutions, which normally include thickened water and jelled fluids, are injected into the formation to enhanced oil recovery by improving sweep efficiency. it is worth noting that some heavy oils behave non-newtonianly. non-newtonian fluids do not have direct proportionality between applied shear stress and shear rate and viscosity varies with shear rate depending on whether the fluid is either pseudoplastic or dilatant. viscosity decreases as shear rate increases for the former whilst the reverse takes place for dilatants. mathematical models of conventional fluids thus fail when applied to non-newtonian fluids. the pressure derivative curve is introduced in this descriptive work for a dilatant fluid and its pattern was observed. tiab's direct synthesis (tds) methodology was used as a tool for interpreting pressure transient data to estimate effective permeability, skin factors and non-newtonian bank radius. the methodology was successfully verified by its application to synthetic examples. also, comparing it to pseudoplastic behavior, it was found that the radial flow regime in the newtonian zone of dilatant fluids took longer to form regarding both the flow behavior index and consistency factor.

Abstract:
the classical and relativistic hamilton-jacobi approach is applied to the one-dimensional homogeneous potential, v(q) = aqn, where a and n are continuously varying parameters. in the non-relativistic case, the exact analytical solution is determined in terms of a, n and the total energy e. it is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem t(q). a variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. for any value of n, it leads to a simple harmonic oscillator if e > 0, an "anti-oscillator" if e < 0, or a free particle if e = 0. however, such a reduction is not possible in the relativistic case. for a bounded relativistic motion, the first order correction to the period is determined for any value of n. for n >> 1, it is found that the correction is just twice that one deduced for the simple harmonic oscillator (n = 2), and does not depend on the specific value of n.