HARNACK ESTIMATES FOR WEAK SOLUTIONS OF EQUATIONS OF NON-NEWTONIAN POLYTROPIC FILTRATION

51. IntroductionIn this paper we investigate the local behavior of nonnegative weak solutions for theequations of non-Newtonian polytropic filtrationac -- div(IDumlp--'Dam) = 0,m(p -- 1) < 1,m > 0,p > l, in D'(flT),u E CI..(0, T; L?o.(n)), urn E Lro.(0, T; WI:)l(fl)), (1.1)where n is an open set of R", N 2 1, 0 < T < ool fiT ~ fix (0, T), and D ~ (k,', e).Equation (1.1) appears in a number of applications to describe the evolution of diffusion.The evolution HLaplacian equationut ~ …     

Shear induced phase transition in PbO under high pressure

We have studied the structural behavior of lead monoxide (PbO) as a function of pressure via angular dispersive X-ray diffraction employing two different pressure transmitting media that were quasi-hydrostatic (N₂) and non-hydrostatic (MgO), respectively. Besides litharge (-PbO) and massicot (β-PbO), which are both stable at ambient pressure, there is an orthorhombic γ-PbO phase which appears upon application of pressure to -PbO. We have found that the orthorhombic γ-PbO phase is favored by shear stress under non-hydrostatic conditions. -PbO shows strong anisotropy in compressibility. The a-axis is rather incompressible with a linear stiffness coefficient of K_a0=540(30) GPa whereas the c-axis stiffness is K_c0=25(1) GPa. The bulk modulus of -PbO is K₀=23.1(3) GPa and its derivative .     

岩盐结构氧化锌物态方程的分子动力学模拟

利用分子动力学方法和有效经验对势模型对ZnO岩盐结构高温高压下的物态方程进行了研究， 发现分子动力学方法得到的ZnO岩盐结构的摩尔体积(300?1273 K，3.2?10.4 GPa)和实验结果吻合；另外，基于经验势模型的可靠性预测了1373?2273 K和0? 50 GPa的ZnO岩盐结构的P-V -T关系，并利用相应的热力学公式拟合得到了ZnO岩盐结构常态下的线性热膨胀系数、等温体模量及其对压力的一阶导数等重要的热力学参量．     

Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate

In this Letter, the problem of forced convection over a horizontal flat plate is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.     

A stochastic lagrangean picture for the three dimensional navier-stokes equation +

We derive a representation formula for the solutions of the navier-Stokes flow in three dimensions in absence of boundary in terms of stochastic current lines. This pictures generalizes an analogous one given in two dimensions and on the other hand the classical Lafrangian picture for the Euler flow. We prove a Vanishing viscosity limit for the whole structure     

“Vapor-liquid” equilibrium measurements and modeling for the cyclohexane + n-hexanoic acid binary system

To simulate cyclohexane to cyclohexanol oxidation reactors, the acquisition and modeling of vapor-liquid equilibria of the key components, under the process conditions, are essential. n-Hexanoic acid is a co-product of the reaction. Vapor-liquid equilibrium data are reported for the cyclohexane + n-hexanoic acid binary system at four temperatures: 413, 423, 464 and 484 K. All measurements have been carried out using an apparatus based on the “static-analytic” method, with two ROLSI™ pneumatic capillary samplers. The generated data are successfully correlated using two equations of state, the Peng-Robinson (PR) and the Perturbed Chain Statistical Association Fluid Theory (PC-SAFT). Both models are capable of representing the experimental data, but the PC-SAFT EoS uses less binary interaction parameters.     

Solution of the least squares method problem of pairwise comparison matrices

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima. This research was supported in part by the Hungarian Scientific Research Fund, Grant No. OTKA K 60480.     

Numerical solution of reaction–diffusion equations by compact operators and modified equation methods

A system of reaction–diffusion equations which governs the propagation of an ozone decomposition laminar flame in Lagrangian co-ordinates is analysed by means of compact operators and modified equation methods. It is shown that the use of fourth-order accurate compact operators yields very accurate solutions if sufficient numbers of grid points are located at the flame front, where very steep gradients of temperature and species concentrations exist. Modified equation methods are shown to impose a restriction on the time step under certain conditions. The solutions obtained by means of compact operators and modified equation methods are compared with solutions obtained by other methods; good agreement is obtained.     

Series solutions of nano boundary layer flows by means of the homotopy analysis method

We present here a ‘similar’ solution for the nano boundary layer with nonlinear Navier boundary condition. Three types of flows are considered: (i) the flow past a wedge; (ii) the flow in a convergent channel; (iii) the flow driven by an exponentially-varying outer flows. The resulting differential equations are solved by the homotopy analysis method. Different from the perturbation methods, the present method is independent of small physical parameters so that it is applicable for not only weak but also strong nonlinear flow phenomena. Numerical results are compared with the available exact results to demonstrate the validity of the present solution. The effects of the slip length ?, the index parameters n and m on the velocity profile and the tangential stress are investigated and discussed.