Transient spherical flow of non-newtonian power-law fluids in porous media

The transient spherical flow behavior of a slightly compressible non-Newtonian, power-law fluids in porous media is studied. A nonlinear partial differential equation of parabolic type is derived. The diffusivity equation for spherical flow is a special case of the new equation. We obtain analytical, asymptotic and approximate solutions by using the methods of Laplace transform and weighted mass conservation. The structures of asymptotic and approximate solutions are similar, which enriches the theory of one-dimensional flow of non-Newtonian fluids through porous media.     

Sensitivity analysis of truss structures and its application to the fully stressed design

Based upon the theorems of structural variations this paper derives a set of expressions for calculating partial derivatives of internal forces, stresses and joint displacements with respect to bar areas for truss structures. Compared with the known formulas for finding the gradients of structural behaviours the calculation effort with the proposed expressions in this paper is usually smaller because the additional virtual loadings needed are relatively fewer. It is of practical significance to various optimization methods in which the calculation of gradients of behaviours is widely used. Moreover, applying the derived formulas to the fully stressed design (FSD), we obtain an improved iterative method for FSD. The numerical examples show that the new method considerably reduces the reanalysis number required to converge to an FSD in comparison with the simple stress ratio method.     

Fixed stream-tube method for solving two-phase plane flow problems and its theoretical analysis

The fixed stream-tube method widely adopted in engineering field for giving an approximate solution to the two-dimensional problems of two-phase flow through porous media is summarized and an improvement has been made in this paper. Its core part, i.e., the fluid displacement within a one-dimensional stream tube with variable cross-sectional area under a given pressure difference across the tube is thoroughly studied. The existence and uniqueness of solution are proved, the exact solution, numerical solution and its convergence, stability analyses are given in this paper.     

Symmetric formulation of tangential stiffnesses for non-associated plasticity

A numerical scheme is presented which makes it possible to use the symmetric equation solvers in tangential stiffness programs for non-associated materials.     

Asymptotic behavior of solutions for some chemical reactions models

1.IntroductionInthispapertweareconcernedwiththeasymptoticbehaviorofglobalpositivesolutionstothefollowingsemilinearreaction-dictionsystemac--didn=--any bltv,(1.1)yi--daal=--any bZw,xEfi,t>0(1.2)ac--daal=any--bZw,(1.3)withhomogeneousNeumannboundaryconditionsonofof~~on--an=on,xeoff,t>o(1.4)andinitialvalueconditionsu(x,0)="o(x),v(x,0)=v000,w(x,0)=w000,xEn,(l.5)wherenCRNisaboundeddomainwithsmoothboundaloff,kdenotestheoutwardnormalderiVativeonoff,anddltd2,d3,a,hi,bZarepositiveconstallts.Problem(…     

A Branch and Contract Algorithm for Problems with Concave Univariate, Bilinear and Linear Fractional Terms

A new deterministic branch and bound algorithm is presented in this paper for the global optimization of continuous problems that involve concave univariate, bilinear and linear fractional terms. The proposed algorithm, the branch and contract algorithm, relies on the use of a bounds-contraction subproblem that aims at reducing the size of the search region by eliminating portions of the domain in which the objective function takes only values above a known upper bound. The solution of contraction subproblems at selected branch and bound nodes is performed within a finite contraction operation that helps reducing the total number of nodes in the branch and bound solution tree. The use of the proposed algorithm is illustrated with several numerical examples.     

Kuramoto-Sivashinsky方程解的定性分析

研究Kuramoto-Sivashinsky方程的两种初边值问题,运用Galerkin方法给出一系列先验估计结果,得到广义解和古典解的存在唯一性、正则性及某些条件下的渐近性质。     

Global W2,p (2<=p

This paper studies the initial-boundary value problem of GBBM equations u_t - Δu_t = div f(u) \qquad\qquad\qquad(a) u(x, 0) = u_0(x)\qquad\qquad\qquad(b) u |∂Ω = 0 \qquad\qquad\qquad(c) in arbitrary dimensions, Ω ⊂ R^n. Suppose that. f(s) ∈ C¹ and |f'(s)| ≤ C (1+|s|^ϒ), 0 ≤ ϒ ≤ \frac{2}{n-2} if n ≥ 3, 0 ≤ ϒ < ∞ if n = 2, u_0 (x) ∈ W^{2⋅p}(Ω) ∩ W^{1⋅p}_0(Ω) (2 ≤ p < ∞), then ∀T > 0 there exists a unique global W^{2⋅p} solution u ∈ W^{1,∞}(0, T; W{2⋅p}(Ω)∩ W^{1⋅p}_0(Ω)), so the known results are generalized and improved essentially.