Variation of hydraulic gradient in nonlinear finite strain consolidation

In the research field of ground water, hydraulic gradient is studied for decades. In the consolidation field, hydraulic gradient is yet to be investigated as an important hydraulic variable. So, the variation of hydraulic gradient in nonlinear finite strain consolidation was focused on in this work. Based on lab tests, the nonlinear compressibility and nonlinear permeability of Ningbo soft clay were obtained. Then, a strongly nonlinear governing equation was derived and it was solved with the finite element method.Afterwards, the numerical analysis was performed and it was verified with the existing experiment for Hong Kong marine clay. It can be found that the variation of hydraulic gradient is closely related to the magnitude of external load and the depth in soils. It is interesting that the absolute value of hydraulic gradient(AVHG) increases rapidly first and then decreases gradually after reaching the maximum at different depths of soils. Furthermore, the changing curves of AVHG can be roughly divided into five phases. This five-phase model can be employed to study the migration of pore water during consolidation.

CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT

In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.

Research of the Conductive Structure of Crust and the Upper Mantle beneath the South-Central Tibetan Plateau

With the super-wide band magnetoteiluric sounding data of the JUong （吉隆）-Cuoqin （措勤） profile （named line 800） which was completed in 2001 and the Dingri （定日）-Cuomai （措迈） profile （named line 900） which was completed in 2004, we obtained the strike direction of each MT station by strike analysis, then traced profiles that were perpendicular to the main strike direction, and finally obtained the resistivity model of each profile by nonlinear conjugate gradients （NLCG） inversion. With these two models, we described the resistivity structure features of the crust and the upper mantle of the center-southern Tibetan plateau and its relationship with Yalung Tsangpo suture： the upper crust of the research area is a resistive layer with resistivity value range of 200-3 000 Ω.m. The depth of its bottom surface is about 15-20 km generally, but the bottom surface of resistive layer is deeper in the middle of these two profiles. At llne 900, it is about 30 km deep, and even at line 800, it is about 38 km deep. There is a gradient belt of resistivity at the depth of 15-45 km, and a conductive layer is beneath it with resistivity even less than 5 Ω.m. This conductive layer is composed of individual conductive bodies, and at the south of the Yalung Tsangpo suture, the conductive bodies are smaller with thickness about 10 km and lean to the north slightly. However, at the north of the Yalung Tsangpo suture, the conductive bodies are larger with thickness about 30 km and also lean to the north slightly. Relatively, the conductive bodies of line 900 are thinner than those of line 800, and the depth of the bottom surface of line 900 is also shallower. At last, after analyzing the effect factors to the resistivity of rocks, it was concluded that the very conductive layer was caused by partial melt or connective water in rocks. It suggests that the middle and lower crust of the center-southern Tibetan plateau is very thick, hot, flabby, and waxy.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

On the Cauchy Problem of Evolution p-Laplacian Equation with Nonlinear Gradient Term

The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.

An improved nonlinear conjugate gradient method with an optimal property

Conjugate gradient methods have played a special role in solving large scale nonlinear problems. Recently, the author and Dai proposed an efficient nonlinear conjugate gradient method called CGOPT, through seeking the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method. In this paper, we make use of two types of modified secant equations to improve CGOPT method. Under some assumptions, the improved methods are showed to be globally convergent. Numerical results are also reported.

Hlder Continuity of the Gradient of Solutions of Nonlinear Degenerate Parabolic Systems

§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if p>2 or singular if 1<p<2. A vector function u=(u1, u2, …, um) defined in ΩT=Ω×[0, T] is called a solution of the system (1.1) if

Exact boundary behavior of large solutions to semilinear elliptic equations with a nonlinear gradient term

This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f.

A CONJUGATE GRADIENT METHOD FOR DISCRETE-TIME OUTPUT FEEDBACK CONTROL DESIGN

In this paper, the discrete-time static output feedback control design problem is con- sidered. A nonlinear conjugate gradient method is analyzed and studied for solving an unconstrained matrix optimization problem that results from this optimal control prob- lem. In addition, through certain parametrization to the optimization problem an initial stabilizing static output feedback gain matrix is not required to start the conjugate gradi- ent method. Finally, the proposed algorithms are tested numerically through several test problems from the benchmark collection.

A COMPUTATIONAL APPROACH FOR OPTIMAL CONTROL SYSTEMS GOVERNED BY PARABOLIC VARIATIONAL INEQUALITIES

Iterative techniques for solving optimal control systems governed by parabolic varia-tional inequalities are presented. The techniques we use are based on linear finite elements method to approximate the state equations and nonlinear conjugate gradient methods to solve the discrete optimal control problem. Convergence results and numerical experiments are presented.