ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS

This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments.First,for the analytical solutions of the equations,we derive their expressions and asymptotical stability criteria.Second,for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations,we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable.Finally,with a typical example with numerical experiments,we illustrate the applicability of the obtained theoretical results.

Dynamics of a Reaction-Diffusion System with Quiescence

In this paper,the dynamical behavior of a reaction-diffusion system with quiescence in a closed environment is investigated.The global existence of the solution is obtained by the upper and lower solution method,and the dissipative structure of the system is derived by constructing Lyapunov functions.

High accuracy non-equidistant method for singular perturbation reaction-diffusion problem

Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.

STOCHASTIC CRACKING AND HEALING BEHAVIORS OF THIN FILMS DURING REACTION-DIFFUSION GROWTH

The stochastic cracking and healing behaviors of reaction-diffusion growth of thin filmswere studied by means of Markov processes analysis. We chose the thermal growth ofoxide scales on metals as an example of reaction-diffusion growth. The thermal growthof oxide films follows power law when no cracking occurs. Our results showed that thegrowth kinetics under stochastic cracking and healing conditions was different fromthat without cracking. It might be altered to either pseudo-linear or pseudo-power lawsdependent upon the intensity and frequency of the cracking of the films. When thehoping items dominated, the growth followed pseudo-linear law; when the diffusionalitems dominated, it followed pseudo-power law with the exponentials lower than theintrinsical values. The numerical results were in good agreement with the meassuredkinetics of isothermal and cyclic oxidation of NiAl-0.1 Y (at. %) alloys in air at 1273K.

Non-classical phenotypes of autoimmune hepatitis and advances in diagnosis and treatment

Non-classical manifestations of autoimmune hepatitis can delay diagnosis and treatment. Our aims were to describe the clinical phenotypes that can confound the diagnosis, detail scoring systems that can ensure their recognition, and outline advances in treatment that can improve their outcome. Prime source and review articles in English were selected throuqh Medline from 1970-2008 and assimilated into personal libraries spanning 32 years. Acute severe or asymptomatic presentations and atypical histological findings,including centrilobular zone 3 necrosis and concurrent bile duct changes, are compatible with the diagnosis. Cholangiographic abnormalities may be present in children and adults with the disease, and autoimmune hepatitis must be considered in patients without autoantibodies or with antimitochondrial antibodies and no other cholestatic features. Asymptomatic patients frequently become symptomatic; mild disease can progress; and there are no confident indices that justify withholding treatment. Two diagnostic scoring systems with complementary virtues have been developed to evaluate patients with confusing features. Normal liver tests and tissue constitute the optimal end point of treatment, and the first relapse is an indication for long- term azathioprine therapy. Cyclosporine, tacrolimus and mycophenolate mofetil are promising salvage therapies,and budesonide with azathioprine may be a superior frontline treatment. We conclude that the non-classical phenotypes of autoimmune hepatitis can be recognized promptly, diagnosed accurately, and treated effectively.

The Stability Research for the Finite Difference Scheme of a Nonlinear Reaction-diffusion Equation

In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.

Numerical Simulation of Reaction-Diffusion during Carburization of HK40 Steel

Two types of carbides M23C6 and M7C3 precipitate orderly as carbon concentration in a high Cr-Ni austenitic steel increases during carburization process. The mathematical model that describes diffusion of carbon and the precipitation of M23C6 and M7C3 has been studied. A criterion to judge when the transformation of M23C6 to M7C3 is over and M7C3 precipitates directly has been given in simulated calculation. By applying the model, the carburization of HK40 steel has been calculated by means of finite difference computation techniques. The pack carburization tests for the HK40 steel have been carried out at 1273 K. The comparison between the experimental and the calculated results show acceptable agreement.

GLOBAL STABILITY OF TRAVELING WAVEFRONTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY

This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts （waves with speeds c 〉 c＊, where c=c＊ is the minimal speed） is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21].

Hydrolysis Process of the Anticancer Agents Novel Non-classical trans-Platinum(Ⅱ) with Aliphatic Amines

The hydrolysis process of the anticancer agents novel non-classical transplatinum（ Ⅱ ） with aliphatic amines and the influence of solvent models therein have been studied by using hybrid density functional theory （B3LYP）. In this study, the stepwise hydrolysis, trans[PtCl2（Am）（isopropylamine）] ＋ 2H2O → trans-[Pt（Am）（isopropylamine）（OH2）2]^2＋＋ 2Cl^-, was explored. Implicit solvent effects were incorporated through polarized continuum models. The stationary points on the potential energy surfaces for the first and second hydrolysis steps,proceeding via a general SN2 pathway, were fully optimized and characterized. It was found that the first hydrolysis reaction is easier than the second one and the hydrolysis of trans- [PtCl2-（isopropylamine）2] is the easiest in our studying systems. The result can assist in under- tanding the hydrolysis mechanism of trans-[PtCl2（Am）（isopropylamine）] and designing novel Pt-based anticancer drugs.

A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain. The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response). Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy. This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy.

Improving the Stability Problem of the Finite Difference Scheme for Reaction-diffusion Equation

This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.

Random Attractors for Stochastic Reaction-Diffusion Equations with Distribution Derivatives on Unbounded Domains

In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.

A Reaction-Diffusion Algorithm for Segmentation of Three-Dimensional Sinusoidal Networks in Rats Fed a High-Fat and High-Cholesterol Diet: New Insights and Evaluation

Microstructures in the liver are primarily composed of hepatocytes, hepatic blood, and biliary vessels. Because each hepatocyte comes in contact with both vessels, these vessels form three-dimensional (3D) periodic network patterns. Confocal microscope images are useful for observing 3D structures;however, it is necessary to explicitly describe the vessel structures using 3D images of sinusoidal endothelial cells. For this purpose, we propose a new approach for image segmentation based on the Turing reaction-diffusion model, in which temporal and spatial patterns are self-organized. Turing conditions provided reliable tools for describing the 3D structures. Moreover, using the proposed method, the sinusoidal patterns of rats fed a high-fat/high-cholesterol diet were examined;these rats exhibited pathological features similar to those of human patients with nonalcoholic steatohepatitis related to metabolic syndrome. The findings showed that the parameter in diffusion terms differed significantly among the experimental groups. This observation provided a heuristic argument for parameter selection leading to pattern recognition problems in diseased rats.

THE ANALYTICAL APPROACH FOR LARGE SCALE NON-CLASSICALLY DAMPED DYNAMIC SYSTEM

This paper gives a dynamic decoupling approach for the analysis of large scale non-classically damped system, in which the complex variable computations were completely avoided not only in solving for the eigenvalue problem but also in the calculation of the dynamic response. The analytical approaches for undamped gyroscopic system, non-classically damped system, including the damped gyroscopic system were unified. Very interesting and useful theoretical results, practical algorithms were obtained which are applicable to both non-defective and defective systems.

UNIFORM QUASI-DIFFERENTIABILITY OF SEMIGROUP TO NONLINEAR REACTION-DIFFUSION EQUATIONS WITH SUPERCRITI C AL EXPONENT

A new approach, is established to show that the semigroup {S（t）≥0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in L^q（Ω） （2 ≤ q 〈 ∞） with respect to the initial value. As an application, this proves the upper-bound of fractal dimension for its global attractor in the corresponding space.

Blow-up for a Class of Degenerate Reaction-diffusion Equation with Nonlocal Source

This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditions for that the solution exists globally or blows up in the finite time.Then the blow-up time is also given.At last,we obtain a property differing from the local source which the blow-up set is the entire interval.

Concrete damage diagnosed using the non-classical nonlinear acoustic method

It is known that the strength of concrete is seriously affected by damage and cracking. In this paper, six concrete samples under different damage levels are studied. The experimental results show a linear dependence of the resonance frequency shift on strain amplitude at the fundamental frequency, and approximate quadratic dependence of the am- plitudes of the second and third harmonics on strain amplitude at the fundamental frequency as well. In addition, the amplitude of the third harmonics is shown to increase with the increase of damage level, which is even higher than that of the second harmonics in samples with higher damage levels. These are three properties of non-classical nonlinear acoustics. The nonlinear parameters increase from 106 to 108 with damage level, and are more sensitive to the damage level of the concrete than the linear parameters obtained by using traditional acoustics methods. So, this method based on non-classical nonlinear acoustics may provide a better means of non-destructive testing （NDT） of concrete and other porous materials.

The First Integral Method to Study a Class of Reaction-Diffusion Equations

In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.

Simulating Some Complex Phenomena in Hydrothermal Ore-Forming Processes by Reaction-Diffusion CNN

Complexity phenomena like dynamic and static patterns, order from disorder, chaos and catastrophe were simulated by the application of 2-D reaction-diffusion CNN of two state variables and two diffusion coefficients transformed from Zhabotinksii model. They revealed somehow the mechanism of hydrothermal ore-forming processes, and answered several questions about the onset of ore forming.

Sign-invariant and Explicit Solutions of Nonlinear Reaction-Diffusion Systems

Using the sign-invariant theory, we study the nonlinear reaction-diffusion systems. We also obtain some new explicit solutions to the nonlinear resulting systems.