Double Elzaki Transform Decomposition Method for Solving Non-Linear Partial Differential Equations

In this paper, we discuss a new method employed to tackle non-linear partial differential equations, namely Double Elzaki Transform Decomposition Method (DETDM). This method is a combination of the Double ELzaki Transform and Adomian Decomposition Method. This technique is hereafter provided and supported with necessary illustrations, together with some attached examples. The results reveal that the new method is very efficient, simple and can be applied to other non-linear problems.

An Analysis of the Impact of Economic-Ecological Balance Mechanism Based on Non-Linear Partial Differential Equations on Land Financial Teaching Methods

This paper clarifies the relationship between the flow paths of the corresponding ecological flows because of the ecological impact for land consolidation, using external energy methods to measure the external input of the project area or the output of ecological products. The application for nonlinear estimation of partial differential equations to land consolidation, the project ecological flow and system efficiency were quantitatively calculated. It shows that the conflict between fairness and efficiency is caused under conditions and levels of value and ecological compensation mechanism is built as a criterion for this ecological economics. Based on the years of use of the land improvement project, the time evolution of regional net ecological value, natural resource dependence, renewable resource dependence, ecological output ratio, ecological carrying capacity and ecological sustainability after the implementation of the project was assessed.

ON THE HOLOMORPHIC SOLUTION OF NON-LINEAR TOTALLY CHARACTERISTIC EQUATIONS WITH SEVERAL SPACE VARIABLES

In this paper the authors study a class of non-linear singular partial differential equation in complex domain C-t x C-x(n). Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of C-t x C-x(n).

一类泛函偏微分方程边值问题解的振动性及其应用

利用泛函微分不等式方法,讨论了一类中立型双曲泛函偏微分方程边值问题解的振动性,并建立了此类边值问题解的一个振动准则.作为应用给出了一个具体例子。

径向流场瓦斯压力分布

研究煤层瓦斯径向流场的流动方程——非线性偏微分方程的解析解迄今仍是数学难题。作者通过变量替换和适当化简,获得其近似的解析解,即径向流场瓦斯压力分布规律表达式,以此建立起煤层瓦斯抽放参数的解析计算式。经计算机的数值计算验证,新的解析式是可靠的,而且精度较高,简便实用。

A Novel Nonlinear Algorithm for Typhoon Cloud Image Enhancement

A novel nonlinear gray transform method is proposed to enhance the contrast of a typhoon cloud image.Generally,the typhoon cloud image obtained by a satellite cannot be directly used to make an accurate prediction of the typhoon＇s center or intensity because the contrast of the received typhoon cloud image may be bad.Our aim is to extrude the typhoon＇s eye in the typhoon cloud image.A normalized arc-tangent transformation operation is designed to enhance global contrast of the typhoon cloud image.Differential evolution algorithm is used to choose the optimal nonlinear transform parameter.Finally,geodesic activity contour model is used to extract the typhoon＇s eye to verify the performance of the proposed method.Experimental results show that the proposed method can efficiently enhance the global contrast of the typhoon cloud image while greatly extruding the typhoon＇s eye.

A Thermal-Hydraulic Coolant Channel Module (CCM) for Single- and Two-Phase Flow

A theoretical “drift-flux based thermal-hydraulic mixture-fluid coolant channel model” is presented. It is the basis to a corresponding digital “Coolant Channel Module (CCM)”. This purpose derived “Separate-Region Mixture Fluid Approach” should yield an alternative platform to the currently dominant “Separate-Phase Models” where each phase is treated separately. Contrary to it, a direct procedure could be established with the objective to simulate in an as general as possible way the steady state and transient behaviour of characteristic parameters of single- and/or (now non-separated) two-phase fluids flowing within any type of heated or non-heated coolant channels. Their validity could be confirmed by a wide range of verification and validation runs, showing very satisfactory results. The resulting universally applicable code package CCM should provide a fundamental element for the simulation of thermal-hydraulic situations over a wide range of complex systems (such as different types of heat exchangers and steam generators as being applied in both conventional but also nuclear power stations, 1D and 3D nuclear reactor cores etc). Thereby the derived set of equations for different coolant channels (distinguished by their key numbers) as appearing in these systems can be combined with other ODE-s and non-linear algebraic relations from additional parts of such an overall model. And these can then to be solved by applying an appropriate integration routine. Within the solution procedure, however, mathematical discontinuities can arise. This due to the fact that along such a coolant channel transitions from single- to two-phase flow regimes and vice versa could take place. To circumvent these difficulties it will in the presented approach be proposed that the basic coolant channel (BC) is subdivided into a number of sub-channels (SC-s), each of them being occupied exclusively by only a single or a two-phase flow regime. After an appropriate nodalization of the BC (and thus its SC-s) and after applying a “modified finite volume method” together with other special activities the fundamental set of non-linear thermal-hydraulic partial differential equations together with corresponding constitutive relations can be solved for each SC separately. As a result of such a spatial discretization for each SC type (and thus the entire BC) the wanted set of non-linear ordinary differential equations of 1st order could be established. Obviously, special attention had to be given to the varying SC entrance or outlet positions, describing the movement of boiling boundaries or mixture levels along the channel. Including even the possibility of SC-s to disappear or be created anew during a transient.

QUEUEING NETWORKS WITH INSTANTANEOUS SEQUENTIAL TRANSITIONS

We study queueing networks with instantaneous transitions of sequential batch departures and sequential batch arrivals. Unlike most of the existing models, this network is shown not to have a product form solution. An "extra arrival condition" is introduced under which the network is shown to possess a product form stationary distribution. Fur- thermore, the product form solution serves as a stochastic upper bound for the original network without the extra arrival process. The results include many queueing network models reported in the literature, e.g. the assembly transfer networks recently introduced by Miyazawa and Taylor, as special cases. We show that the network with the extra arrival process is "structurally reversible" in the sense that its reversed process has the same network structure. Local balances for this network are presented and discussed.

Scaling limits of interacting diffusions in domains

We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. They are general microscopic models that can be used to describe macroscopic phenomena with coupled boundary conditions, such as the popula- tion dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the empirical measures of the spatial positions of the particles. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.