980 resultados para fifth-order nonlinearity


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This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

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数值模式是潮波研究的一种有利手段,但在研究中会面临各种具体问题,包括开边界条件的确定、底摩擦系数和耗散系数的选取等。数据同化是解决这些问题的一种途径,即利用有限数量的潮汐观测资料对潮波进行最优估计,其根本目的是迫使模型预报值逼近观测值,使模式不要偏离实际情况太远。本文采用了一种优化开边界方法,沿着数值模型的开边界优化潮汐水位信息,目的是设法使数值解在动力约束的意义下接近观测值,获得研究区域的潮汐结果。边界值由指定优化问题的解来定,以提高模拟区域的潮汐精度,最优问题的解是基于通过开边界的能量通量的变化,处理开边界处的观测值与计算值之差的最小化。这里提供了辐射型边界条件,由Reid 和Bodine(本文简称为RB)推导,我们将采用的优化后的RB方法(称为ORB)是优化开边界的特殊情况。 本文对理想矩形海域( E- E, N- N, 分辨率 )进行了潮波模拟,有东部开边界,模式采用ECOM3D模式。对数据结果的误差分析采用,振幅平均偏差,平均绝对偏差,平均相对误差和均方根偏差四个值来衡量模拟结果的好坏程度。 需要优化入开边界的解析潮汐值本文采用的解析解由方国洪《海湾的潮汐与潮流》(1966年)方法提供,为验证本文所做的解析解和方文的一致,本文做了其第一个例子的关键值a,b,z,结果与其结果吻合的相当好。但略有差别,分析的可能原因是两法在具体迭代方案和计算机保留小数上有区别造成微小误差。另外,我们取m=20,得到更精确的数值,我们发现对前十项的各项参数值,取m=10,m=20各项参数略有改进。当然我们可以获得m更大的各项参数值。 同时为了检验解析解的正确性讨论m和l变化对边界值的影响,结果指出,增大m,m=20时,u的模最大在本身u1或u2的模的6%;m=100时,u的模最大在本身u1或u2的模的4%;m再增大,m=1000时,u的模最大在本身u1或u2的模的4%,改变不大。当l<1时, =0处u的模最大为2。当l=1时, =0处u的模最大为0.1,当l>1时,l越大,u的模越小,当l=10时,u的模最大为0.001,可以认为为0。 为检验该优化方法的应用情况,我们对理想矩形区域进行模拟,首先将本文所采用的优化开边界方法应用于30m的情况,在开边界优化入开边界得出模式解,所得模拟结果与解析解吻合得相当好,该模式解和解析解在整个区域上,振幅平均绝对偏差为9.9cm,相位平均绝对偏差只有4.0 ,均方根偏差只有13.3cm,说明该优化方法在潮波模型中有效。 为验证该优化方法在各种条件下的模拟结果情况,在下面我们做了三类敏感性试验: 第一类试验:为证明在开边界上使用优化方法相比于没有采用优化方法的模拟解更接近于解析解,我们来比较ORB条件与RB条件的优劣,我们模拟用了两个不同的摩擦系数,k分别为:0,0.00006。 结果显示,针对不同摩擦系数,显示在开边界上使用ORB条件的解比使用RB条件的解无论是振幅还是相位都有显著改善,两个试验均方根偏差优化程度分别为84.3%,83.7%。说明在开边界上使用优化方法相比于没有采用优化方法的模拟解更接近于解析解,大大提高了模拟水平。上述的两个试验得出, k=0.00006优化结果比k=0的好。 第二类试验,使用ORB条件确定优化开边界情况下,在东西边界加入出入流的情况,流考虑线性和非线性情况,结果显示,加入流的情况,潮汐模拟的效果降低不少,流为1Sv的情况要比5Sv的情况均方根偏差相差20cm,而不加流的情况只有0.2cm。线性流和非线性流情况两者模式解相差不大,振幅,相位各项指数都相近, 说明流的线性与否对结果影响不大。 第三类试验,不仅在开边界使用ORB条件,在模式内部也使用ORB条件,比较了内部优化和不优化情况与解析解的偏差。结果显示,选用不同的k,振幅都能得到很好的模拟,而相位相对较差。另外,在内部优化的情况下,考虑不同的k的模式解, 我们选用了与解析解相近的6个模式解的k,结果显示,不同的k,振幅都能得到很好的模拟,而相位较差。 总之,在开边界使用ORB条件比使用RB条件好,振幅相位都有大幅度改进,在加入出入流情况下,流的大小对模拟结果有影响,但线形流和非线性流差别不大。内部优化的结果显示,模式采用不同的k都能很好模拟解析解的振幅。

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The primary approaches for people to understand the inner properties of the earth and the distribution of the mineral resources are mainly coming from surface geology survey and geophysical/geochemical data inversion and interpretation. The purpose of seismic inversion is to extract information of the subsurface stratum geometrical structures and the distribution of material properties from seismic wave which is used for resource prospecting, exploitation and the study for inner structure of the earth and its dynamic process. Although the study of seismic parameter inversion has achieved a lot since 1950s, some problems are still persisting when applying in real data due to their nonlinearity and ill-posedness. Most inversion methods we use to invert geophysical parameters are based on iterative inversion which depends largely on the initial model and constraint conditions. It would be difficult to obtain a believable result when taking into consideration different factors such as environmental and equipment noise that exist in seismic wave excitation, propagation and acquisition. The seismic inversion based on real data is a typical nonlinear problem, which means most of their objective functions are multi-minimum. It makes them formidable to be solved using commonly used methods such as general-linearization and quasi-linearization inversion because of local convergence. Global nonlinear search methods which do not rely heavily on the initial model seem more promising, but the amount of computation required for real data process is unacceptable. In order to solve those problems mentioned above, this paper addresses a kind of global nonlinear inversion method which brings Quantum Monte Carlo (QMC) method into geophysical inverse problems. QMC has been used as an effective numerical method to study quantum many-body system which is often governed by Schrödinger equation. This method can be categorized into zero temperature method and finite temperature method. This paper is subdivided into four parts. In the first one, we briefly review the theory of QMC method and find out the connections with geophysical nonlinear inversion, and then give the flow chart of the algorithm. In the second part, we apply four QMC inverse methods in 1D wave equation impedance inversion and generally compare their results with convergence rate and accuracy. The feasibility, stability, and anti-noise capacity of the algorithms are also discussed within this chapter. Numerical results demonstrate that it is possible to solve geophysical nonlinear inversion and other nonlinear optimization problems by means of QMC method. They are also showing that Green’s function Monte Carlo (GFMC) and diffusion Monte Carlo (DMC) are more applicable than Path Integral Monte Carlo (PIMC) and Variational Monte Carlo (VMC) in real data. The third part provides the parallel version of serial QMC algorithms which are applied in a 2D acoustic velocity inversion and real seismic data processing and further discusses these algorithms’ globality and anti-noise capacity. The inverted results show the robustness of these algorithms which make them feasible to be used in 2D inversion and real data processing. The parallel inversion algorithms in this chapter are also applicable in other optimization. Finally, some useful conclusions are obtained in the last section. The analysis and comparison of the results indicate that it is successful to bring QMC into geophysical inversion. QMC is a kind of nonlinear inversion method which guarantees stability, efficiency and anti-noise. The most appealing property is that it does not rely heavily on the initial model and can be suited to nonlinear and multi-minimum geophysical inverse problems. This method can also be used in other filed regarding nonlinear optimization.

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In the engineering reinforcement of-rock and soil mass, engineers must consider how to obtain better reinforcing effect at the cost of less reinforcing expense, which, in fact, is the aim of reinforcement design. In order to accomplish the purpose, they require not only researching the material used to reinforce and its structure, but also taking into account of several important geological factors, such as the structure and property of rock and soil mass. How to improve the reinforcing effect according to engineering geomechanical principle at the respect of the reinforcement of engineering soil and rock mass is studied and discussed in this paper. The author studies the theory, technology and practice of geotechnical reinforcement based on engineering geomechanics, taking example for the soil treatment of Zhengzhou Airport, the effect analysis of reinforcement to the slope on the left bank of Wuqiangxi Hydropower Station and the reinforcing design of the No. 102 Landslide and unique sand-slide slope on the Sichuan-Tibet Highway. The paper is comprised of two parts for the convenience of discussion. In the first part, from the first chapter to the fifth chapter, trying to perform the relevant research and application at the viewpoint of soil mass engineering geomechanics, the author mainly discusses the study of reinforcing soft ground soil through dynamical consolidation and its application. Then, in the second part, from the sixth chapter to the eleventh chapter, the study of new technologies in the rock slope reinforcement and their application are discussed. The author finds that not only better reinforcing effect can be gained in the research where the principle and method of rock mass engineering geomechanics is adopted, but also new reinforcing technologies can be put forward. Zhengzhou Airport is an important one in central plains. It lies on Yellow River alluvial deposit and the structure of stratum is complex and heterogeneous. The area of airport is very large, which can result in differential settlement easily, damage of airport and aircraft accident, whereas, there are no similar experiences to dispose the foundation, so the foundation treatment become a principal problem. During the process of treatment, the method of dynamic compaction was adopted after compared with other methods using the theory of synthetic integration. Dynamic compaction is an important method to consolidate foundation, which was successfully used in the foundation of Zhengzhou Airport. For fill foundation, controlling the thickness of fill so as to make the foundation treatment can reach the design demand and optimum thickness of the fill is a difficult problem. Considering this problem, the author proposed a calculation method to evaluate the thickness of fill. The method can consider not only the self-settlement of fill but also the settlement of the ground surface under applied load so as to ensure the settlement occurred during the using period can satisfy the design demand. It is proved that the method is correct after using it to choose reasonable energy of dynamic compaction to treat foundation. At the same time, in order to examine the effect of dynamic compaction, many monitor methods were adopted in the test such as static loading test, modulus of resilience test, deep pore pressure -test, static cone penetration test and the variation of the pore volume measurement. Through the tests, the author summarized the discipline of the accumulation and dissipation of pore pressure in Yellow River alluvial deposit under the action of dynamic compaction, gave a correct division of the property change of silt and clay under dynamic compaction, determined the bearing capacity of foundation after treatment and weighted the reinforcing effect of dynamic consolidation from the variation of the soil particle in microcosmic and the parameter of soil mass' density. It can be considered that the compactness of soil is in proportion to the energy of dynamic compaction. This conclusion provided a reference to the research of the "Problem of Soil Structure-the Central Problem of Soil Mechanics in 21 Century ". It is also important to strengthen rock mass for water conservancy and electric power engineering. Slip-resistance pile and anchoring adit full of reinforced concrete are usually adopted in engineering experience to strengthen rock mass and very important for engineering. But there also some deficiency such as the weakest section can't be highlighted, the monitor is inconvenient and the diameter of pile and adit is very large etc. The author and his supervisor professor Yangzhifa invented prestressed slip-resistance pile and prestressed anchoring adit full of reinforced concrete, utilizing the advantage that the prestressed structure has better anti-tensile characteristic (this invention is to be published). These inventions overcome the disadvantages of general slip-resistance pile and anchoring adit full of reinforced concrete and have the functions of engineering prospecting, strengthening, drainage and monitor simultaneous, so they have better strengthened effect and be more convenient for monitor and more economical than traditional methods. Drainage is an important factor in treatments of rock mass and slop. In view of the traditional drainage method that drainage pore often be clogged so as to resulted in incident, professor Yangzhifa invented the method and setting of guide penetration by fiber bundle. It would take good effect to use it in prestressed slip-resistance pile and anchoring adit full of reinforced concrete. In this paper, the author took example for anchoring adit full of reinforced concrete used to strengthen Wuqiangxi left bank to simulate the strengthened effect after consolidated by prestressed slip-resistance pile, took example for 102 landslide occurred along Sichuan-Tibet highway to simulate the application of slip-resistance pile and the new technology of drainage. At the same time the author proposed the treatment method of flowing sand in Sichuan-Tibet highway, which will benefit the study on strengthening similar engineering. There are five novelties in the paper with the author's theoretical study and engineering practice: 1. Summarizing the role of pore water pressure accumulation and dissipation of the Yellow River alluvial and diluvial soil under the action of dynamical consolidation, which has instructive significance in the engineering construction under the analogical engineering geological conditions in the future. It has not been researched by the predecessors. 2. Putting forward the concept of density D in microcosmic based on the microcosmical structure study of the soil sample. Adopting D to weight the reinforcing effect of dynamic consolidation is considered to be appropriate by the means of comparing the D values of Zhengzhou Airport's ground soil before with after dynamically consolidating reinforcement, so a more convenient balancing method can be provided for engineering practice. 3. According to the deep research into the soil mass engineering geology, engineering rock and soil science, soil mechanics, as well as considerable field experiments, improving the consolidating method in airport construction, from the conventional method, which is dynamically compactmg original ground surface firstly, then filling soil and dynamically layer-consolidating or layer-compacting at last to the upgraded method, which is performing dynamical consolidation after filling soil to place totally at the extent of the certain earth-filling depth. The result of the dynamical consolidation not only complies with the specifications, but also reduces the soil treatment investment by 10 million RMB. 4. Proposing the method for calculating the height of the filled soil by the means of estimating the potential displacement produced in the original ground surface and the filled earth soil under the possible load, selecting the appropriate dynamically-compacting power and determining the virtual height of the filled earth soil. The method is proved to be effective and scientific. 5. According to the thought of Engineering Geomechanics Metal-Synthetic Methodology (EGMS), patenting two inventions (to the stage of roclamation, with Professor Yang Zhi-fa, the cooperative tutor, and etc.) in which multi-functions, engineering geological investigation, reinforcement, drainage and strength remedy, are integrated all over in one body at the viewpoint of the breakage mechanism of the rock slope.

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The topic of this study is about the propagation features of elastic waves in the anisotropic and nonlinear media by numerical methods with high accuracy and stability. The main achievements of this paper are as followings: Firstly, basing on the third order elastic energy formula, principle of energy conservation and circumvolved matrix method, we firstly reported the equations of non-linear elastic waves with two dimensions and three components in VTI media. Secondly, several conclusions about some numerical methods have been obtained in this paper. Namely, the minimum suitable sample stepth in space is about 1/8-1/12 of the main wavelength in order to distinctly reduce the numerical dispersion resulted from the numerical mehtod, at the same time, the higher order conventional finite difference (CFD) schemes will give little contribution to avoid the numerical solutions error accumulating with time. To get the similar accuracy with the fourth order center finite difference method, the half truncation length of SFFT should be no less than 7. The FDFCT method can present with the numerical solutions without obvious dispersion when the paprameters of FCT is suitable (we think they should be in the scope from 0.0001 to 0.07). Fortunately, the NADM method not only can reported us with the higher order accuracy solutions (higher than that of the fourth order finite difference method and lower than that of the sixth order finite difference method), but also can distinctly reduce the numerical dispersion. Thirdly, basing on the numerial and theoretical analysis, we reported such nonlinear response accumulating with time as waveform aberration, harmonic generation and resonant peak shift shown by the propagation of one- and two-dimensional non-linear elasticwaves in this paper. And then, we drew the conclusion that these nonlinear responses are controlled by the product between nonlinear strength (SN) and the amplitude of the source. At last, the modified FDFCT numerical method presented by this paper is used to model the two-dimensional non-linear elastic waves propagating in VTI media. Subsequently, the wavelet analysis and polarization are adopted to investigate and understand the numerical results. And then, we found the following principles (attention: the nonlinear strength presented by this paper is weak, the thickness of the -nonlinear media is thin (200m), the initial energy of the source is weak and the anisotropy of the media is weak too): The non-linear response shown by the elastic waves in VTI media is anisotropic too; The instantaneous main frequency sections of seismic records resulted from the media with a non-linear layer have about 1/4 to 1/2 changes of the initial main frequency of source with that resulted from the media without non-linear layer; The responses shown by the elasic waves about the anisotropy and nonlinearity have obvious mutual reformation, namely, the non-linear response will be stronger in some directions because of the anisotropy and the anisotropic strength shown by the elastic waves will be stronger when the media is nonlinear.

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Stochastic reservoir modeling is a technique used in reservoir describing. Through this technique, multiple data sources with different scales can be integrated into the reservoir model and its uncertainty can be conveyed to researchers and supervisors. Stochastic reservoir modeling, for its digital models, its changeable scales, its honoring known information and data and its conveying uncertainty in models, provides a mathematical framework or platform for researchers to integrate multiple data sources and information with different scales into their prediction models. As a fresher method, stochastic reservoir modeling is on the upswing. Based on related works, this paper, starting with Markov property in reservoir, illustrates how to constitute spatial models for catalogued variables and continuum variables by use of Markov random fields. In order to explore reservoir properties, researchers should study the properties of rocks embedded in reservoirs. Apart from methods used in laboratories, geophysical means and subsequent interpretations may be the main sources for information and data used in petroleum exploration and exploitation. How to build a model for flow simulations based on incomplete information is to predict the spatial distributions of different reservoir variables. Considering data source, digital extent and methods, reservoir modeling can be catalogued into four sorts: reservoir sedimentology based method, reservoir seismic prediction, kriging and stochastic reservoir modeling. The application of Markov chain models in the analogue of sedimentary strata is introduced in the third of the paper. The concept of Markov chain model, N-step transition probability matrix, stationary distribution, the estimation of transition probability matrix, the testing of Markov property, 2 means for organizing sections-method based on equal intervals and based on rock facies, embedded Markov matrix, semi-Markov chain model, hidden Markov chain model, etc, are presented in this part. Based on 1-D Markov chain model, conditional 1-D Markov chain model is discussed in the fourth part. By extending 1-D Markov chain model to 2-D, 3-D situations, conditional 2-D, 3-D Markov chain models are presented. This part also discusses the estimation of vertical transition probability, lateral transition probability and the initialization of the top boundary. Corresponding digital models are used to specify, or testify related discussions. The fifth part, based on the fourth part and the application of MRF in image analysis, discusses MRF based method to simulate the spatial distribution of catalogued reservoir variables. In the part, the probability of a special catalogued variable mass, the definition of energy function for catalogued variable mass as a Markov random field, Strauss model, estimation of components in energy function are presented. Corresponding digital models are used to specify, or testify, related discussions. As for the simulation of the spatial distribution of continuum reservoir variables, the sixth part mainly explores 2 methods. The first is pure GMRF based method. Related contents include GMRF model and its neighborhood, parameters estimation, and MCMC iteration method. A digital example illustrates the corresponding method. The second is two-stage models method. Based on the results of catalogued variables distribution simulation, this method, taking GMRF as the prior distribution for continuum variables, taking the relationship between catalogued variables such as rock facies, continuum variables such as porosity, permeability, fluid saturation, can bring a series of stochastic images for the spatial distribution of continuum variables. Integrating multiple data sources into the reservoir model is one of the merits of stochastic reservoir modeling. After discussing how to model spatial distributions of catalogued reservoir variables, continuum reservoir variables, the paper explores how to combine conceptual depositional models, well logs, cores, seismic attributes production history.

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The research objectives were to investigate the psychological structure of employees' organizational commitments(OCs), and its antecedents, and to examine the relative effects of employees' OCs to their performances. In order to deeply uncover the nature of OCs, some standard methods, such as in-depth interview, focus-group, semi-open questionnaire, standard questionnaire etc., were employed. In data analysis, not only some common statistical methods, such as multivariate analysis of variance, cross-table analysis, factor analysis, but also some forefront ones, such as confirmatory factor analysis and path analysis of SEM, were used. The paper covers six chapters: 1) In the first chapter, Firstly some previous empirical studies, which examined structures, antecedents, correlates, and/or consequences of organizational commitment in China and Western countries, were summarized. This summary covers most of the respectable researchers' works of this field, such as H.S.Becker, B.Buchanan, L.W.Porter, G. Ritzer, H.M.Trice, J.A.Alutto, L.G.Hrebiniak, R.T.Mowday, J.P.Meyer, N.J.Allen, G.W.McGee, R.C.Ford, R.Eisenberger, etc. Then three theoretical hypothesis were put forward as following: ① In China, OCs should be multidimensional psychological structures, which means there should exist more than one type of OCs; ② There should be some different antecedents to different OCs; ③ Employees with different types of OC should perform differently in their works. Finally the theoretical and practical significance were discussed. 2) In the second chapter, great efforts were made to investigate the OC types. Firstly, in-depth interview with managers and employees, semi-open questionnaire, and some other methods were used in the pilot research to gather much qualitative material. Then OC questionnaire was designed to get quantitative data in about 20 enterprises, including state-owned, collective-owned, wholly foreign-funded, and joint-ventures. During revising of this questionnaire, there were about 5000 samples surveyed. after factor analysis, the data shows that there should be 5 types of OCs in China, which were respectively named as Affective Commitment, Normative commitment, Ideal Commitment, Economic Commitment, Choice Commitment. Thirdly, confirmatory factor analysis method was used to successfully confirm this 5-factor model. Finally, Cronbach a and test-retest correlate indicate that this questionnaire is reliable. Since factor analysis result has show its construct validity, a simple criterion-related validity research was conducted. 3) In order to investigate the correlation between different OC and employee performance and different antecedents of OC, 5 other questionnaires, such as Employee Satisfaction Questionnaire, Perceived Organizational Support Questionnaire, Social Exchange Questionnaire, Altruism Scale, and Leader Confidence Scale were revised in the third chapter. 4)In the fourth chapter, a lot of correlates, cross-table analysis were conducted to show the correlation between different OCs and 10 performances, which indicate employees with different OCs will show different performance in 10 variables, such as altruism, etc. 5) In the fifth chapter, correlate analysis, multivariate of analysis, and path analysis of SEM were used to investigate the antecedents of OC. A satisfactory model showing the correlation between OC and their antecedents was confirmed. 6) In the last chapter, all researches about OC, and its limitations were summarized.

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Most knowledge representation languages are based on classes and taxonomic relationships between classes. Taxonomic hierarchies without defaults or exceptions are semantically equivalent to a collection of formulas in first order predicate calculus. Although designers of knowledge representation languages often express an intuitive feeling that there must be some advantage to representing facts as taxonomic relationships rather than first order formulas, there are few, if any, technical results supporting this intuition. We attempt to remedy this situation by presenting a taxonomic syntax for first order predicate calculus and a series of theorems that support the claim that taxonomic syntax is superior to classical syntax.

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We have argued elsewhere that first order inference can be made more efficient by using non-standard syntax for first order logic. In this paper we show how a fragment of English syntax under Montague semantics provides the foundation of a new inference procedure. This procedure seems more effective than corresponding procedures based on either classical syntax of our previously proposed taxonomic syntax. This observation may provide a functional explanation for some of the syntactic structure of English.

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Hulun Lake, China’s fifth-largest inland lake, experienced severe declines in water level in the period of 2000-2010. This has prompted concerns whether the lake is drying up gradually. A multi-million US dollar engineering project to construct a water channel to transfer part of the river flow from a nearby river to maintain the water level was completed in August 2010. This study aimed to advance the understanding of the key processes controlling the lake water level variation over the last five decades, as well as investigate the impact of the river transfer engineering project on the water level. A water balance model was developed to investigate the lake water level variations over the last five decades, using hydrological and climatic data as well as satellite-based measurements and results from land surface modelling. The investigation reveals that the severe reduction of river discharge (- 364±64 mm/yr, ~70% of the five-decade average) into the lake was the key factor behind the decline of the lake water level between 2000 and 2010. The decline of river discharge was due to the reduction of total runoff from the lake watershed. This was a result of the reduction of soil moisture due to the decrease of precipitation (-49±45 mm/yr) over this period. The water budget calculation suggests that the groundwater component from the surrounding lake area as well as surface run off from the un-gauged area surrounding the lake contributed ~ net 210 Mm3/yr (equivalent to ~ 100 mm/yr) water inflows into the lake. The results also show that the water diversion project did prevent a further water level decline of over 0.5 m by the end of 2012. Overall, the monthly water balance model gave an excellent prediction of the lake water level fluctuation over the last five decades and can be a useful tool to manage lake water resources in the future.

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J. Keppens and Q. Shen. Compositional model repositories via dynamic constraint satisfaction with order-of-magnitude preferences. Journal of Artificial Intelligence Research, 21:499-550, 2004.

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Booth, Ken, Dunne, T., Worlds in Collision: Terror and the Future of Global Order (New York: Palgrave Macmillan, 2002), pp.x+376 RAE2008

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G?l, Ayla. 'Iraq and world order: a Turkish perspective', in: 'The Iraq Crisis and World Order: Structural, Institutional and Normative Challenges', (Eds) Thakur, R., Sidhu, W. P. S., United Nations University Press, Hong Kong , pp.114-133, 2006 RAE2008

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Bain, William, 'One Order, Two Laws: Recovering the 'Normative' in English School Theory', Review of International Studies, (2007) 33(4) pp.557-575 RAE2008