2013年数模美赛c题论文.doc

Problem solvingWith science and technology developing rapidly today,the health problem of our planet becomes increasingly serious at the same time.So the whole society desires to use a model to describe and forecast the Earth health.Task 1Related concepts To form a model that suits for the requests,for the first ,we create one index to describe the Earth health,which is called EHI (Abbreviation of Earth Health Index). Decisive factors of EHI and Corresponding index Decisive factors of EHICorresponding indexEarth Air Condition API (Air Pollution Index)Earth Water Condition IWS(Improved Water Source)Earth Land Status FAR(Forest Area Rate )Earth Species status GEF(Biodiversity benefits index)Reasons of choosing the factors abovel The Earth consists of organic life and inorganic environment.Both of the two parts have the effect on EHI.l Biosphere is the largest ecosystem on the Earth.It consists of atmosphere, hydrosphere and lithosphere.The first 3 factors ,visual performance of the above 3 parts,can comprehensively stand for inorganic environment. l Specie is the only objective existing form of organic life on the Earth.So the species status can mostly measure the condition of organic life health level.l To implement the qualitative calculation of EHI,we choose corresponding index on behalf of the 4 factors.Calculating methods of EHIl Local EHI Providing that we d like to calculate the EHI of the whole planet,its obvious to choose one place and calculate its local EHI first.After that,we can use the data of single places to calculate the whole planets EHI.Setting;(one certain place,certain time)According to the interrelation of factors,the local EHI can be described by the area of the quadrilateral which is formed by four segments.Each segment indicates one kind of index.The level of the index can be indicated by the length of the segment.According to the Schematic diagram;l global network model buildingKnowing each places local EHI,we started to choose connecting nodes and build global network model of EHI.We choose 12 connecting nodes among the planet .The distribution of nodes is below;Principium of choosing network connecting nodesl Select the nodes according to the geographical division.l Each node must indicate the EHI of A particular region .l The area of 12 regions should maintain a relative balance.l The network formed by all the nodes should reach the global coverage to the maximum extentl Global EHI calculatingSetting;l Number the connecting nodes of the letter “ i ”l The area of each region = Ail The local EHI of each node = Sil Global EHI Three-dimensional graphic According to the calculating principle,the global EHI can be described by the volume of graphic. .Using the final result “S”,the global EHI is obvious.People can use this index to judge the health condition of the whole planet.The global network model can deal with all kinds of factor-changing including natural factors and social factors.No matter which kind of factor changes,it may cause the change of the 4 decisive factors.With the basic factors changing,the final result of EHI will change into a new number.It thus reflects the level changing of global health. TASK 2The global network can be used to predict the future development of planet health condition.Using the model, you will know the developing trend of EHI.The procedure is below.l Factual basis Data4 basic factorsTime2003 - 2008Object12 connecting nodesFromWorld Bank databaseWe use some countriesdata to describe 12 connecting nodesdata.The correspond is below;NumberRegionArea(SQ tkm2)Country1North America24230United states, Canada2Asia3621 0Russia, China3Europe10160France Italy Greece4Southeast Asia4570Indonesia5Oceania8970Australia6Middle East12320Egypt Saudi Arabia7South America17840Brazil8Atlantic Ocean94300Dominican 9Pacific Ocean181344Fiji 10Indian Ocean74920Maldives 11Arctic Ocean14750Norway12Africa21200Congo(DEM,REP)Basic Database GEF200320042005200620072008US909090949494Canada222222222222China656565676767Russia373737343434Italy444444France444555Greece333333Indonesia909090818181Australia969696888888Egypt333333Saudi Arabia333333Brazil100100100100100100Fiji100100100100100100Dominica Republic100100100100100100Maldives100100100100100100Norway100100100100100100API200320042005200620072008US222222212019Canada201919171716China828278756966Russia232019171616Italy302827262523France151414141313Greece403836343332Indonesia979790837774Australia161515151414Egypt12412611911110399Saudi Arabia135127118112107104Brazil292725232121Fiji252423211919Dominica Republic242219181717Maldives383535313229Norway171716161516Congo8989.890919192FAR1990200020052010US32.432.83333.2Canada34.134.134.134.1China16.81920.722.2Russia49.449.449.449.4Italy25.828.529.833.1France26.52828.729.1Greece25.627.929.130.3Indonesia65.454.95452.1Australia20.120.22019.4Egypt000.10.1Saudi Arabia0.50.50.50.5Brazil6864.562.761.4Fiji0000Dominica Republic0000Maldives0000Norway0000Congo70.168.469.7768.0IWS 200320042005200620072008US999999999999Canada100100100100100100China848587878989Russia888888888888Italy100100100100100100France100100100100100100Greece100100100100100100Indonesia797980808081Australia100100100100100100Egypt979798989899Saudi Arabia000000Brazil959796979797Fiji100100100100100100Dominica Republic100100100100100100Maldives100100100100100100Norway100100100100100100Congo444444454545Using the methods above, we can calculate the local EHI of each network node,The calculating result is below; 20032004200520062007200810.49930.49980.49990.50740.50790.508720.43420.43710.44120.43920.44380.444930.06260.06340.06540.06650.06760.068840.3240.32490.32550.32860.32940.329750.57020.56940.5780.55150.55480.559160.57270.57340.57330.54930.54970.549170.76830.77640.77270.77730.7780.776780.47500.47600,47700.47900,47600,475090.47600.47800.48100.48200.48300.4830100.48300.48400.48400.48500.48500.4840110.46200.46500.46500.46900.46800.4710120.24090.24190.24230.25920.26030.2604Using the data above, we draw the images of each connecting node.Here are the local EHI image of each node.Also, we can obviously calculate the global EHI of each year. The data and image are below;DataYear200320042005200620072008EHI0.4474 0.4491 0.4505 0.4495 0.4507 0.4514ImageTo predict the future trend of EHI, we use the Software MATLAB to do the fuction fitting.Operating We use existing data to find an adaptable fuction which suits for it.As results reached by the software,the suitable fuction is below;Explanation;l In the formula, letter A,B,C,D,E,F,M are coefficients.l All the coefficients are determined by the complex conditions of specific connecting nodes.l The 12 solutions of each kind of coefficient can be expressed as a certain matrix.A: p1= 0.002329 0.002236 0.001331 0.001339 -0.003669 -0.006524 0.000973 0.001474 0.001561 0.0004794 0.001311 0.005169 ; B: p2= -4.167 -4.043 -2.604 -2.358 7.922 13.64 -1.176 -2.478 -2.65 -0.4775 -2.162 -10.11 ; C: p3= -0.002182 0.001647 -2.91e-006 0.009545 0.007509 -0.001384 -0.0005095 0.0007418 5.447e-005 0.001176 -0.005093 -0.008302 ; D: p4= 2.8 2.8 3.4 3 2.8 2 .8 2.4 3.6 3.6 2.8 2.4 2.8 ;M: p5= 1.549 1.59 0.9853; 1.57 1.413 1.744 1.705 2.012 1.168 1.672 2.32 1.749;E: p6=5531, 3.08, -9.827, 1.46, 12.05, 4334, -5.738, 4670, 4507 13.09, 1.558, 4732;F: p7=3257, -2001, 0.3918, 0.8031, -1993, 2584, -2001, 2009, 1991, -2000, -2003, 3357;l Local image of the trendl We can also get the fuction coefficients of global EHI. CoefficientABCDMEFResult0.0006675-0.8887 -0.008302 2.8-0.0978525052542 l According to the fuction of the global EHI,we can get the image of its future trend.From the image above, we find that ;l The image can be regarded as a special kind of Damped oscillation.l The line of oscillating spindle.can be described as a time fuction.Its analytic formula is p(x)=0.0006675x - 0.8887.Since A is minimum.the principal value of the fuction p(x) grow slowly.l One factor of the formula (x +E) /F can describe the amplitude of the function.From the image above,we know that the factor basically keeps stable.And the factoralmost doesnt attenuate.So its obvious that amplitude basically keeps stable.From the features of the function ,we can make a prediction about the future trend of global health.l In a long decade,the EHI grows slowly.So we can predict that the health condition of the planet basically maintain a stable level.It keeps a oscillating balance.l Providing that the negative factors become more serious,the coefficient A will turn to negative number. The trend of EHI will begin to fall oscillatingly.So when the coefficient A=0, it comes to a critical state.Supposing that serious effects take place, the amplitude will suddenly increase.If the function image touches spindle x, it will come to a terrible critical state.If crossing the state,nothing can be useful to do.The Earth will tend to die.Task 3To test the model, we need to analyze the connection of each node. When natural environment or social environment factors changes in a region of the Earth. global EHI will be affected.We need to argue about the relationship between local factors and the global EHI.Results are as follows: When local factors start to work,it will firstly affect the change of 4 decisive factors.Setting Decisive factors: Changes of decisive factors: Before factors local EHI: After factors local EHI Due to the fact that each kind of factor is diffusive , the influence of factors will be graded with two variables which are propagation distance and time. According to the microscopic theory of substancediffusing process and Quantum mechanics theory,we can Argue about the model below:Setting(Microscopic Background)affecting origin A coordinate: Random point B coordinate: Distance between A and B: The affects probability density among the room:Time pasting: tThe factors affect on point B: By Integral operation micro push to macroThe formula is still validConclusion Something about l Natural Factors “n” is called Diffusion coefficient.It is the physicalQuality of substance. l Social Factors is a constant.(the speed of all social factorsaffect can be regarded as the same) TestTEST1:Natural Factors In 2003, The terrible tsunami strucked Indonesia.One year later,we take the country Malidives a