美赛论文模板(超实用)
美赛数学建模模板
美赛数学建模模板-CAL-FENGHAI.-(YICAI)-Company One1摘要：第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a statio nary main.例2:……is a real-life common phenomenon with many complexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例 1：We find the optimal number of tollbooths in a highway toll-plaza for a giv en number of highway lanes: the number of tollbooths that minimizes average delay experie nced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and m otion of water in the pipe and examining the engineering parameters of sprinklers availab le in the market.例4: After mathematically analyzing the …… problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goal is... that (minimizes the time )……….2．解决这个问题的伟大意义反面说明。
美赛论文模版
摘要：第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexi t ies.例3：An (effective plan) is crucial to………b. 直接指出问题：例1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures wi t h the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematically analyzing the …… problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goal is... that (mini mizes the time )……….2．解决这个问题的伟大意义反面说明。
美国大学生数学建模比赛的论文格式
ContentsⅠIntroduction (1)1.1Problem Background (1)1.2Previous Research (2)1.3Our Work (2)ⅡGeneral Assumptions (3)ⅢNotations and Symbol Description (3)3.1 Notations (4)3.2 Symbol Description (4)ⅣSpread of Ebola (5)4.1 Traditional Epidemic Model (5)4.1.1.The SEIR Model (5)4.1.2 (6)4.1.3 (6)4.2 Improved Model (7)4.2.1.The SEIHCR Model (8)4.2.2 (9)ⅤPharmaceutical Intervention (9)5.1 Total Quantity of the Medicine (10)5.1.1.Results from WHO Statistics (10)5.1.2.Results from SEIHCR Model (11)5.2 Delivery System (12)5.2.1.Locations of Delivery (13)5.2.2 (14)5.3 Speed of Manufacturing (15)ⅥOther Important Interventions (16)6.1 Safer Treatment of Corpses (17)6.2 Conclusion (18)ⅦControl and Eradication of Ebola (19)7.1 How Ebola Can Be Controlled (20)7.2 When Ebola Will Be Eradicated (21)ⅧSensitivity Analysis (22)8.1 Impact of Transmission Rate (23)8.2 Impact of the Incubation Priod (24)ⅨStrengths and Weaknesses (25)9.1 Strengths (26)9.2 Weaknesses (27)9.3 Future Work (28)Letter to the World Medical Association (30)References (31)ⅠIntroduction1.1.Promblem Background1.2.Previous Research1.3.Our WorkⅡGeneral Assumptions●●ⅢNotations and Symbol Description3.1. Notataions3.2. Symbol DescriptionSymbol DescriptionⅣSpread of Ebola4.1. Traditional Epidemic Model4.1.1. The SEIR Model4.1.2. Outbreak Data4.1.3. Reslts of the SEIR Model4.2. Improved Model4.2.1. The SEIHCR Model4.2.2. Choosing paametersⅤPharmaceutical Intervention 5.1. Total Quantity of the Medicine 5.1.1. Results from WHO Statistics5.2. Delivery System5.2.1. Locations of Delivery5.2.2. Amount of Delivery5.3. Speed of Manufacturong5.4. Medicine EfficacyⅥOther Important Interventions 6.1. Safer Treatment of Corpses6.2. ConclusionⅦControl and Eradication of Ebola 7.1. How Ebola Can Be Controlled7.2. When Ebola Will Be EradicatedⅧSensitivity Analysis8.1. Impact of Transmission Rate8.2. Impact of Incubation PeriodⅨStrengths and Weaknesses 9.1. Strengths●●●9.2. Weaknesses●●●9.3.Future WorkLetter to the World Medical AssociationTo whom it may concern,Best regards,Team #32150References ［1］［2］［3］［4］。
美国大学生数学建模竞赛美赛--论文
Each team member must sign the statement below: (Failure to obtain signatures from each team member will result in disqualification of the entire team.)
2015 Mathematical Contest in Modeling (MCM/ICM) Control Sheet Please review this page before submitting your solution to ensure that all of the information is correct Do not make changes by hand to the information on this control sheet. If you need to change any of the information on this sheet, login via the Advisor Login link on the MCM web site, make the changes online, and print a new sheet. You may NOT photocopy this control sheet to give to a new team, nor may you assign any team a control number. Each team must have its own control number, obtained by registering via the MCM web site. Advisor Jinpeng Yu Name: Department: Control Engineering Institution: Qingdao University Address: 308 Ningxia Road,Shinan District,Qingdao,Shandong,China Qingdao, Shandong 266000 Phone: 18653250086 Fax: 053285953064 Email: zhanghaoran06@ Home Phone: 053285953064 The names of the team members will appear on your team's certificate exactly as they appear on this page, including all capitalization and punctuation, if any. Gender data is optional and will be used for statistical purposes only; it will not appear on the certificate. Team Member Haoran Zhang Yu Ma Guiying Dong Gender M M F Your team's control number is: 40906 (Place this control number on all pages of your solution paper and on any support material.) Problem Chosen: B
美赛论文模板(超实用)
TitileSummaryDuring cell division, mitotic spindles are assembled by microtubule-based motor proteins1, 2. The bipolar organization of spindles is essential for proper segregation of chromosomes, and requires plus-end-directed homotetrameric motor proteins of the widely conserved kinesin-5 (BimC) family3. Hypotheses for bipolar spindle formation include the 'push−pull mitotic muscle' model, in which kinesin-5 and opposing motor proteins act between overlapping microtubules2, 4, 5. However, the precise roles of kinesin-5 during this process are unknown. Here we show that the vertebrate kinesin-5 Eg5 drives the sliding of microtubules depending on their relative orientation. We found in controlled in vitro assays that Eg5 has the remarkable capability of simultaneously moving at 20 nm s-1 towards the plus-ends of each of the two microtubules it crosslinks. For anti-parallel microtubules, this results in relative sliding at 40 nm s-1, comparable to spindle pole separation rates in vivo6. Furthermore, we found that Eg5 can tether microtubule plus-ends, suggesting an additional microtubule-binding mode for Eg5. Our results demonstrate how members of the kinesin-5 family are likely to function in mitosis, pushing apart interpolar microtubules as well as recruiting microtubules into bundles that are subsequently polarized by relative sliding. We anticipate our assay to be a starting point for more sophisticated in vitro models of mitotic spindles. For example, the individual and combined action of multiple mitotic motors could be tested, including minus-end-directed motors opposing Eg5 motility. Furthermore, Eg5 inhibition is a major target of anti-cancer drug development, and a well-defined and quantitative assay for motor function will be relevant for such developmentsContentTitile (1)Summary (1)1Introduction (1)1.1Restatement of the Problem (1)1.2Background (1)1.1.1Common Solving Technique (1)1.1.2Previous Works (1)1.3Example (1)2Analysis of the Problem (1)2.1Outline of the Approach (1)2.2Basic Assumptions (2)2.3Definitions and Key Terms (2)3Calculating and Simplifying the Model (2)4The Model Results (3)5Validating the Model (3)6Strengths and Weaknesses (3)6.1Strengths (3)6.2Weaknesses (3)7Food for Thought (3)8Conclusion (3)References (4)Appendices (4)Appendix A Source Code (4)Appendix B (4)1Introduction1.1Restatement of the Problem …1.2Background…1.1.1Common Solving Technique…1.1.2Previous Works…1.3Example…2Analysis of the Problem …2.1Outline of the Approach…2.2Basic Assumptions●●●●●2.3Definitions and Key Terms●●●●Table 1.…Symbol Meaning Unit3Calculating and Simplifying the Model …4The Model Results……5Validating the Model…6Strengths and Weaknesses6.1S trengths●●●●6.2W eaknesses●●●●7Food for Thought…8Conclusion….References…AppendicesAppendix A Source CodeHere are the simulation programmes we used in our model as follow. Input matlab source:……….Appendix B…….Input C++ source：…………..…………..。
美赛数学建模比赛论文资料材料模板
The Keep-Right-Except-To-Pass RuleSummaryAs for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic.As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left.As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow .Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall.Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic controlContentContent (2)1. Introduction (3)2. Analysis of the problem (3)3. Assumption (3)4. Symbol Definition (3)5. Models (3)5.1 Building of the Cellular automaton model (3)5.1.1 Verify the effectiveness of the keep right except to pass rule (4)5.1.2 Numerical simulation results and discussion (5)5.1.3 Conclusion (8)5.2 The solving of second question (8)5.2.1 The building of the stochastic multi-lane traffic model (8)5.2.2 Conclusion (8)5.3 Taking the an intelligent vehicle system into a account (8)5.3.1 Introduction of the Intelligent Vehicle Highway Systems (9)5.3.2 Control problem (9)5.3.3 Results and analysis (9)5.3.4 The comprehensive analysis of the result (9)6. Improvement of the model (10)6.1 strength and weakness (10)6.1.1 Strength (10)6.1.2 Weakness (10)6.2 Improvement of the model (10)7. Reference (12)1. IntroductionAs is known to all, it ’s essential for us to drive automobiles, thus the driving rules is crucial important. In many countries like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless they are passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular automaton to build models, then analyze the performance of this rule in light and heavy traffic. Firstly, we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; thirdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules, and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptions● The highway of double row three lanes that we study can representmulti-lane freeways.● The data that we refer to has certain representativeness and descriptive● Operation condition of the highway not be influenced by blizzard or accidental factors ● Ignore the driver's own abnormal factors, such as drunk driving and fatigue driving ● The operation form of highway intelligent system that our analysis can reflectintelligent system● In the intelligent vehicle system, the result of the sampling data has high accuracy.4. Symbol Definitioni The number of vehiclest The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years.Let )(t x i be the position of vehicle i at time t , )(t v i be the speed of vehicle i at time t ,p be the random slowing down probability, and R be the proportion of trucks and buses, the distance between vehicle i and the front vehicle at time t is:1)()(1--=-t x t x gap i i i , if the front vehicle is a small vehicle.3)()(1--=-t x t x gap i i i , if the front vehicle is a truck or bus.5.1.1 Verify the effectiveness of the keep right except to pass ruleIn addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow:There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.● Lane changing rules based lane speed controlIf vehicle on the high-speed lane meets control v v <, ),1)(min()(max v t v t gap i f i +≥, safe b i gap t gap ≥)(, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where control v is the minimum speed of the corresponding lane.● The application of the Nasch model evolutionLet d P be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not take the initiative to change lanes), )(t gap f i indicates the distance between the vehicle and the nearest front vehicle, )(t gap b i indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.● Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one)[4].Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets ),1)(min()(max v t v t gap i f i +≥ and safe b i gap t gap ≥)(, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.5.1.2 Numerical simulation results and discussionIn order to facilitate the subsequent discussions, we define the space occupation rate as L N N p truck CAR ⨯⨯+=3/)3(, where CAR N indicates the number of small vehicles on the driveway,truck N indicates the number of trucks and buses on the driveway, and L indicates the total length of the road. The vehicle flow volume Q is the number of vehicles passing a fixed point per unit time,T N Q T /=, where T N is the number of vehicles observed in time duration T .The average speed ∑∑⨯=T it i a v T N V 11)/1(, t i v is the speed of vehicle i at time t . Take overtaking ratio f p as the evaluation indicator of the safety of traffic flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic average of 20 samples [5].Overtaking ratio of different control rule conditionsBecause different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.(a) Based on passing lane control (b) Based on speed controlFig.5.1.3Fig.5.1.3Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3:(1) when the vehicle density is less than 0.05, the overtaking ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it will become difficult to overtake, so the overtaking ratio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear.Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate thespeed control. 1f P is the overtaking ratio of small vehicles over large vehicles, 2f P is the overtaking ratio ofsmall vehicles over small vehicles, 3f P is the overtaking ratio of large vehicles over small vehicles, 4f P is the overtaking ratio of large vehicles over large vehicles.).It can be seen from Fig. 5.1.4:(1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, which is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake. ● Impact of different control rules on vehicle speedFig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and average speed under different control conditions. (Figures in left-hand indicates passing lane control, figures in right-hand indicates speed control. a X is the average speed of all the vehicles, 1a X is the average speed of all the small vehicles, 2a X is the average speed of all the buses and trucks.).It can be seen from Fig. 5.1.5:(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.(2) When vehicle density is less than 0.15,a X ,1a X and 2a X are almost the same under both control conditions.● Effect of different control conditions on traffic flowFig.5.1.6Fig. 5.1.6Relationships among vehicle density, proportion of large vehicles and traffic flow under different control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.It can be seen from Fig. 5.1.6：(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition.5.1.3 ConclusionIn this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.5.2 The solving of second question5.2.1 The building of the stochastic multi-lane traffic model5.2.2 ConclusionOn one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam BP(situation, applying ))results with a tendency of moving to the right lane for this,2(xRdriver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process )7.0,2(B where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.5.3 Taking the an intelligent vehicle system into a accountFor the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by usto perfect the performance of the freeway by lots of analysis.5.3.1 Introduction of the Intelligent Vehicle Highway SystemsWe will use the microscopic traffic simulator model for traffic simulation purposes. The MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the states when the speed limits are applied in Fig.5.3.1. We implement a METANET model for prediction purpose[14].5.3.2 Control problemAs a constraint, the dynamic speed limits are given a maximum and minimum allowed value. The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For the calculation of the optimal control values, all speed limits are constrained to this range. When the optimal values are found, they are rounded to a multiplicity of 10 km/h, since this is more clear for human drivers, and also technically feasible without large investments.5.3.3 Results and analysisWhen the density is high, it is more difficult to control the traffic, since the mean speed might already be below the control speed. Therefore, simulations are done using densities at which the shock wave can dissolve without using control, and at densities where the shock wave remains. For each scenario, five simulations for three different cases are done, each with a duration of one hour. The results of the simulations are reported in Table5.1, 5.2, 5.3.●Enforced speed limits●Intelligent speed adaptationFor the ISA scenario, the desired free-flow speed is about 100% of the speed limit. The desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100% of the speed limit, and a standard deviation of 5% of the speed limit. Based on this percentage, the influence of the dynamic speed limits is expected to be good[19].5.3.4 The comprehensive analysis of the resultFrom the analysis above, we indicate that adopting the intelligent speed control system can effectively decrease the travel times under the control of an intelligent system, in other words, the measures of dynamic speed control can improve the traffic flow.Evidently, under the intelligent speed control system, the effect of the dynamic speed control measure is better than that under the lane speed control mentioned in the first problem. Becauseof the application of the intelligent speed control system, it can provide the optimal speed limit in time. In addition, it can guarantee the safe condition with all kinds of detection device and the sensor under the intelligent speed system.On the whole, taking all the analysis from the first problem to the end into a account, when it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed control system.Thus, under the state of the light traffic, we propose a new conclusion different from that in the first problem: the rule of keep right except to pass is more effective than that of lane speed control.And when it is in the heavy traffic, for sparing no effort to improve the operation efficiency of the freeway, we combine the dynamical speed control measure with the rule of keep right except to pass, drawing a conclusion that the application of the dynamical speed control can improve the performance of the freeway.What we should highlight is that we can make some different speed limit as for different section of road or different size of vehicle with the application of the Intelligent Vehicle Highway Systems.In fact, that how the freeway traffic operate is extremely complex, thereby, with the application of the Intelligent Vehicle Highway Systems, by adjusting our solution originally, we make it still effective to freeway traffic.6. Improvement of the model6.1 strength and weakness6.1.1 Strength●it is easy for computer simulating and can be modified flexibly to consider actual trafficconditions ,moreover a large number of images make the model more visual.●The result is effectively achieved all of the goals we set initially, meantime the conclusion ismore persuasive because of we used the Bernoulli equation.●We can get more accurate result as we apply Matlab.6.1.2 Weakness●The relationship between traffic flow and safety is not comprehensively analysis.●Due to there are many traffic factors, we are only studied some of the factors, thus ourmodel need further improved.6.2 Improvement of the modelWhile we compare models under two kinds of traffic rules, thereby we come to the efficiency of driving on the right to improve traffic flow in some circumstance. Due to the rules of comparing is too less, the conclusion is inadequate. In order to improve the accuracy, Wefurther put forward a kinds of traffic rules: speed limit on different type of cars.The possibility of happening traffic accident for some vehicles is larger, and it also brings hidden safe troubles. So we need to consider separately about different or specific vehicle types from the angle of the speed limiting in order to reduce the occurrence of traffic accidents, the highway speed limit signs is in Fig.6.1.Fig.6.1Advantages of the improving model are that it is useful to improve the running condition safety of specific type of vehicle while considering the difference of different types of vehicles. However, we found that the rules may be reduce the road traffic flow through the analysis. In the implementation it should be at the85V speed of each model as the main reference basis. Inrecent years, the85V of some researchers for the typical countries from Table 6.1[ 21]:Author Country ModelOttesen andKrammes2000America LCDCLDCVC⨯---=01.0012.057.144.10285Andueza2000 Venezuela].[308.9486.7)/894()/2795(25.9885curvehorizontalLDCRaRVT++--=].[tan819.27)/3032(69.10085gentLRVT+-=Jessen2001 America][00239.0614.0279.080.86185LSDADTGVVP--+=][00212.0432.010.7285NLSDADTVVP-+=Donnell2001 America22)2(8500724.040.10140.04.78TLGRV--+=22)3(85008369.048.10176.01.75TLGRV--+=22)4(8500810.069.10176.05.74TLGRV--+=22)5(8500934.008.21.83TLGV--=BucchiA.BiasuzziK.And SimoneA.2005 ItalyDCV124.0164.6685-=DCEV4.046.3366.5585--=Meanwhile, there are other vehicles driving rules such as speed limit in adverse weather conditions. This rule can improve the safety factor of the vehicle to some extent. At the same time, it limits the speed at the different levels.7. Reference[1] M. Rickert, K. Nagel, M. Schreckenberg, A. Latour, Two lane traffic simulations usingcellular automata, Physica A 231 (1996) 534–550.[20] J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffic Management and Control inIntelligent Vehicle Highway Systems,18(2009).[21] Yang Li, New Variable Speed Control Approach for Freeway. (2011) 1-66。
美赛论文模板
T eam Control NumberFor office use only0000For office use onlyT1 F1T2 F2T3 Problem Chosen F3T4 A F42014 Mathematical Contest in Modeling (MCM) Summary Sheet(Attach a copy of this page to each copy of your solution paper.)Repeaters Coordination And DistributionFebruary 6,2015AbstractIn this paper, it aims to computing problem on Relay Strategy (repeaters coordination and distribution). According to advanced radio cellular coverage technology, usage of frequency attenuation and geometric mapping methods, Hata model， cellular coverage solution and FDM (Frequency Division Multiplexing) model were established. The algorithms used MATLAB to simulate, with the final modeling results of sensitivity analysis and improvement & promotion on models.Question one : For a circular flat area of radius 40 miles radius, determine the minimum number of repeaters necessary to accommodate 1,000 simultaneous users. Assume that the spectrum available is 145 to 148 MHz, the transmitter frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency, and there are 54 different PL tones available.Answer:1. Based on Frequency attenuation expression and calculation with MATLAB, it figuredout the eligible coverage radiuses, which are 30km for BS (base station), and 14.9km for repeater.2. Assuming the users in a given area under uniform distribution, using advancedcellular coverage solution, we can calculate that minimum number of required repeater is 36 under cellular features.3. Based on the US VHF spectrum allocation standard, the minimum spacing for adjacentchannels is 30kHz. And with up to 54 different PL tones, maximum 4320 channels can be allocated to provide 1000 simultaneous users to use at the same time. Conclusion:The minimum number of repeaters necessary to accommodate 1,000 simultaneous users is 36.Question Two : How does your solution change if there are 10,000 users?Answer:1. Since the given spectrum is in a fixed range, even if 54 different PL tones can not be allocated enough channels for 10,000 simultaneous users. So the number of repeaters will be increased, meanwhile, the given area will be divided into different parts.2. On the assumption that uniform distribution of the population in the given area, it will be divided into 3 sub-regions equally by analyzing the binding domain, frequency spectrum and PL tones three independent factors. And then the number of repeaters within each sub-region will be classified discussion.3. The FDM (Frequency Division Multiplexing) model is established here to improve channel efficiency to accommodate up to 10,000 simultaneous users Conclusion:The minimum number of repeaters necessary to accommodate 10,000 simultaneous users is 126.Question Three : Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas. Answer:Basically, under the same condition for question 1&2, the mountainous area will be analyzed as following:1. The function for relationship between radio attenuation x caused by obstacles and the eligible coverage radius d for repeater is 2249.354371.4110x d -=, which is to analyze the impact on the number of repeaters under full signal coverage. 2. For the mountain barrier, based on the different situation of mountains, the addition of repeaters on the suitable location will be discussed to achieve full coverage. This paper describes model established by using of cellular coverage technology and frequency attenuation expression, to achieve simple, fast, accurate algorithm. And also illustrated the effect takes the entire article. In the end, the sensitivity analysis and error calculation are applied for modeling, making the model practically.Key words: Cellular Coverage technology, frequency attenuation expression, channel allocation, MatlabRepeaters coordination and distributionContent1 Restatement of the Problem (1)1.1 Introduction (1)1.2 The Problem (1)2 Simplifying Assumption (1)3 Phrase explain (1)4 Model (2)4.1 Model I (2)4.1.1 Analysis of the Problem (2)4.1.2 Model Design (2)5 Sensitivity analysis (2)6 Model extension (2)7 Evaluating our model (2)7.1 The strengths of model (2)7.2 The weaknesses of model (2)References (3)1 Restatement of the Problem1.1 IntroductionThe VHF radio spectrum involves line-of-sight transmission and reception. This limitation can be overcome by “repeaters,” which pick up weak signals, amplify them, and retransmit them on a different frequency. Thus, using a repeater, low-power users (such as mobile stations) can communicate with one another in situations where direct user-to-user contact would not be possible. However, repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies.1.2 The ProblemYour job is to:◆Design a scheme that determines the minimum number of repeaters necessaryto accommodate 1,000 simultaneous users in a circular flat area of radius40 miles radius.And assume that the spectrum available is 145 to 148 MHz,the transmitter frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency, and there are 54 different PL tones available.◆Change your scheme to accommodate 1,0000 simultaneous users base on yourmodel.◆Discuss the case where there might be defects in line-of-sight propagationcaused by mountainous areas.2 Simplifying Assumption3 Phrase explain4 Model4.1 Model I4.1.1 Analysis of the Problem4.1.2 Model Design5 Sensitivity analysisSymbol◆N: the number of total repeaters in the circle area ◆Q: the number of the users in the circle area◆k: the number of the red circle in figure 2最前面最好有一个Symbol List6 Model extension7 Evaluating our model7.1 The strengths of model7.2 The weaknesses of modelReferences参考文献不要引用非常差的期刊的论文，要引用比较厉害的英文期刊，证明你有足够的阅读文献量。
【完整解析】美赛-数学建模-写作模版(各部分)
Summary：clearly describe your approach to the problem and,most prominently,your most important conclusions.●Restatement and clarification of the problem:State in your own words what you aregoing to do.●Explain assumptions and rationale（principle）/justification:Emphasize the assumptionsthat bear on the problem.Clearly list all variables used in your model.●Include your model design and justification for type model used or developed.●Describe model testing and sensitivity analysis,including error analysis,etc.●Discuss the strengths and weaknesses of your model or approach摘要第一段：写论文解决什么问题.1．问题的重述a.介绍重点词开头：例1：“Hand move”irrigation,a cheap but labor-intensive system used on small farms,consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An(effective plan)is crucial to………b.直接指出问题：例1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes:the number of tollbooths that minimizes average delay experienced by cars.我们找到了在给定XX的情况下最佳的……例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.XX需要具有B性能的C例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.我们通过分析参数B确定A，并且检验了现实情况C例4:After mathematically analyzing the……problem,our modeling group would like to present our conclusions,strategies,(and recommendations)to the…….在数学分析B后，我们的模型组将呈现了我们的结论和建议We begin by considering only the rigid recoil effects of the bat–ball col-LisionOur main goal is to understand the sweet spot.A secondary goal is tounderstand the differences between the sweet spots of different bat types.Because the collision happens on such a short time-scale(around1ms),we treat the bat as a free body.That is to say,we are not concerned with the batter’s hands exerting force on the bat that may be transferred to the ball....Our paper is organized as follows....例5：Our goal is...that(minimizes the time)……….2．解决这个问题的伟大意义反面说明。
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Titile
Summary
During cell division, mitotic spindles are assembled by microtubule-based motor proteins1, 2. The bipolar organization of spindles is essential for proper segregation of chromosomes, and requires plus-end-directed homotetrameric motor proteins of the widely conserved kinesin-5 (BimC) family3. Hypotheses for bipolar spindle formation include the 'push−pull mitotic muscle' model, in which kinesin-5 and opposing motor proteins act between overlapping microtubules2, 4, 5. However, the precise roles of kinesin-5 during this process are unknown. Here we show that the vertebrate kinesin-5 Eg5 drives the sliding of microtubules depending on their relative orientation. We found in controlled in vitro assays that Eg5 has the remarkable capability of simultaneously moving at 20 nm s-1 towards the plus-ends of each of the two microtubules it crosslinks. For anti-parallel microtubules, this results in relative sliding at 40 nm s-1, comparable to spindle pole separation rates in vivo6. Furthermore, we found that Eg5 can tether microtubule plus-ends, suggesting an additional microtubule-binding mode for Eg5. Our results demonstrate how members of the kinesin-5 family are likely to function in mitosis, pushing apart interpolar microtubules as well as recruiting microtubules into bundles that are subsequently polarized by relative sliding. We anticipate our assay to be a starting point for more sophisticated in vitro models of mitotic spindles. For example, the individual and combined action of multiple mitotic motors could be tested, including minus-end-directed motors opposing Eg5 motility. Furthermore, Eg5 inhibition is a major target of anti-cancer drug development, and a well-defined and quantitative assay for motor function will be relevant for such developments
Content
Titile (1)
Summary (1)
1Introduction (1)
1.1Restatement of the Problem (1)
1.2Background (1)
1.1.1Common Solving Technique (1)
1.1.2Previous Works (1)
1.3Example (1)
2Analysis of the Problem (1)
2.1Outline of the Approach (1)
2.2Basic Assumptions (2)
2.3Definitions and Key Terms (2)
3Calculating and Simplifying the Model (2)
4The Model Results (3)
5Validating the Model (3)
6Strengths and Weaknesses (3)
6.1Strengths (3)
6.2Weaknesses (3)
7Food for Thought (3)
8Conclusion (3)
References (4)
Appendices (4)
Appendix A Source Code (4)
Appendix B (4)
1Introduction
1.1Restatement of the Problem …
1.2Background
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1.1.1Common Solving Technique
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1.1.2Previous Works
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1.3Example
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2Analysis of the Problem …
2.1Outline of the Approach
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2.2Basic Assumptions
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2.3Definitions and Key Terms
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Table 1.
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Symbol Meaning Unit
3Calculating and Simplifying the Model …
4The Model Results
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5Validating the Model
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6Strengths and Weaknesses
6.1S trengths
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6.2W eaknesses
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7Food for Thought
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8Conclusion
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References
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Appendices
Appendix A Source Code
Here are the simulation programmes we used in our model as follow. Input matlab source:
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Appendix B
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Input C++ source：
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