2019 US race a problem
Paper Source: https://github.com/MATHmodels
Abstract [nonsense dry 1: 9 On]
The introduction of a word
Overview of Issues - Overview of Methods - Overview of the results of [three models, factor analysis model, to solve the problem]
Modify the parameter sensitivity analysis [see] impact
Word meaning
Introduction
1. Reiteration
The original problem
Question A: Ecological game
in the fictional TV series "Game of Thrones", the epic fantasy novels "A Song of Ice and Fire" series is based on [1], it is composed of three dragon "Dragon mother" Dani Liz tower Ge Lian brought up, when the hatch, a small dragon, about 10 kilograms, a year later, grow to about 30-40 kg. They have continued to grow in life, depending on the conditions and amount of food they can get. In terms of this issue, it is assumed that three imaginary dragons living today. Assumptions described above the basic biology of the dragon is accurate. [Yellow 1] You need to do some additional assumptions dragon, for example, the dragon can fly great distances, breathing fire against the great trauma. When you solve the problem needs to be a clear relationship between your assumptions and function, size, diet, physical constraints or changes in other characteristics associated with animals. Your team responsible for analyzing the characteristics of the dragon, behavior, habits, diet [Yellow 2] as well as interaction with the environment. To do this, you must consider many issues. At least address the following questions: What dragon ecological impact and requirements? Dragon's energy consumption is how much, what their caloric intake requirements? How much area needs to support three dragons? A much-scale ecological community needs to support one-stop to provide different levels of assistance to the dragon? [Yellow 3] In answering these questions, we want to know what factors you consider. Like other migratory animals, the dragon may also travel around the world very different climate. How important is the climatic conditions of your analysis? For example, in the arid region, moving between warm temperate regions and the Arctic will train maintenance and growth of resources required to train an enormous impact you? [Yellow 4] Once you have completed the analysis of the Dragon, the drafting of a letter to the two "A Song of Ice and Fire" author George RR Martin, how to guide the story to keep the real ecological basis, particularly with respect to the dragon from arid areas to temperate regions and movement Arctic. Although you can not be directly applied to the analysis of the Dragon actual physical situation, but the use of mathematical modeling itself many practical characteristics for modeling situations. In addition to the case of modeling activity itself, describe and discuss virtual dragon outside the field of your modeling work may help to inform and provide insight?
The file you submitted should include: a summary table, two letters, the solution is not more than 20 pages of summaries and up to 23 letters. Note: Any reference list and appendix do not count limit of 23, should appear after the completion of the solution. Note: Do not use unauthorized images and materials, the use of these images and materials are limited copyright law. Notice how your thoughts and references to sources and materials used in the report.
2. Analysis [sentence paragraphs of the article]
Ideas / domain knowledge to use
Question 1 idea dragon body weight Logistic growth model
Question 2 Dragon Flame chemical kinetic model of thinking,
Question 3 Ideas Long - sheep - habitat models.
Assumption and justifications
Narrative six points overall hypothesis hypothesis []
Notations
Special column
Dragon’s Physical Characteristics and Diet
1.Description of Dragon’s Weight and lenth
Environment settings - Set limits - Setting metrics
2.Dragon’s Weight Logistic Growth Model
W (t) trend description - symbolic significance
Based on the principle - Factors to Consider
The simplest model does not consider these factors when
According to the principle of correction factors 1
According to the principle of the correction factor 2 again
The default setting - Description of formulas Cauchy problem [value]
According to available data, the parameter is calculated - Illustrated
Image rendering function
End model weight
3.Dragon’s Length Analysis Based on Analogy
Description ideas - based on the principle - Considerations
Each Factors
List length formula
Source - Parameter Calculation
Adult calculate the results
Return value of the function chart
- 3.1Dragon’s Energy Expenditure and Caloric intake
Analysis ideas - an equivalent amount computing objects conversion
- 3.2Dragon’s Diet and Energy Consumption during Flight
Problem is reduced - with an amount can be considered in place of - the subsequent need to give some parameters
- 3.3Dragon’s Fire Chemical Kinetics Model
Thinking parameter calculating - given the nature of the parameter values Chemistry Parameters
Flame component analysis
Components corresponding to the body structure - Spitfire processes - Analysis based on [chemical equation]
Further analysis by combustion parameter table []
Model building
Calculation results
Dragon-Sheep-Habitat Model
1.Analysis of Dragon’s Habitat Demand
Assumed and - consider the factors set assumed - principles involved - involved in Formula
Initial value Description
The initial model - simple differential model
Join the subject requirements model correction factor 1-
Parameters - the outcome - the drawn image
The image is analyzed
To illustrate the specificity of a parameter - change - Drawing - list - analysis
Calculate the final desired results and draw conclusions
2Dragon’s Impact on The Ecosystem: Balance or Collapse?
According to the section model analysis environment
Analysis of Dragon’s Habitat Demand
1.Analysis of Dragon’s Habitat Demand Regions【影响1】
According impact
Analogy basis - Conclusion
2.Three Regions’ Capability about Self-Recovery and Supporting Dragons【影响2】
According impact
Calculation basis - Conclusion
3.Minimum Resource and Habitat Demand for Dragon’s Survival in Three Regions【影响3】
Calculation basis - to draw interesting image [Oh]
Sensitivity Analysis [initially assumed values within a range of a set sensitivity is determined to change the parameters results in full, a time factor becomes a (Control Variable)]
Description of factors to determine
1.Impact of Inherent Growth Rate r on Dragon’s Weight
Parameter description, drawing
Analysis - Conclusion
2.Impact of Environmental factor σ on Dragon’s Weight
Parameter description, drawing
Analysis - Conclusion
3.Impact of Environmental Temperature T on Dragon’s Weight
Parameter description, drawing
Analysis - Conclusion
4.Impact of Environmental Temperature T on Dragon’s Weight
Model Evaluation and Further Discussion
1.Evaluation of Models
By - model - the analogy method - to solve the problem
Description of rationality model
Innovative description
Insufficient explanation point
2.Further Discussion
How can proceed
Portable in other areas
Reference
Appendices
Plots [not shown in FIG supplement]
Codes [rarely, drawing two, 1 model, probably hand solving equations]
[Yellow 1] Title hypothesis
[Yellow 2] summarizes problems [1] corresponding to a physical feature analysis model dragon, minimum estimate their daily energy expenditure and calorie intake. [] Energy consumption corresponding to a model
[Yellow 3] summed up the problem [2] model corresponds to a real impact on the ecological environment of the world of research there is the dragon, the dragon is determined to maintain the size of the area of daily life, and to meet the ecological conditions and the range of biological communities needed to survive long.
[Yellow 4] summed up the problem with the change of 3 local temperature, and other similar animals, the dragon will move to different places. Therefore, we need to analyze their differences needs to survive in dry, warm and cold regions.
