2019 MCM Problem A

【原題+翻譯】

2019 MCM Problem A: Game of Ecology 
In the fictional television series Game of Thrones, based on the series of epic fantasy novels A Song of Ice and Fire[1], three dragons are raised by Daenerys Targaryen, the “Mother of Dragons.” When hatched, the dragons are small, roughly 10 kg, and after a year grow to roughly 30-40 kg. They continue to grow throughout their life depending on the conditions and amount of food available to them.  For the purposes of this problem, consider these three fictional dragons are living today. Assume that the basic biology of dragons described above is accurate. You will need to make some additional assumptions about dragons that might include, for example, that dragons are able to fly great distances, breath fire, and resist tremendous trauma. As you address the problem requirements, it should be clear how your assumptions are related to the physical constraints of the functions, size, diet, changes, or other characteristics associated with the animals.  Your team is assigned to analyze dragon characteristics, behavior, habits, diet, and interaction with their environment. To do so, you will have to consider many questions. At a minimum, address the following: What is the ecological impact and requirements of the dragons? What are the energy expenditures of the dragons, and what are their caloric intake requirements? How much area is required to support the three dragons? How large a community is necessary to support a dragon for varying levels of assistance that can be provided to the dragons? Be clear about what factors you are considering when addressing these questions.  As with other animals that migrate, dragons might travel to different regions of the world with very different climates. How important are the climate conditions to your analysis? For example, would moving a dragon between an arid region, a warm temperate region, and an arctic region make a big difference in the resources required to maintain and grow a dragon?  Once your dragon analysis is complete, draft a two-page letter to the author of A Song of Ice and Fire, George R.R. Martin, to provide guidance about how to maintain the realistic ecological underpinning of the story, especially with respect to the movement of dragons from arid regions to temperate regions and to arctic regions. While your dragon analysis does not directly apply to a real physical situation, the mathematical modeling itself makes use of many realistic features used in modeling a situation. Aside from the modeling activities themselves, describe and discuss a situation outside of the realm of fictional dragons that your modeling efforts might help inform and provide insight? 
 
Your submission should consist of:  

•  One-page Summary Sheet,  
•  Two-page letter,  
•  Your solution of no more than 20 pages, for a maximum of 23 pages with your summary and letter.  
•  Note: Reference list and any appendices do not count toward the 23-page limit and should appear after your completed solution.

NOTE: You should not make use of unauthorized images and materials whose use is restricted by copyright laws. Please be careful in how you use and cite the sources for your ideas and the materials used in your report. 
 
Reference 1. Penguin Random House (2018). A Song of Ice and Fire Series. Retrieved from https://www.penguinrandomhouse.com/series/SOO/a-song-of-ice-and-fire/. 
 

---

谷歌翻譯個人微調版：

2019年MCM問題：生態博弈

由小說《冰與火之歌[ 1 ]》改編的玄幻電視劇《權力的遊戲》中，三條龍是由“龍之母”丹妮莉絲·塔格利安（DaenerysTargaryen）養大的。

龍剛剛孵化時很小，大約10公斤，一年後成長到大約30-40公斤。它們在一生中都在繼續生長，這取決於它們所能獲得的食物的條件和數量。

現在的問題，假設這三條虛構的龍生活在今天。假設上面描述的龍的基本生物學是準確的。你需要對龍做一些額外的假設，例如，龍可以飛很遠的距離，呼吸火焰，抵抗巨大的創傷。在您解決問題需求時，應該清楚您的假設與功能、大小、飲食、變化或與動物相關的其他特徵的物理約束之間的關係。

你的團隊負責分析龍的特徵、行為、習慣、飲食以及與環境的互動。要做到這一點，你必須考慮許多問題。至少要解決以下問題：

• 龍的生態影響和要求是什麼？
• 龍的能量消耗是多少，它們的熱量攝入要求是什麼？
• 支撐三條龍需要多少面積？
• 一個社群需要多大的規模來支援一條龍，從而為龍提供不同程度的援助？

在回答這些問題時，要清楚你在考慮哪些因素。

與其他遷徙的動物一樣，龍也可能會在氣候迥異的世界各地旅行。

• 氣候條件對你的分析有多重要？

例如，一條龍在乾旱地區、溫暖的溫帶地區和北極地區之間移動，這會對一條龍生長所需的資源產生巨大的影響嗎？

一旦你的龍的分析完成，起草一封兩頁的信給《冰與火之歌》的作者喬治R.R.馬丁，以指導如何保持故事的現實生態基礎，特別是關於龍從乾旱地區到溫帶地區和北極地區的運動。雖然您的Dragon分析不能直接應用於實際物理情況，但數學建模本身使用了許多用於建模情況的實際特性。除了建模活動本身，描述和討論虛擬龍領域之外的情況，您的建模工作可能有助於通知和提供洞察力？

 

您提交的檔案應包括： 

 one頁的彙總表， 

 two頁的信， 

解決方案：在 your超過20頁23頁，用你最大的總結和信。 

 note：參考列表和任何附件的數量也不應該在23頁的限制和appear完成後您的解決方案。

注意：你不應該讓他擅自使用和材料的限制使用的是影像的版權法。請介紹你如何使用的是在你的思想來源和引用的材料用在你的report. 

Reference 1. Penguin Random House (2018). A Song of Ice and Fire Series. Retrieved from https://www.penguinrandomhouse.com/series/SOO/a-song-of-ice-and-fire/.