Research, understand and refine a problem

Before solving a problem we need to understand it, and often also more precisely define what we are solving. For this we can of course draw on what we know from before, but most likely we will need to find and read additonal information. The mcm competition rule states that we can consult any inanimate source so this includes:
  1. Wikipedia,
  2. Textbooks,
  3. Scientific articles.
  4. Other web pages
The trustworthuness of sources vary. Generally the first three categories are considered trustworthy. Wikipedia is reviewed by other users, scientific books articles generally by 1 to 3 experts in the field. If we rely on arbitrary, self published web pages we should find backup sources and double check that they are correct. You can find these resources by:
  1. General Google searches
  2. Specific scientific search engines (e.g. google scholar,
  3. References in articles we found. This allows us to find older work than the paper we have.
  4. Citation searches: use a scientific search engine to find papers that cite a particular paper you already have found relevant. This allows us to find newer work.
The last point is important. It is expected to properly reference sources in academic writing (and you will have to in your report also), so the references in each article is a potential source for dozens of more articles. In most cases the detailed references are at the end of a document. Some web sources (e.g. Wikipedia) also follows this convention, while more informal web pages may have links to references anywhere in the text. Starting with a few articles we can easily find more Once we have some material to read we have to interpret the problem more precisely and compare to models and results we read. Often a problem is not fully defined, but we need to make additional assumpions to make the problem specification precise enough tpo allow mathematical modeling and solution. Write down these assumptions and also write down a motivation why they are good/reasonable assumptions.

Exercise

For next time consider the 2011 ICM problem (copied below). Choose and try to address one of the subquestions below. Consider the question, try to further pin it down by making it more precise, introduce your assumptions etc. See if you can answer a question or a subpart from your readings and/or with a simple calculation. Here are some articles to get started. Consider which ones are trustworthy and why. If you find an interesting article let us know.

2011 The Interdisciplinary Contest in Modeling (ICM)

How environmentally and economically sound are electric vehicles? Is their widespread use feasible and practical?

Here are some issues to consider, but, of course, there are many more, and you will not be able to consider all the issues in your model(s):
  1. Would the widespread use of electric vehicles actually save fossil fuels or would we merely be trading one use of fossil fuel for another given that electricity is currently mostly produced by burning fossil fuels? What conditions would need to be put in place to maximize the savings through use of electric vehicles?
  2. Consider how much the amount of electricity generated by alternatives such as wind and solar would need to climb during the twenty-first century to make the widespread use of electric vehicles feasible and environmentally beneficial. Assess whether or not the needed growth of these alternate sources of electricity is likely and possible.
  3. Would charging batteries at off-peak times be beneficial and increase the feasibility of widespread use of electric vehicles? How quickly would batteries need to charge to maximize the efficiency and practicality of electric vehicles? How would progress in these areas change the equation regarding the environmental savings and practicality of widespread use of electric vehicles?
  4. What method of basic transportation is most efficient? Is the efficiency of different methods dependent of the nation or region in which it is used?
  5. Pollution caused directly by electric vehicles is low, but are there hidden sources of pollutants associated with electric vehicles? Gasoline and diesel fuel burned in internal combustion engines for transportation account for nitrites of oxygen, vehicle-born monoxide and carbon dioxide pollution but are these bi-products something we really should worry about? What are the short and long term effects of these substances on the climate and our health?
  6. How would the pollution caused by the increasing need to dispose of increasing numbers of large batteries effect the comparison between the environmental effects of electric vehicles versus the effects of fossil fuel-burning vehicles?
  7. You also should consider economic and human issues such as the convenience of electric vehicles. Can batteries be recharged or replaced fast enough to meet most transportation needs or would their ranges be limited? Would electric vehicles have only a limited role in transportation, good only for short hauls (commuters or light vehicles on short trips) or could they practically be used for heavier and longer-range transportation and shipping? Should governments give subsidies to developers of electric vehicle technologies and if so, why, how much, and in what form?