GSMMC 2022 Abstracts and Reports

Below are the problems to be presented at the 2022 Graduate Student Mathematical Modeling Camp.​

​Manuchehr Aminian, Cal Poly Pomona​

Geospatial travel data is enormously valuable for local governments to makeinformed decisions on urban planning, zoning, fiscal policy, and so on. When governments collect such data using taxpayer money, there are expectations for (a) transparency in data and data collection, (b) privacy of participants involved indata collection, (c) utility of data to make informed decisions. These three priorities are often at odds with one another. The project sponsor wants us to mathematically model these tradeoffs, suggest approaches to privacy of individuals, and do a risk analysis of a hypothetical malicious actor seeking to discover details of individuals in the data. The sponsor would like these applied to data from a large travel data set from the Minneapolis/St. Paul metropolitan area during 2018-2019.​ 

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​Valeria Barra, California Institute of Technology​

Clouds can be very fascinating and romantic to stare at, but they provide great challenges from a mathematical and numerical modeling point of view. In fact, clouds currently are one of the greatest sources of uncertainty in climate forecasts. One of the reasons why they are so difficult to capture in current numerical models is the extreme range of scales involved: from processes happening on the length scales of individual cloud droplets, to the large-scale eddies driving the air circulation of a cloudy field. It is important to keep track of the microscopic properties of cloud particles in order to properly resolve, for example, the physics of rain or snow formation. On the other hand, it is also very important to keep the simulation computationally affordable. How to make things simple without oversimplifying?​

We will look at this question from the point of view of a snowflake. Snowflake crystals come in many different shapes and sizes. This can, inturn, affect their growth rates, collision rates and their sedimentation rates. Although these are all very important aspects to take into account, typically, current cloud models used in the climate andatmospheric science communities can only afford to predict cumulative quantities, such as the total mass of snow produced in a cloud.​

This project will start by considering a simple, idealized model of the shape of a snowflake. Building upon this idealized model, we will then consider possible variations or extensions to make the model more realistic. The main goal for this workshop will be to come up with possible mathematical models that are detailed enough to capture the different possible snowflake shapes, but simple enough that they can be integrated into a more complex cloud model, and therefore be useful for climate predictions. Some additional questions that we could answer during this workshop can then help us build our understanding of how precipitation rates can be affected by different snowflake geometries, and how we could potentially include more complexity​. 

Read the final report​

​​​​Christopher Raymond, University of Delaware​

Students will be exposed to:

• Population dynamics type modeling leading to a nonlinear system of ODEs.
• Nondimensionalization and scaling of models.
• Analysis of a nonlinear system of ODEs: finding stationary and periodic solutions and their stability
• Extensions to the model: PDEs, conservation laws, other ways to modify and extend the basic model
• Numerical methods for solution of the models using MATLAB​​

Read the final report​​