Profiles on Profiles on Profiles

This week started off with brainstorming questions to see where we wanted to go with the solution that we reviewed that was published by Denisov and Beichman. Two of the questions that we began to ask were how does time become a factor in the stability of the solution and how much do we want […]

Taking a Step Back

This week we worked on understanding in detail the behavior of one of the steady state solutions for Model 2s (the model where both producers and scroungers die linearly and the scroungers depend on the producers to eat):                              P → ( r […]

Scroungers Report

This week consisted of making more models with the goal of finding one in which producers, scroungers and food coexist and are stable with the logic that: Producers find food on their own Scroungers eat the left overs of the producers or they run into food on their own (however, the latter is less likely) […]

Just like us, u_2 can do it!

This week we focused on deriving the velocity function u which we had realized was made of two components u=(u1,u2) . As we had learned before the first component u1=0 but we then figured out that the second component which began as a double integral was truly a single integral with an integrand with a […]

Scroungers Progress Report #Scroungers

This week we worked on different ordinary differential equation models to help us understand the interactions between scroungers, producers and prey. In this process we learned how to interpret models by using Mathematica to solve for the steady state solutions of our models; we then use the Jacobian of the system of equations that make […]

Streaming through Week 2

Towards the beginning of the week, our team decided to take a closer look at some of the literature provided to us in order to understand some context to the problem we will be working on. We also looked at new functions and their hyperbolic behavior, Sinh[x] and Cosh[x]. These two functions were pivotal to […]

Week 2: Starting Research Projects

Goals:  Further practice with Mathematica Learn to use LaTeX for typing mathematics Start work on individual research problems Our Research Teams:  Pattern Formation in Animal Foraging (#scroungers) with Nessy Tania Caira Anderson Issa Susa Vortex Patch Dynamics (#vortexpatches) with Jen Beichman Victoria Camarena Christian Madrigal Sasha Shrouder Suggested Readings:  Pattern Formation Tania et al. Vortex […]

Week 1: PDE and Mathematical Computing Minicourses

Goals:  Learn basics of PDEs and computing with Mathematica Form research groups Write MathFest presentation abstracts Mathematica Materials:  Mathematica Day 1: Mathematica Notebook Mathematica Day 1: Worksheet Mathematica Day 2: Solving ODEs and steady state solutions Mathematica Day 3: Fourier Series Demo Mathematica Day 3: Heat Separation [advanced_iframe src=”//″ width=”100%” height=”600″]