Images from our research

The following images arise from research carried out by the faculty, organized by subfield.

If you are looking for a list of recent undergraduate research projects, visit this page instead.

Chaos theory

Chaotic trajectory in the logistic equation

How can we calculate the probability density function that determines the statistical properties of chaotic orbits or trajectories? The animation above illustrates the chaotic trajectory taken by a population that starts at 20% capacity when the logistic equation of its population is $4x(1-x)$.

- Jiu Ding   

 

Computational algebra

Refinement of monomial ordering in dynamic algorithm

How can we efficiently choose a monomial ordering during a dynamic algorithm to compute a Gröbner basis? The animation above illustrates how the growth of the basis increases dramatically the number of orderings we can choose.

- John Perry    

Graph theory

Graph

The graph above is a counterexample to a conjecture on the size of the neighborhoods of independent sets.

- Jeremy Lyle    

Partial differential equations

 

 

Ground state and contour     Ground state and contour

The ground state and contour of the problem $\Delta u + u^3=0$, $u>0$ on $D$, $u=0$ on $\partial D$, with $D$ being a nonconcentric annular domain.

- Haiyan Tian