Images from our research

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

Chaos theory

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 $4x(1-x)$.

Computational algebra

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.

Partial differential equations

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.