Jason Mireles-James
Florida Atlantic University, FL·Mathematics & Statistics
Many physical systems without friction, from electrons in semiconductors to stars and planets moving in galaxies, are modeled as Hamiltonian systems. Without friction, nothing settles motion down into simple end states.
- Fields
Mathematics & Statistics
Physics
- Topics
Hamiltonian systems
dynamical systems
nonlinear dynamics
- Grants
- 1 known grant, through Jun 2027
What they work on
- Extend high-order computational methods for hyperbolic invariant objects to the parabolic case, where nearby trajectories separate slowly, in Hamiltonian systems.
- Develop methods to grow atlases of stable and unstable manifolds from high-order chart maps, giving a global picture of phase space structure.
- Compute intersections between invariant manifolds using efficient search strategies, to understand transport between phase space regions and complex recurrent motion.
- Apply combined computational and analytical tools to open problems in celestial mechanics, including the search for low-energy transfer orbits for spaceflight.
More about the research
Instead, the motion is organized by geometric structures such as equilibrium solutions, periodic (repeating) orbits and invariant tori, which are doughnut-shaped surfaces that trajectories stay on. Understanding these structures in fine detail is hard but needed for problems in celestial mechanics and space mission design.
Why it matters
Mapping the hidden structures that steer motion in frictionless systems could help mission planners design or discover new low-energy transfer orbits for spacecraft traveling within the solar system. Such orbits could reduce fuel needs. The tools also apply to many physical models, from semiconductors to galactic dynamics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Chongchun Zeng
Georgia Institute of Technology, GA·Mathematics & Statistics
Analyze two-dimensional water waves linearized at shear flows, where speed varies with depth, establishing the bifurcation of instability and linear inviscid damping for gravity water waves.
Laura DeMarco
Harvard University, MA·Mathematics & Statistics
Characterize the special subvarieties — geometric pieces preserved by the map — that arise in families of dynamical systems built from endomorphisms of algebraic varieties, aiming at a general classification within a unifying conjectural framework.
Maegan Tucker
Georgia Institute of Technology, GA·Engineering
Extend contraction theory, a mathematical test of whether nearby motions of a system converge, to hybrid systems that mix smooth motion with sudden impacts. Use it to estimate regions of attraction for contact-rich robots.
The school
Florida Atlantic University: 7 labs on PI Pages, $88M a year on research, 124 research doctorates a year.
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