The crescent Moon


I'm interested in celestial mechanics and the numerical methods used in its analysis.


I'm interested in celestial mechanics and the numerical methods used in its analysis.
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General Relativity and Long-term Stability

My most recent work has been to study the dynamical stability of the solar system by investigating the effects of the general relativistic perihelion precession rate of the planets. We developed a simple, unified, Fokker-Planck advection-diffusion model that can reproduce the instability time of Mercury with, without, and with time-varying GR precession

We show that while ignoring GR precession does move Mercury's precession frequency closer to a resonance with Jupiter, this alone does not explain the increased instability rate. It is necessary that there is also a significant increase in the rate of diffusion. However, the solar system's stability is robust to small changes, and long-term solar system integrations can be trusted if the diffusion of the system is physically dominated.

See the animation below in the Numerical Integrators section for more insight into the precession of Mercury under the influence of GR.

Stellar Flybys and Long-term Stability

I have investigated how to quantify the effects of stellar flybys on planetary systems. The architecture and evolution of planetary systems are shaped in part by stellar flybys. The strength and frequency of stellar flybys vary over system lifetimes as local stellar environments mature. Within this context, I am looking at stellar encounters which are too weak to immediately destabilize a planetary system but are nevertheless strong enough to measurably perturb a system's dynamical state.

The strength of these perturbations on the Solar System are on the order of 0.1%. The Solar System is dynamically robust to a vast majority of the long-term effects from stellar flybys. I determined this using a simple analytic model and confirmed it with ensembles of thousands of direct N-body simulations. A better understanding of how stellar flybys affect long-term changes to orbital structure enriches our understanding of the evolution of exoplanet systems. This increased confidence improves our understanding of the mechanisms which shape planetary systems over stellar lifetimes.

Numerical Integrators

I also work with the numerical methods associated with n-body integrators including their analysis, improvement, and convergence testing. In our paper On the accuracy of symplectic integrators for secularly evolving planetary systems, we discuss how symplectic integrators have made it possible to study the long-term evolution of planetary systems with direct N-body simulations. We reassess the accuracy of such simulations by running a convergence test on 20 Myr integrations of the Solar System using various symplectic integrators. We find that the specific choice of metric for determining a simulation's accuracy is important. Only looking at metrics related to integrals of motions such as the energy error can overestimate the accuracy of a method. As one specific example, we show that symplectic correctors do not improve the accuracy of secular frequencies compared to the standard Wisdom-Holman method without symplectic correctors, despite the fact that the energy error is three orders of magnitudes smaller.

The adjacent animation shows how Mercury\'s orbit precesses over time due to the effects of General Relativity. This integration was done with REBOUND using the WHCKL integrator and REBOUNDx using the gr_potential effect.


This is work that I did as an undergraduate under the mentorship of Manuel Berrondo and culminated as an honours undergraduate thesis.

Abstract: The complexity and pattern found in animal aggregations, such as starling murmurations, reveals emergent phenomena which arise from the simple, individual interactions of its members. Simulated in a two-dimensional algorithmic model, self-driven particles (boids) group together and display emergent flocking characteristics. The model is based on the ideas of consensus and frustration, where consensus is a nonlinear topological averaging that drives the boids toward one of three unique phases, and frustration is a perturbation that pushes the boids beyond these simple phases and toward disordered behavior. The nonlinearity merged with the perturbation produces characteristics which go beyond the dynamic interplay of global and local phase transitions. The emergent results are interpreted in terms of global and local order parameters, and correlation functions. The results also strongly agree with observational data and empirical analysis.

Multiple animations of this work can be found on my YouTube channel