Orbital Mechanics
Astrophysics — Harvey Mudd CollegeWhy Higher Order Mean Motion Resonances are Weak: A Physical and Geometric Model
Mean motion resonances (MMRs) play a pivotal role in planetary dynamics, serving as both a source of stability and chaos. MMR strengths scale at small eccentricities as ek, where k is the order of the resonance — a crucial result which helps characterize unstable regions where MMRs overlap. The traditional derivation using a perturbation series expansion provides little physical intuition. In this project we present a simple physical explanation for this scaling result. In the limit that planets are closely spaced, interplanetary interactions are negligible except at close encounters when one planet overtakes the other and imparts a gravitational "kick" to the planet's mean motion. By considering previously known Fourier expansions for these kicks, we show that the k-fold symmetry in conjunction locations leads to a cancellation of terms up to order ek−1.
Neutrino Physics
Particle PhysicsBenchmarking Supernova Pointing using Machine Learning — CERN
Core-collapse supernovae are some of the most energetic events in the universe, but many aspects of the explosion mechanism and the associated neutrino emission remain poorly understood. The next-generation Hyper-Kamiokande (HK) experiment in Japan will be the world's largest water Cherenkov detector and is expected to collect orders of magnitude more neutrinos than the current Super-Kamiokande detector during the next nearby core collapse supernova. We simulate supernova events in HK and apply machine-learning algorithms to reconstruct the supernova direction and differentiate between different theoretical emission models. We compare three architectures — convolutional neural networks (CNNs), graph neural networks (GNNs), and sparse CNNs — and evaluate their ability to infer the supernova direction from simulated photomultiplier tube hit patterns. Our results show that the sparse CNN significantly outperforms the other architectures: for a supernova at 8 kpc, it reconstructs the direction to within 2.4° on average.
An Inference-Based Study of Neutrino Oscillation — American Museum of Natural History
The solar electron number density has important implications for understanding solar and stellar physics, yet its precise distribution within the Sun is unknown. While current models are derived from measurements at the solar surface, it would be a novel approach to use Earth-based measurements to predict electron distribution in the Sun. Electron number density dictates the flavor evolution of neutrinos as they stream radially outward from the Sun, and thus determines their flavor when they reach detectors on Earth. In this study, we explored an inference-based approach that uses neutrino flavor measurements from Earth-bound detectors to extrapolate the Sun's electron density function. We studied logistic and exponential forms of electron number density and ultimately sought the sparsest amount of data required to place useful constraints on the model.