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We present a new method for constructing equilibrium phase models for stellar systems, which we call the iterative method. It relies on constrained, or guided evolution, so that the equilibrium solution has a number of desired parameters…
In the last decade, developments in tropical geometry have provided a number of uses directly applicable to problems in statistical learning. The TML package is the first R package which contains a comprehensive set of tools and methods…
This paper presents a task and motion planning (TAMP) framework for a robotic manipulator in order to retrieve a target object from clutter. We consider a configuration of objects in a confined space with a high density so no collision-free…
Robotic manipulation in complex, constrained spaces is vital for widespread applications but challenging, particularly when navigating narrow passages with elongated objects. Existing planning methods often fail in these low-clearance…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
We present a robust method to correct for motion in volumetric in-utero MRI time series. Time-course analysis for in-utero volumetric MRI time series often suffers from substantial and unpredictable fetal motion. Registration provides voxel…
The Tisserand graph (TG) is a graphical tool commonly employed in the preliminary design of gravity-assisted trajectories. The TG is a two-dimensional map showing essential orbital information regarding the Keplerian orbits resulting from…
We give a constructive proof of the existence of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov's normalization algorithm to the case of planetary systems, for which…
Molecular clouds are observed to be turbulent, but the origin of this turbulence is not well understood. As a result, there are two different approaches to simulating molecular clouds, one in which the turbulence is allowed to decay after…
The radial velocity method is one of the most successful techniques for the discovery and characterization of exoplanets. Modern spectrographs promise measurement precision of ~0.2-0.5 m/s for an ideal target star. However, the intrinsic…
We consider the classical problem of the construction of invariant tori exploiting suitable Hamiltonian normal forms. This kind of approach can be translated by means of the Lie series method into explicit computational algorithms, which…
We present MORDOR (MORphological DecOmposeR, a new algorithm for structural decomposition of simulated galaxies based on stellar kinematics. The code measures the properties of up to five structural components (a thin/cold and a thick/warm…
We propose an experimental scheme to construct an optical lattice where the atoms are confined to the surface of a torus. This construction can be realized with spatially shaped laser beams which could be realized with recently developed…
The mutual orbital alignment in multiple planetary systems is an important parameter for understanding their formation. There are a number of elaborate techniques to determine the alignment parameters using photometric or spectroscopic…
We introduce the Stellar decomposition, a model for efficient topological data structures over a broad range of simplicial and cell complexes. A Stellar decomposition of a complex is a collection of regions indexing the complex's vertices…
A method to establish regions of phase space through which pass no invariant tori transverse to a given direction field is applied to the planar circular restricted three-body problem. Implications for the location of stable orbits for…
Safe UAV navigation is challenging due to the complex environment structures, dynamic obstacles, and uncertainties from measurement noises and unpredictable moving obstacle behaviors. Although plenty of recent works achieve safe navigation…
This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
Star formation is intimately linked to the dynamical evolution of molecular clouds. Turbulent fragmentation determines where and when protostellar cores form, and how they contract and grow in mass via accretion from the surrounding cloud…