Symmetry Reduction of Optimal Control Systems and Principal Connections

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry. In particular, we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups, as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting. Our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems. Affine and kinematic optimal control systems are of particular interest: We explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure

Evidence for a rapid decrease in Pluto's atmospheric pressure revealed by a stellar occultation in 2019

We report observations of a stellar occultation by Pluto on 2019 July 17. A single-chord high-speed (time resolution $= 2\,$s) photometry dataset was obtained with a CMOS camera mounted on the Tohoku University 60 cm telescope (Haleakala, Hawaii). The occultation light curve is satisfactorily fitted to an existing Pluto's atmospheric model. We find the lowest pressure value at a reference radius of $r = 1215~{\rm km}$ among those reported after 2012, indicating a possible rapid (approximately $21^{+4}_{-5} \%$ of the previous value) pressure drop between 2016 (the latest reported estimate) and 2019. However, this drop is detected at a $2.4\sigma$ level only and still requires confirmation from future observations. If real, this trend is opposite to the monotonic increase of Pluto's atmospheric pressure reported by previous studies. The observed decrease trend is possibly caused by ongoing ${\rm N_2}$ condensation processes in the Sputnik Planitia glacier associated with an orbitally driven decline of solar insolation, as predicted by previous theoretical models. However, the observed amplitude of the pressure decrease is larger than the model predictions.Comment: 7 pages, 3 figures, accepted for publication in Astronomy and Astrophysic

High capacitance carbon-based xerogel film produced without critical drying

This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in APPLIED PHYSICS LETTERS. 93(19):193112 (2008) and may be found at https://doi.org/10.1063/1.2976684 .ArticleAPPLIED PHYSICS LETTERS. 93(19):193112 (2008)journal articl

Stripe charge ordering in SrO-terminated SrTiO3(001) surfaces

The local electronic structure of the SrO-terminated SrTiO3(001) surface was explored using scanning tunneling microscopy. At low bias voltages in the empty states, a unidirectional structure with a periodicity of 3 unit cells, superimposed on a c(2 x 2) reconstructed structure, was found to develop along the crystallographic a axis. This structure indicates a charge-ordered stripe induced by carrier doping from oxygen vacancies in the SrO and the subsurface TiO2 planes. In the filled states, localized deep in-gap states were observed in addition to large energy gaps in the tunneling spectra. This result represents inelastic tunneling due to significant electron-lattice interaction associated with unidirectional lattice distortion in the SrO-terminated surface.Comment: 6 pages, 5 figures, accepted for publication in PR

Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints

We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton-Jacobi equation as the Dirac-Hamilton-Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the theory specializes to the recently developed nonholonomic Hamilton-Jacobi theory. We are particularly interested in applications to a certain class of degenerate nonholonomic Lagrangian systems with symmetries, which we refer to as weakly degenerate Chaplygin systems, that arise as simplified models of nonholonomic mechanical systems; these systems are shown to reduce to non-degenerate almost Hamiltonian systems, i.e., generalized Hamiltonian systems defined with non-closed two-forms. Accordingly, the Dirac-Hamilton-Jacobi equation reduces to a variant of the nonholonomic Hamilton-Jacobi equation associated with the reduced system. We illustrate through a few examples how the Dirac-Hamilton-Jacobi equation can be used to exactly integrate the equations of motion.Comment: 44 pages, 3 figure

Full particle simulation of a perpendicular collisionless shock: A shock-rest-frame model

The full kinetic dynamics of a perpendicular collisionless shock is studied by means of a one-dimensional electromagnetic full particle simulation. The present simulation domain is taken in the shock rest frame in contrast to the previous full particle simulations of shocks. Preliminary results show that the downstream state falls into a unique cyclic reformation state for a given set of upstream parameters through the self-consistent kinetic processes.Comment: 4 pages, 2 figures, published in "Earth, Planets and Space" (EPS), the paper with full resolution images is http://theo.phys.sci.hiroshima-u.ac.jp/~ryo/papers/shock_rest.pd