Frobenius theorem and invariants for Hamiltonian systems

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assurately restricted to a two-dimensional foliation. In some cases, Frobenius theorem allows the explicit construction of an associated invariant. It is proven the inverse result that, if an invariant is known, then it always can be furnished by Frobenius theorem

A Survey of Positioning Systems Using Visible LED Lights

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.As Global Positioning System (GPS) cannot provide satisfying performance in indoor environments, indoor positioning technology, which utilizes indoor wireless signals instead of GPS signals, has grown rapidly in recent years. Meanwhile, visible light communication (VLC) using light devices such as light emitting diodes (LEDs) has been deemed to be a promising candidate in the heterogeneous wireless networks that may collaborate with radio frequencies (RF) wireless networks. In particular, light-fidelity has a great potential for deployment in future indoor environments because of its high throughput and security advantages. This paper provides a comprehensive study of a novel positioning technology based on visible white LED lights, which has attracted much attention from both academia and industry. The essential characteristics and principles of this system are deeply discussed, and relevant positioning algorithms and designs are classified and elaborated. This paper undertakes a thorough investigation into current LED-based indoor positioning systems and compares their performance through many aspects, such as test environment, accuracy, and cost. It presents indoor hybrid positioning systems among VLC and other systems (e.g., inertial sensors and RF systems). We also review and classify outdoor VLC positioning applications for the first time. Finally, this paper surveys major advances as well as open issues, challenges, and future research directions in VLC positioning systems.Peer reviewe

On the linearization of the generalized Ermakov systems

A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into this category but others, more generic, systems are also included

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

Neutrino-driven Turbulent Convection and Standing Accretion Shock Instability in Three-Dimensional Core-Collapse Supernovae

We conduct a series of numerical experiments into the nature of three-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase of core-collapse supernovae using 3D general-relativistic hydrodynamic simulations of a $27$-$M_\odot$ progenitor star with a neutrino leakage/heating scheme. We vary the strength of neutrino heating and find three cases of 3D dynamics: (1) neutrino-driven convection, (2) initially neutrino-driven convection and subsequent development of the standing accretion shock instability (SASI), (3) SASI dominated evolution. This confirms previous 3D results of Hanke et al. 2013, ApJ 770, 66 and Couch & Connor 2014, ApJ 785, 123. We carry out simulations with resolutions differing by up to a factor of $\sim$4 and demonstrate that low resolution is artificially favorable for explosion in the 3D convection-dominated case, since it decreases the efficiency of energy transport to small scales. Low resolution results in higher radial convective fluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrino heating. In the SASI-dominated case, lower resolution damps SASI oscillations. In the convection-dominated case, a quasi-stationary angular kinetic energy spectrum $E(\ell)$ develops in the heating layer. Like other 3D studies, we find $E(\ell) \propto \ell^{-1}$ in the "inertial range," while theory and local simulations argue for $E(\ell) \propto \ell^{-5/3}$. We argue that current 3D simulations do not resolve the inertial range of turbulence and are affected by numerical viscosity up to the energy containing scale, creating a "bottleneck" that prevents an efficient turbulent cascade.Comment: 24 pages, 15 figures. Accepted for publication in The Astrophysical Journal. Added one figure and made minor modifications to text according to suggestions from the refere

Dust reverberation-mapping of the Seyfert 1 galaxy WPVS48

Using robotic telescopes of the Universitatssternwarte Bochum near Cerro Armazones in Chile, we monitored the z=0.0377 Seyfert 1 galaxy WPVS48 (2MASX J09594263-3112581) in the optical (B and R) and near-infrared (NIR, J and Ks) with a cadence of two days. The light curves show unprecedented variability details. The NIR variation features of WPVS48 are consistent with the corresponding optical variations, but the features appear sharper in the NIR than in the optical, suggesting that the optical photons undergo multiple scatterings. The J and Ks emission, tracing the hot (1600 K) dust echo, lags the B and R variations by on average 64 +/- 4 days and 71 +/- 5 days, respectively (restframe). WPVS48 lies on the known tau-M_V relationship. However, the observed lag is about three times shorter than expected from the dust sublimation radius r_sub inferred from the optical-UV luminosity, and explanations for this common discrepancy are searched for. The sharp NIR echos argue for a face-on torus geometry and allow us to put forward two potential scenarios: 1) as previously proposed, in the equatorial plane of the accretion disk the inner region of the torus is flattened and may come closer to the accretion disk. 2) The dust torus with inner radius r_sub is geometrically and optically thick, so that the observer only sees the facing rim of the torus wall, which lies closer to the observer than the torus equatorial plane and therefore leads to an observed foreshortened lag. Both scenarios are able to explain the factor three discrepancy between tau and r_sub. Longer-wavelength dust reverberation data might enable one to distinguish between the scenarios.Comment: 4 pages, 6 figures, Published in Astronomy and Astrophysic