Inertial Motions of a Rigid Body with a cavity filled with a viscous liquid

We study inertial motions of the coupled system, S, constituted by a rigid body containing a cavity that is completely filled with a viscous liquid. We show that for data of arbitrary size (initial kinetic energy and total angular momentum) every weak solution (a la Leray-Hopf) converges, as time goes to infinity, to a uniform rotation, thus proving a famous "conjecture" of Zhukovskii. Moreover we show that, in a wide range of initial data, this rotation must occur along the central axis of inertia of S that has the largest moment of inertia. Furthermore, necessary and sufficient conditions for the rigorous nonlinear stability of permanent rotations are provided, which improve and/or generalize results previously given by other authors under different types of approximation of the original equations and/or suitable symmetry assumptions on the shape of the cavity. Finally, we present a number of results obtained by a targeted numerical simulation that, on the one hand, complement the analytical findings, whereas, on the other hand, point out new features that the analysis is yet not able to catch, and, as such, lay the foundation for interesting and challenging future investigation.Comment: Some of the main results proved in this paper were previously announced in Comptes Rendus Mecanique, Vol. 341, 760--765 (2013

Nonlinear Stability Analysis of a Spinning Top with an Interior Liquid-Filled Cavity

Consider the motion of the the coupled system, $\mathscr S$, constituted by a (non-necessarily symmetric) top, $\mathscr B$, with an interior cavity, $\mathscr C$, completely filled up with a Navier-Stokes liquid, $\mathscr L$. A particular steady-state motion $\bar{\sf s}$ (say) of $\mathscr S$, is when $\mathscr L$ is at rest with respect to $\mathscr B$, and $\mathscr S$, as a whole rigid body, spins with a constant angular velocity \bar{\V\omega} around a vertical axis passing through its center of mass $G$ in its highest position ({\em upright spinning top}). We then provide a completely characterization of the nonlinear stability of $\bar{\sf s}$ by showing, roughly speaking, that $\bar{\sf s}$ is stable if and only if |\bar{\V\omega}| is sufficiently large, all other physical parameters being fixed. Moreover we show that, unlike the case when $\mathscr C$ is empty, under the above stability conditions, the top will eventually return to the unperturbed upright configuration

Data Presentation and Visualization (DPV) Interface Control Document

Data Presentation and Visualization (DPV) is a subset of the modeling and simulation (M&S) capabilities at Kennedy Space Center (KSC) that endeavors to address the challenges of how to present and share simulation output for analysts, stakeholders, decision makers, and other interested parties. DPV activities focus on the development and provision of visualization tools to meet the objectives identified above, as well as providing supporting tools and capabilities required to make its visualization products available and accessible across NASA

Distributed Observer Network (DON), Version 3.0, User's Guide

The Distributed Observer Network (DON) is a data presentation tool developed by the National Aeronautics and Space Administration (NASA) to distribute and publish simulation results. Leveraging the display capabilities inherent in modern gaming technology, DON places users in a fully navigable 3-D environment containing graphical models and allows the users to observe how those models evolve and interact over time in a given scenario. Each scenario is driven with data that has been generated by authoritative NASA simulation tools and exported in accordance with a published data interface specification. This decoupling of the data from the source tool enables DON to faithfully display a simulator's results and ensure that every simulation stakeholder will view the exact same information every time

Surgical management of rhinosinusitis in onco-hematological patients

ObjectivesIn onco-hematological diseases, the incidence of paranasal sinuses infection dramatically increase and requires a combination of medical and surgical therapy. Balloon dilatation surgery (DS) is a minimally invasive, tissue preserving procedure. The study evaluates the results of DS for rhinosinusitis in immunocompromised patients.MethodsA retrospective chart review was conducted in 110 hematologic patients with rhinosinusitis. Twenty-five patients were treated with DS technique and 85 patients with endoscopic sinus surgery (ESS). We considered the type of anesthesia and the extent of intra- and postoperative bleeding. Patients underwent Sino-Nasal Outcome Test (SNOT-20) to evaluate changes in subjective symptoms and global patient assessment (GPA) questionnaire to value patient satisfaction.ResultsLocal anesthesia was employed in 8 cases of DS and in 15 of ESS. In 50 ESS patients, an anterior nasal packing was placed and in 12 cases a repacking was necessary. In the DS group, nasal packing was required in 8 cases and in 2 cases a repacking was placed (P=0.019 and P=0.422, respectively). The SNOT-20 change score showed significant improvement of health status in both groups. However the DS group showed a major improvement in 3 voices: need to blow nose, runny nose, and facial pain/pressure. The 3-month follow-up GPA questionnaire showed an higher satisfaction of DS group.ConclusionBalloon DS represents a potentially low aggressive treatment and appears to be relatively safe and effective in onco-hematologic patients. All these remarks may lead the surgeon to consider a larger number of candidates for surgical procedure