Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

All-particle cosmic ray energy spectrum measured with 26 IceTop stations

We report on a measurement of the cosmic ray energy spectrum with the IceTop air shower array, the surface component of the IceCube Neutrino Observatory at the South Pole. The data used in this analysis were taken between June and October, 2007, with 26 surface stations operational at that time, corresponding to about one third of the final array. The fiducial area used in this analysis was 0.122 km^2. The analysis investigated the energy spectrum from 1 to 100 PeV measured for three different zenith angle ranges between 0{\deg} and 46{\deg}. Because of the isotropy of cosmic rays in this energy range the spectra from all zenith angle intervals have to agree. The cosmic-ray energy spectrum was determined under different assumptions on the primary mass composition. Good agreement of spectra in the three zenith angle ranges was found for the assumption of pure proton and a simple two-component model. For zenith angles {\theta} < 30{\deg}, where the mass dependence is smallest, the knee in the cosmic ray energy spectrum was observed between 3.5 and 4.32 PeV, depending on composition assumption. Spectral indices above the knee range from -3.08 to -3.11 depending on primary mass composition assumption. Moreover, an indication of a flattening of the spectrum above 22 PeV were observed.Comment: 38 pages, 17 figure

Neutrino oscillation studies with IceCube-DeepCore

AbstractIceCube, a gigaton-scale neutrino detector located at the South Pole, was primarily designed to search for astrophysical neutrinos with energies of PeV and higher. This goal has been achieved with the detection of the highest energy neutrinos to date. At the other end of the energy spectrum, the DeepCore extension lowers the energy threshold of the detector to approximately 10 GeV and opens the door for oscillation studies using atmospheric neutrinos. An analysis of the disappearance of these neutrinos has been completed, with the results produced being complementary with dedicated oscillation experiments. Following a review of the detector principle and performance, the method used to make these calculations, as well as the results, is detailed. Finally, the future prospects of IceCube-DeepCore and the next generation of neutrino experiments at the South Pole (IceCube-Gen2, specifically the PINGU sub-detector) are briefly discussed

The Marine Microbial Eukaryote Transcriptome Sequencing Project (MMETSP): Illuminating the Functional Diversity of Eukaryotic Life in the Oceans through Transcriptome Sequencing

Microbial ecology is plagued by problems of an abstract nature. Cell sizes are so small and population sizes so large that both are virtually incomprehensible. Niches are so far from our everyday experience as to make their very definition elusive. Organisms that may be abundant and critical to our survival are little understood, seldom described and/or cultured, and sometimes yet to be even seen. One way to confront these problems is to use data of an even more abstract nature: molecular sequence data. Massive environmental nucleic acid sequencing, such as metagenomics or metatranscriptomics, promises functional analysis of microbial communities as a whole, without prior knowledge of which organisms are in the environment or exactly how they are interacting. But sequence-based ecological studies nearly always use a comparative approach, and that requires relevant reference sequences, which are an extremely limited resource when it comes to microbial eukaryotes

The Interaction Between the Substrate and Frost Layer Through Condensate Distribution

Microscopic observations of frost deposition on a variety of substrates having different contact angles, (polytetrafluoroethylene PTFE, kapton, glass and others) allow the quantification of substrate effects on frost structure during inception and growth. The deposition of water vapor at the beginning of the frosting process on a clean glass substrate is found to be as condensate (condensation frosting) rather than as ice (ablimation frosting) for a substrate temperatures above -33??C and an absolute humidity above 0.15 g/kg. The inception of "condensation frosting" (the condensation period and early frost growth period) is further examined microscopically as a function of air and substrate temperatures, absolute humidity, and substrate contact angle. The water distribution on the substrate at the end of the condensation period is found to be strongly dependent on substrate temperature, humidity ratio, and substrate contact angle. Colder substrates result in smaller more uniform droplets and substrates with lower contact angles result in shorter, larger diameter droplets with a larger percentage of the substrate covered. The effective density of the condensate on hydrophobic substrates is found to be lower than that on hydrophilic substrates. The structure and form of the ice immediately after freezing is substrate dependent. High-speed imaging of the freezing process is used to study the propagation of the freezing front in a droplet. The images show that a protrusion is formed at the top of the droplets during freezing. From observations, this protrusion is hypothesized to result from the convective condition at the droplet surface and the difference in specific volume between liquid and solid water. Additionally, the apparent ejection of water vapor during freezing of a droplet on a hydrophobic substrate was observed. This ejection of water vapor is thought to be caused by the wanning of the droplet caused by the release of latent heat. In contrast to trends observed during the early growth period, the growth rate of mature frost is found to decrease with substrate contact angle while frost density is found to increase. This behavior is explained in terms of the effect of substrate contact angle on the structure and form of the incipient frost, which constitutes the initial condition for further (mature) frost growth. A higher conductivity layer is formed on the hydrophilic than on the hydrophobic substrate. A model relating crystal orientation to conductivity is used to simulate the frost growth rate and density on the two different substrates and match the experimental data. Using similar reasoning, the higher conductivity frost formed on colder substrates is also explained.Air Conditioning and Refrigeration Project 10