Forces and Conservation Laws for Motion on Our Spheroidal Earth

We explore the forces and conservation laws that govern the motion of a hockey puck that slides without friction on a smooth, rotating, self-gravitating spheroid. The earth\u27s oblate spheroidal shape (apart from small-scale surface features) is determined by balancing the gravitational forces that hold it together against the centrifugal forces that try to tear it apart. The earth achieves this shape when the apparent gravitational force on the puck, defined as the vector sum of the gravitational and centrifugal forces, is perpendicular to the earth\u27s surface at every point on the surface. Thus, the earth\u27s spheroidal deformations neutralize the centrifugal and gravitational forces on the puck, leaving only the Coriolis force to govern its motion. Motion on the spheroid therefore differs profoundly from motion on a rotating sphere, for which the centrifugal force plays a key role. Kinetic energy conservation reflects this difference: On a stably rotating spheroid, the kinetic energy is conserved in the rotating frame, whereas on a rotating sphere, it is conserved in the inertial frame. We derive these results and illustrate them using CorioVis software for visualizing the motion of a puck on the earth\u27s spheroidal surface

Periodic nonlinear sliding modes for two uniformly magnetized spheres

A uniformly magnetized sphere slides without friction along the surface of a second, identical sphere that is held fixed in space, subject to the magnetic force and torque of the fixed sphere and the normal force. The free sphere has two stable equilibrium positions and two unstable equilibrium positions. Two small-amplitude oscillatory modes describe the sliding motion of the free sphere near each stable equilibrium, and an unstable oscillatory mode describes the motion near each unstable equilibrium. The three oscillatory modes remain periodic at finite amplitudes, one bifurcating into mixed modes and circumnavigating the free sphere at large energies. For small energies, the free sphere is confined to one of the two discontiguous domains, each surrounding a stable equilibrium position. At large energies, these domains merge and the free sphere may visit both positions. The critical energy at which these domains merge coincides with the cumulation point of an infinite cascade of mixed-mode bifurcations. These findings exploit the equivalence of the force and torque between two uniformly magnetized spheres and the force and torque between two equivalent point dipoles, and offer clues to the rich nonlinear dynamics of this system

Similar Microbial Communities Found on Two Distant Seafloor Basalts.

The oceanic crust forms two thirds of the Earth's surface and hosts a large phylogenetic and functional diversity of microorganisms. While advances have been made in the sedimentary realm, our understanding of the igneous rock portion as a microbial habitat has remained limited. We present the first comparative metagenomic microbial community analysis from ocean floor basalt environments at the Lō'ihi Seamount, Hawai'i, and the East Pacific Rise (EPR; 9°N). Phylogenetic analysis indicates the presence of a total of 43 bacterial and archaeal mono-phyletic groups, dominated by Alpha- and Gammaproteobacteria, as well as Thaumarchaeota. Functional gene analysis suggests that these Thaumarchaeota play an important role in ammonium oxidation on seafloor basalts. In addition to ammonium oxidation, the seafloor basalt habitat reveals a wide spectrum of other metabolic potentials, including CO2 fixation, denitrification, dissimilatory sulfate reduction, and sulfur oxidation. Basalt communities from Lō'ihi and the EPR show considerable metabolic and phylogenetic overlap down to the genus level despite geographic distance and slightly different seafloor basalt mineralogy

Raman Spectroscopic Analysis of Geological and Biogeological Specimens of Relevance to the ExoMars Mission

H.G.M.E., I.H., and R.I. acknowledge the support of the STFC Research Council in the UK ExoMars programme. J.J. and P.V. acknowledge the support of the Grant Agency of the Czech Republic (210/10/0467) and of the Ministry of Education of the Czech Republic (MSM0021620855).Peer reviewedPublisher PD

Periodic Bouncing Modes for Two Uniformly Magnetized Spheres. I. Trajectories

We consider a uniformly magnetized sphere that moves without friction in a plane in response to the field of a second, identical, fixed sphere, making elastic hard-sphere collisions with this sphere. We seek periodic solutions to the associated nonlinear equations of motion. We find closed-form mathematical solutions for small-amplitude modes and use these to characterize and validate our large-amplitude modes, which we find numerically. Our Runge-Kutta integration approach allows us to find 1243 distinct periodic modes with the free sphere located initially at its stable equilibrium position. Each of these modes bifurcates from the finite-amplitude radial bouncing mode with infinitesimal-amplitude angular motion and supports a family of states with increasing amounts of angular motion. These states offer a rich variety of behaviors and beautiful, symmetric trajectories, including states with up to 157 collisions and 580 angular oscillations per period. A vibrant online learning community shares information about building beautiful sculptures from collections of small neodymium magnet spheres, with YouTube tutorial videos attracting over a hundred million views.1,2 These spheres offer engaging hands-on exposure to principles of magnetism and are used both in and out of the classroom to teach principles of mathematics, physics, chemistry, biology, and engineering.3 We showed recently that the forces and torques between two uniformly magnetized spheres are identical to the forces and torques between two point magnetic dipoles. In this paper, we exploit this equivalence to study the conservative nonlinear dynamics of a uniformly magnetized sphere subject to the magnetic forces and torques produced by a second, fixed, uniformly magnetized sphere, assuming frictionless hard-sphere elastic collisions between them. Our search for periodic states uncovers a wide variety of periodic modes, some of which are highly complex and beautiful

Periodic Bouncing Modes for Two Uniformly Magnetized Spheres. II. Scaling

A uniformly magnetized sphere moves without friction in a plane in response to the field of a second, identical, fixed sphere and makes elastic hard-sphere collisions with this sphere. Numerical simulations of the threshold energies and periods of periodic finite-amplitude nonlinear bouncing modes agree with small-amplitude closed-form mathematical results, which are used to identify scaling parameters that govern the entire amplitude range, including power-law scaling at large amplitudes. Scaling parameters are combinations of the bouncing number, the rocking number, the phase, and numerical factors. Discontinuities in the scaling functions are found when viewing the threshold energy and period as separate functions of the scaling parameters, for which large-amplitude scaling exponents are obtained from fits to the data. These discontinuities disappear when the threshold energy is viewed as a function of the threshold period, for which the large-amplitude scaling exponent is obtained analytically and for which scaling applies to both in-phase and out-of-phase modes. The purpose of this work is to investigate the scaling relationships between the threshold energy, the threshold period, the bouncing number, the rocking number, and the phase of 1497 periodic modes found previously for the motion of a uniformly magnetized sphere subject to the field of a second, identical, fixed sphere. This large dataset offers the opportunity to identify scaling relationships to high precision for this highly nonlinear problem. Such scaling relationships recall techniques used in studying phase transitions and fractals and invite the search for universal scaling laws that may also apply to other systems. This work is motivated by our interest in the properties of collections of small neodymium magnet spheres that are used to create beautiful magnetic sculptures and are used both in and out of the classroom to teach principles of mathematics, physics, chemistry, biology, and engineering

Peg Penetration in Three Commercially Important Tasmanian Eucalypt Species

Commercially important species of Tasmanian hardwood timber were immersed in 30% (v/v) polyethylene glycol (PEG) of molecular weights 400, 600, and 1000 and incubated up to seven days at three temperatures (30°C, 45°C, 60°C). Slices obtained from the incubated timber samples were stained with cobalt thiocyanate to indicate the depth of penetration by PEG 400, 600, or 1000 after incubation from two to seven days at the various temperatures. Analysis of the data showed that there was an observable difference in the rate of penetration between each species of eucalypt used in the trial. Incubation time, temperature, and PEG molecular weight were all factors affecting the rate of PEG penetration in a linear fashion and basic density (BD) was the physical property that best supported the trends in this study. This paper is a baseline study that provides the foundation for the quantification and prediction of the movement of PEG into three species of Tasmanian eucalypt timber

Strategic Incapacitation and the Policing of Occupy Wall Street in New York City, 2011

The US national response to the 11 September 2001 terrorist attacks accelerated the adoption and refinement of a new repertoire of protest policing we call ‘strategic incapacitation’ now employed by law enforcement agencies nationwide to police protest demonstrations. The occupation movement which formally began 17 September 2011 was the most significant social movement to utilise transgressive protest tactics in the United States in the last 40 years and posed a substantial challenge to law enforcement agencies. This research seeks to better understand the implementation of strategic incapacitation tactics through a detailed analysis of the policing of the first 2 months of Occupy Wall Street (OWS) protests in New York City. Original data for this study are derived from 2-week-long field observations made in New York City during the first and second month anniversaries of the OWS occupation in Zuccotti Park. These are supplemented by activist interviews, activist accounts posted on OWS websites, Facebook pages and Twitter feeds as well as news reports, official police documents, press releases and interviews with legal observers

Quality of Runoff from Four Northwest Arkansas Pasture Fields Treated with Organic and Inorganic Fertilizer

Long-term land application of animal manures, even at agronomic rates, can promote accumulation of soil phosphorus (P) which can, in turn, contribute to increased P loadings to downstream waters. The objective of this study was to assess the soil and runoff effects of replacing animal manure as a soil amendment with inorganic fertilizer (ammonium nitrate, NH4NO3) on fields that had been treated previously with animal manures. Runoff from two pairs of small fields (0.57 to 1.46 ha) was sampled from September 1991 to April 1994. All fields had been treated previously with animal manures; after runoff monitoring began, one field of each pair received only NH4NO3, while the other of each pair continued to receive animal manure. Both soil and runoff P concentrations exhibited statistically significant decreasing trends over the monitoring period. The results demonstrate the potential for positively influencing runoff quality in a relatively short duration by replacing animal manures with ammonium nitrate for fields already having sufficient soil P

Persistent androgen receptor-mediated transcription in castration-resistant prostate cancer under androgen-deprived conditions

The androgen receptor (AR) is a ligand-inducible transcription factor that mediates androgen action in target tissues. Upon ligand binding, the AR binds to thousands of genomic loci and activates a cell-type specific gene program. Prostate cancer growth and progression depend on androgen-induced AR signaling. Treatment of advanced prostate cancer through medical or surgical castration leads to initial response and durable remission, but resistance inevitably develops. In castration-resistant prostate cancer (CRPC), AR activity remains critical for tumor growth despite androgen deprivation. Although previous studies have focused on ligand-dependent AR signaling, in this study we explore AR function under the androgen-deprived conditions characteristic of CRPC. Our data demonstrate that AR persistently occupies a distinct set of genomic loci after androgen deprivation in CRPC. These androgen-independent AR occupied regions have constitutively open chromatin structures that lack the canonical androgen response element and are independent of FoxA1, a transcription factor involved in ligand-dependent AR targeting. Many AR binding events occur at proximal promoters, which can act as enhancers to augment transcriptional activities of other promoters through DNA looping. We further show that androgen-independent AR binding directs a gene expression program in CRPC, which is necessary for the growth of CRPC after androgen withdrawal