A Lagrange-D'Alembert formulation of the equations of motion of a helicopter carrying an externally suspended load

The exact nonlinear equations of motion are derived for a helicopter with an extenal load suspended by fore and aft, rigid-link cables. Lagrange's form of D'Alembert's principle is used. Ten degrees of freedom are necessary to represent the motion of this system in an inertial reference frame: six for the helicopter relative to inertial space and four for the load relative to the helicopter

Detailed state model of CaMKII activation and autophosphorylation

By combining biochemical experiments with computer modelling of biochemical reactions we elucidated some of the currently unresolved aspects of calcium-calmodulin-dependent protein kinase II (CaMKII) activation and autophosphorylation that might be relevant for its physiological function and provided a model that incorporates in detail the mechanism of CaMKII activation and autophosphorylation at T286 that is based on experimentally determined binding constants and phosphorylation rates. To this end, we developed a detailed state model of CaMKII activation and autophosphorylation based on the currently available literature, and constrained it with data from CaMKII autophosphorylation essays. Our model takes exact phosphorylation patterns of CaMKII holoenzymes into account, and is valid at physiologically relevant conditions where the concentrations of calcium and calmodulin are not saturating. Our results strongly suggest that even when bound to less than fully calcium-bound calmodulin, CaMKII is in the active state, and indicate that the autophosphorylation of T286 by an active non-phosphorylated CaMKII subunit is significantly faster than by an autophosphorylated CaMKII subunit. These results imply that CaMKII can be efficiently activated at significantly lower calcium concentrations than previously thought, which may explain how CaMKII gets activated at calcium concentrations existing at synapses in vivo. We also investigated the significance of CaMKII holoenzyme structure on CaMKII autophosphorylation and obtained estimates of previously unknown binding constants

Emotional response inhibition is greater in older than younger adults

Emotional information rapidly captures our attention and also often invokes automatic response tendencies, whereby positive information motivates approach, while negative information encourages avoidance. However, many circumstances require the need to override or inhibit these automatic responses. Control over responses to emotional information remains largely intact in late life, in spite of age-related declines in cognitive control and inhibition of responses to non-emotional information. The goal of this behavioral study was to understand how the aging process influences emotional response inhibition for positive and negative information in older adults. We examined emotional response inhibition in 36 healthy older adults (ages 60–89) and 44 younger adults (ages 18–22) using an emotional Go/No-Go task presenting happy (positive), fearful (negative), and neutral faces. In both younger and older adults, happy faces produced more approach-related behavior (i.e., fewer misses), while fearful faces produced more avoidance-related behavior, in keeping with theories of approach/avoidance-motivated responses. Calculation of speed/accuracy trade-offs between response times and false alarm rates revealed that younger and older adults both favored speed at the expense of accuracy, most robustly within blocks with fearful faces. However, there was no indication that the strength of the speed/accuracy trade-off differed between younger and older adults. The key finding was that although younger adults were faster to respond to all types of faces, older adults had greater emotional response inhibition (i.e., fewer false alarms). Moreover, younger adults were particularly prone to false alarms for happy faces. This is the first study to directly test effects of aging on emotional response inhibition. Complementing previous literature in the domains of attention and memory, these results provide new evidence that in the domain of response inhibition older adults may more effectively employ emotion regulatory ability, albeit on a slower time course, compared to younger adults. Older adults’ enhanced adaptive emotion regulation strategies may facilitate resistance to emotional distraction. The present study extends the literature of emotional response inhibition in younger adulthood into late life, and in doing so further elucidates how cognitive aging interacts with affective control processes

The Early Evolution of Primordial Pair-Instability Supernovae

The observational signatures of the first cosmic explosions and their chemical imprint on second-generation stars both crucially depend on how heavy elements mix within the star at the earliest stages of the blast. We present numerical simulations of the early evolution of Population III pair-instability supernovae with the new adaptive mesh refinement code CASTRO. In stark contrast to 15 - 40 Msun core-collapse primordial supernovae, we find no mixing in most 150 - 250 Msun pair-instability supernovae out to times well after breakout from the surface of the star. This may be the key to determining the mass of the progenitor of a primeval supernova, because vigorous mixing will cause emission lines from heavy metals such as Fe and Ni to appear much sooner in the light curves of core-collapse supernovae than in those of pair-instability explosions. Our results also imply that unlike low-mass Pop III supernovae, whose collective metal yields can be directly compared to the chemical abundances of extremely metal-poor stars, further detailed numerical simulations will be required to determine the nucleosynthetic imprint of very massive Pop III stars on their direct descendants.Comment: submitted to ApJ, comments welcom

Viable tax constitutions

Taxation is only sustainable if the general public complies with it. This observation is uncontroversial with tax practitioners but has been ignored by the public finance tradition, which has interpreted tax constitutions as binding contracts by which the power to tax is irretrievably conferred by individuals to government, which can then levy any tax it chooses. However, in the absence of an outside party enforcing contracts between members of a group, no arrangement within groups can be considered to be a binding contract, and therefore the power of tax must be sanctioned by individuals on an ongoing basis. In this paper we offer, for the first time, a theoretical analysis of this fundamental compliance problem associated with taxation, obtaining predictions that in some cases point to a re-interptretation of the theoretical constructions of the public finance tradition while in others call them into question

The Radio Signatures of the First Supernovae

Primordial stars are key to primeval structure formation as the first stellar components of primeval galaxies, the sources of cosmic chemical enrichment and likely cosmic reionization, and they possibly gave rise to the supermassive black holes residing at the centres of galaxies today. While the direct detection of individual Pop III stars will likely remain beyond reach for decades to come, we show their supernova remnants may soon be detectable in the radio. We calculate radio synchrotron signatures between 0.5 - 35 GHz from hydrodynamical computations of the supernova remnants of Pop III stars in minihaloes. We find that hypernovae yield the brightest systems, with observed radio fluxes as high as 1 - 10 muJy. Less energetic Type II supernovae yield remnants about a factor of 30 dimmer and pair-instability supernova remnants are dimmer by a factor of more than 10,000. Because of the high gas densities of the progenitor environments, synchrotron losses severely limit the maximum emission frequencies, producing a distinctive peaked radio spectrum distinguishable from normal galactic supernova remnant spectra. Hypernovae radio remnants should be detectable by existing radio facilities like eVLA and eMERLIN while Type II supernova remnants will require the Square Kilometre Array. The number counts of hypernova remnants at z > 20 with fluxes above 1 muJy are expected to be one per hundred square degree field, increasing to a few per square degree if they form down to z = 10. The detection of a z > 20 Type II supernova remnant brighter than 1 nJy would require a 100 - 200 square degree field, although only a 1 - 2 square degree field for those forming down to z = 10. Hypernova and Type II supernova remnants are easily separated from one another by their light curves, which will enable future surveys to use them to constrain the initial mass function of Pop III stars.Comment: 12 pages, 9 figures; major revision; to appear in MNRA

The Birth of a Galaxy: Primordial Metal Enrichment and Stellar Populations

By definition, Population III stars are metal-free, and their protostellar collapse is driven by molecular hydrogen cooling in the gas-phase, leading to large characteristic masses. Population II stars with lower characteristic masses form when the star-forming gas reaches a critical metallicity of 10^{-6} - 10^{-3.5} Z_\odot. We present an adaptive mesh refinement radiation hydrodynamics simulation that follows the transition from Population III to II star formation. The maximum spatial resolution of 1 comoving parsec allows for individual molecular clouds to be well-resolved and their stellar associations to be studied in detail. We model stellar radiative feedback with adaptive ray tracing. A top-heavy initial mass function for the Population III stars is considered, resulting in a plausible distribution of pair-instability supernovae and associated metal enrichment. We find that the gas fraction recovers from 5 percent to nearly the cosmic fraction in halos with merger histories rich in halos above 10^7 solar masses. A single pair-instability supernova is sufficient to enrich the host halo to a metallicity floor of 10^{-3} Z_\odot and to transition to Population II star formation. This provides a natural explanation for the observed floor on damped Lyman alpha (DLA) systems metallicities reported in the literature, which is of this order. We find that stellar metallicities do not necessarily trace stellar ages, as mergers of halos with established stellar populations can create superpositions of t-Z evolutionary tracks. A bimodal metallicity distribution is created after a starburst occurs when the halo can cool efficiently through atomic line cooling.Comment: 11 pages, 7 figures; replaced with accepted version to ApJ; additional movies and images can be found at http://www.astro.princeton.edu/~jwise/research/GalaxyBirth.htm

The Formation and Fragmentation of Disks around Primordial Protostars

The very first stars to form in the Universe heralded an end to the cosmic dark ages and introduced new physical processes that shaped early cosmic evolution. Until now, it was thought that these stars lived short, solitary lives, with only one extremely massive star, or possibly a very wide binary system, forming in each dark matter minihalo. Here we describe numerical simulations that show that these stars were, to the contrary, often members of tight multiple systems. Our results show that the disks that formed around the first young stars were unstable to gravitational fragmentation, possibly producing small binary and higher-order systems that had separations as small as the distance between the Earth and the Sun.Comment: This manuscript has been accepted for publication in Science. This version has not undergone final editing. Please refer to the complete version of record at http://www.sciencemag.org

Formation and evolution of primordial protostellar systems

We investigate the formation of the first stars at the end of the cosmic dark ages with a suite of three-dimensional, moving mesh simulations that directly resolve the collapse of the gas beyond the formation of the first protostar at the centre of a dark matter minihalo. The simulations cover more than 25 orders of magnitude in density and have a maximum spatial resolution of 0.05 R_sun, which extends well below the radius of individual protostars and captures their interaction with the surrounding gas. In analogy to previous studies that employed sink particles, we find that the Keplerian disc around the primary protostar fragments into a number of secondary protostars, which is facilitated by H2 collisional dissociation cooling and collision-induced emission. The further evolution of the protostellar system is characterized by strong gravitational torques that transfer angular momentum between the secondary protostars formed in the disc and the surrounding gas. This leads to the migration of about half of the secondary protostars to the centre of the cloud in a free-fall time, where they merge with the primary protostar and enhance its growth to about five times the mass of the second most massive protostar. By the same token, a fraction of the protostars obtain angular momentum from other protostars via N-body interactions and migrate to higher orbits. On average, only every third protostar survives until the end of the simulation. However, the number of protostars present at any given time increases monotonically, suggesting that the system will continue to grow beyond the limited period of time simulated here.Comment: 19 pages, 13 figures, accepted for publication in MNRAS, movies of the simulations may be downloaded at http://www.mpa-garching.mpg.de/~tgrei