Eudoxus, Callippus and the Astronomy of the Timaeus

Whether the astronomy of the Timaeus had any significant influence on Eudoxus' theory of homocentric spheres is a matter of contention. Some commentators deny any such influence.1 Here I argue for a view of the Timaeus' astronomy, and of Eudoxus' astronomy, whereby Eudoxus' work was as much a natural development of the Timaeus as Callippus' work was of Eudoxus. I also argue for an important interpretative principle. This is that Plato, Eudoxus and Callippus could not account for all the phenomena they were aware of, and were aware of that fact. If the Timaeus presents a prototype, Eudoxus can then be seen to develop this astronomy, making the model more sophisticated and complex while staying within the cosmological principles, and attempting to solve the key problems which were left unsolved by the Timaeus model. He does this in much the same way as Callippus made Eudoxus' model more complex and sophisticated, and attempted to solve the leading problems in that model. I also consider some further objections to a significant interaction between Plato and Eudoxus, based on supposed philosophical differences, dating, and the evidence of later commentators. I conclude that these provide no significant obstacle to considering there to be a fruitful liaison between Plato and Eudoxus

Second-order structure function analysis of scatterometer winds over the Tropical Pacific

22 pages, 16 figures, 1 tableKolmogorov second-order structure functions are used to quantify and compare the small-scale information contained in near-surface ocean wind products derived from measurements by ASCAT on MetOp-A and SeaWinds on QuikSCAT. Two ASCAT and three SeaWinds products are compared in nine regions (classified as rainy or dry) in the tropical Pacific between 10°S and 10°N and 140° and 260°E for the period November 2008 to October 2009. Monthly and regionally averaged longitudinal and transverse structure functions are calculated using along-track samples. To ease the analysis, the following quantities were estimated for the scale range 50 to 300 km and used to intercompare the wind products: (i) structure function slopes, (ii) turbulent kinetic energies (TKE), and (iii) vorticity-to-divergence ratios. All wind products are in good qualitative agreement, but also have important differences. Structure function slopes and TKE differ per wind product, but also show a common variation over time and space. Independent of wind product, longitudinal slopes decrease when sea surface temperature exceeds the threshold for onset of deep convection (about 28°C). In rainy areas and in dry regions during rainy periods, ASCAT has larger divergent TKE than SeaWinds, while SeaWinds has larger vortical TKE than ASCAT. Differences between SeaWinds and ASCAT vortical TKE and vorticity-to-divergence ratios for the convectively active months of each region are large. © 2014. American Geophysical Union. All Rights ReservedThe ASCAT-12.5 and ASCAT-25 data used in this work can be ordered online from the EUMETSAT Data Centre (www.eumetsat.int) as SAF type data in BUFR or NetCDF format. They can also be ordered from PO.DAAC (podaac.jpl.nasa.gov) in NetCDF format only. The SeaWinds-NOAA and QuikSCAT-12.5 data are also available from PO.DAAC. The SeaWinds-KNMI data are available from the KNMI archive upon an email request to [email protected]. Rain-rates and sea surface temperatures were obtained from the Tropical Rainfall Measuring Mission's (TRMM) Microwave Imager (TMI) archive at the Remote Sensing Systems web site (www.ssmi.com). SeaWinds Radiometer (SRAD) rain-rates were obtained from the QuikSCAT 25 km L2B science data product that is available from PO.DAAC. This work has been funded by EUMETSAT in the context of the Numerical Weather Prediction Satellite Applications Facility (NWP SAF). The contribution of GPK has been supported by EUMETSAT as part of the SAF Visiting Scientists programmePeer Reviewe

Resilience of riverbed vegetation to uprooting by flow

Riverine ecosystem biodiversity is largely maintained by ecogeomorphic processes including vegetation renewal via uprooting and recovery times to flow disturbances. Plant roots thus heavily contribute to engineering resilience to perturbation of such ecosystems. We show that vegetation uprooting by flow occurs as a fatigue-like mechanism, which statistically requires a given exposure time to imposed riverbed flow erosion rates before the plant collapses. We formulate a physically based stochastic model for the actual plant rooting depth and the time-to-uprooting, which allows us to define plant resilience to uprooting for generic time-dependent flow erosion dynamics. This theory shows that plant resilience to uprooting depends on the time-to-uprooting and that root mechanical anchoring acts as a process memory stored within the plant–soil system. The model is validated against measured data of time-to-uprooting of Avena sativa seedlings with various root lengths under different flow conditions. This allows for assessing the natural variance of the uprooting-by-flow process and to compute the prediction entropy, which quantifies the relative importance of the deterministic and the random components affecting the process

Field Theory for a Deuteron Quantum Liquid

Based on general symmetry principles we study an effective Lagrangian for a neutral system of condensed spin-1 deuteron nuclei and electrons, at greater-than-atomic but less-than-nuclear densities. We expect such matter to be present in thin layers within certain low-mass brown dwarfs. It may also be produced in future shock-wave-compression experiments as an effective fuel for laser induced nuclear fusion. We find a background solution of the effective theory describing a net spin zero condensate of deuterons with their spins aligned and anti-aligned in a certain spontaneously emerged preferred direction. The spectrum of low energy collective excitations contains two spin waves with linear dispersions -- like in antiferromagnets -- as well as gapped longitudinal and transverse modes related to the Meissner effect -- like in superconductors. We show that counting of the Nambu-Goldstone modes of spontaneously broken internal and space-time symmetries obeys, in a nontrivial way, the rules of the Goldstone theorem for Lorentz non-invariant systems. We discuss thermodynamic properties of the condensate, and its potential manifestation in the low-mass brown dwarfs.Comment: 19 LaTeX pages; v2: 2 refs added, JHEP versio

The formation of voids in a universe with cold dark matter and a cosmological constant

A spherical Lagrangian hydrodynamical code has been written to study the formation of cosmological structures in the early Universe. In this code we take into account the presence of collisionless non-baryonic cold dark matter (CDM), the cosmological constant and a series of physical processes present during and after the recombination era, such as photon drag resulting from the cosmic background radiation and hydrogen molecular production. We follow the evolution of the structure since the recombination era until the present epoch. As an application of this code we study the formation of voids starting from negative density perturbations which evolved during and after the recombination era. We analyse a set of COBE-normalized models, using different spectra to see their influence on the formation of voids. Our results show that large voids with diameters ranging from 10h^{-1} Mpc up to 50h^{-1} Mpc can be formed in a universe model dominated by the cosmological constant (\Omega_\Lambda ~ 0.8). This particular scenario is capable of forming large and deep empty regions (with density contrasts \delta < -0.6). Our results also show that the physical processes acting on the baryonic matter produce a transition region where the radius of the dark matter component is greater than the baryonic void radius. The thickness of this transition region ranges from about tens of kiloparsecs up to a few megaparsecs, depending on the spectrum considered. Putative objects formed near voids and within the transition region would have a different amount of baryonic/dark matter when compared with \Omega_b/\Omega_d. If one were to use these galaxies to determine, by dynamical effects or other techniques, the quantity of dark matter present in the Universe, the result obtained would be only local and not representative of the Universe as a whole.Comment: MNRAS (in press); 9 pages, no figure

Magic, Curses and Healing

Magic and curses played a strong role in Greek popular culture. As I shall explain below, many Greeks believed themselves to live in an “extended world” where it was possible to have relations with both the living and the dead by magical means. Diseases could be caused by the gods or magical means and were susceptible to magical treatment. On one view this belief in magic was dispelled by the Presocratic philosophers, though, as we shall see, matters were not quite so straightforward. Here we shall clarify the nature and context of Greek and Roman magic and explore some of the issues involved in its study

The Creation and Destruction of the World

Here we explore various ideas about the creation and destruction of the world, including theories posited by the Presocratics, Plato, Aristotle, Epicureans, Stoics, and the Neoplatonists

Folate catabolites in spot urine as non-invasive biomarkers of folate status during habitual intake and folic acid supplementation.

Folate status, as reflected by red blood cell (RCF) and plasma folates (PF), is related to health and disease risk. Folate degradation products para-aminobenzoylglutamate (pABG) and para-acetamidobenzoylglutamate (apABG) in 24 hour urine have recently been shown to correlate with blood folate. Since blood sampling and collection of 24 hour urine are cumbersome, we investigated whether the determination of urinary folate catabolites in fasted spot urine is a suitable non-invasive biomarker for folate status in subjects before and during folic acid supplementation. Immediate effects of oral folic acid bolus intake on urinary folate catabolites were assessed in a short-term pre-study. In the main study we included 53 healthy men. Of these, 29 were selected for a 12 week folic acid supplementation (400 µg). Blood, 24 hour and spot urine were collected at baseline and after 6 and 12 weeks and PF, RCF, urinary apABG and pABG were determined. Intake of a 400 µg folic acid bolus resulted in immediate increase of urinary catabolites. In the main study pABG and apABG concentrations in spot urine correlated well with their excretion in 24 hour urine. In healthy men consuming habitual diet, pABG showed closer correlation with PF (rs = 0.676) and RCF (rs = 0.649) than apABG (rs = 0.264, ns and 0.543). Supplementation led to significantly increased folate in plasma and red cells as well as elevated urinary folate catabolites, while only pABG correlated significantly with PF (rs = 0.574) after 12 weeks. Quantification of folate catabolites in fasted spot urine seems suitable as a non-invasive alternative to blood or 24 hour urine analysis for evaluation of folate status in populations consuming habitual diet. In non-steady-state conditions (folic acid supplementation) correlations between folate marker (RCF, PF, urinary catabolites) decrease due to differing kinetics

Superconducting nanowire photon number resolving detector at telecom wavelength

The optical-to-electrical conversion, which is the basis of optical detectors, can be linear or nonlinear. When high sensitivities are needed single-photon detectors (SPDs) are used, which operate in a strongly nonlinear mode, their response being independent of the photon number. Nevertheless, photon-number resolving (PNR) detectors are needed, particularly in quantum optics, where n-photon states are routinely produced. In quantum communication, the PNR functionality is key to many protocols for establishing, swapping and measuring entanglement, and can be used to detect photon-number-splitting attacks. A linear detector with single-photon sensitivity can also be used for measuring a temporal waveform at extremely low light levels, e.g. in long-distance optical communications, fluorescence spectroscopy, optical time-domain reflectometry. We demonstrate here a PNR detector based on parallel superconducting nanowires and capable of counting up to 4 photons at telecommunication wavelengths, with ultralow dark count rate and high counting frequency