On the origin of the Korteweg-de Vries equation

The Korteweg-de Vries equation has a central place in a model for waves on shallow water and it is an example of the propagation of weakly dispersive and weakly nonlinear waves. Its history spans a period of about sixty years, starting with experiments of Scott Russell in 1834, followed by theoretical investigations of, among others, Lord Rayleigh and Boussinesq in 1871 and, finally, Korteweg and De Vries in 1895. In this essay we compare the work of Boussinesq and Korteweg-de Vries, stressing essential differences and some interesting connections. Although there exist a number of articles, reviewing the origin and birth of the Korteweg-de Vries equations, connections and differences, not generally known, are reported.Comment: minor corrections; 25 pages, 3 figure

Inclusive Quasi-Elastic Charged-Current Neutrino-Nucleus Reactions

The Quasi-Elastic (QE) contribution of the nuclear inclusive electron scattering model developed in Nucl. Phys. A627 (1997) 543 is extended to the study of electroweak Charged Current (CC) induced nuclear reactions, at intermediate energies of interest for future neutrino oscillation experiments. The model accounts for, among other nuclear effects, long range nuclear (RPA) correlations, Final State Interaction (FSI) and Coulomb corrections. Predictions for the inclusive muon capture in $^{12}$C and the reaction $^{12}$C $(\nu_\mu,\mu^-)X$ near threshold are also given. RPA correlations are shown to play a crucial role and their inclusion leads to one of the best existing simultaneous description of both processes, with accuracies of the order of 10-15% per cent for the muon capture rate and even better for the LSND measurement.Comment: 31 pages and 14 figures, accepted for publication as a regular article in Physical Review

Nutrient partitioning and response to insulin challenge at different planes of nutrition during lactation in goats of high vs. low milk production potential

The aim of this experiment was to determine the effect of genetic selection for milk production on nutrient partitioning at a high vs. a low plane of nutrition. Twelve Indigenous goat does and eight Saanen x Indigenous crossbred does were allocated to either a basal diet formulated to provide energy for maintenance or the basal diet supplemented with maize so as to maintain a plasma glucose concentration of 3.5 mmol/l throughout lactation. Milk yield was not reduced by the low plane of nutrition in either genotype. The sustained rate of milk production at the low level of nutrition was achieved by increased mobilisation of endogenous nutrients from body reserves, evidenced as a greater loss of body mass at the low plane of nutrition in both breeds. The Saanen crossbred genotype, which produced twice as much milk as the Indigenous genotype, lost 19% of initial mass by week 10 of lactation, whereas mass losses in the indigenous goat never exceeded 7%, with the result that repletion of initial (week one) mass was achieved by week six of lactation. Plasma glucose concentrations were depressed to a smaller extent by insulin in the Saanen crossbred than in the Indigenous goat at weeks 3, 7 and 11 of lactation. Although there was evidence for a genotype x nutrition interaction during early lactation, this did not persist throughout lactation. The majority of data derived from this study indicates that the two genotypes reacted in a similar manner to plane of nutrition, with the main differences between milk yield potential being occasioned by differences in the extent of mobilisation of endogenous body reserves mediated by differences in insulin sensitivity. (South African Journal of Animal Science, 2000, 30(3): 178-185

The yellow hypergiants HR 8752 and rho Cassiopeiae near the evolutionary border of instability

High-resolution near-ultraviolet spectra of the yellow hypergiants HR 8752 and rho Cassiopeiae indicate high effective temperatures placing both stars near the T_eff border of the ``yellow evolutionary void''. At present, the temperature of HR 8752 is higher than ever. For this star we found Teff=7900+-200 K, whereas rho Cassiopeiae has Teff=7300+-200 K. Both, HR 8752 and rho Cassiopeiae have developed strong stellar winds with Vinf ~ 120 km/s and Vinf ~ 100 km/s, respectively. For HR 8752 we estimate an upper limit for the spherically symmetric mass-loss of 6.7X10^{-6}M_solar/yr. Over the past decades two yellow hypergiants appear to have approached an evolutionary phase, which has never been observed before. We present the first spectroscopic evidence of the blueward motion of a cool super/hypergiant on the HR diagram.Comment: 13 pages including 3 figures. Accepted for publication in ApJ Letter

Crossing the `Yellow Void' -- Spatially Resolved Spectroscopy of the Post- Red Supergiant IRC+10420 and Its Circumstellar Ejecta

IRC +10420 is one of the extreme hypergiant stars that define the empirical upper luminosity boundary in the HR diagram. During their post--RSG evolution, these massive stars enter a temperature range (6000-9000 K) of increased dynamical instability, high mass loss, and increasing opacity, a semi--forbidden region, that de Jager and his collaborators have called the `yellow void'. We report HST/STIS spatially resolved spectroscopy of IRC +10420 and its reflection nebula with some surprising results. Long slit spectroscopy of the reflected spectrum allows us to effectively view the star from different directions. Measurements of the double--peaked Halpha emission profile show a uniform outflow of gas in a nearly spherical distribution, contrary to previous models with an equatorial disk or bipolar outflow. Based on the temperature and mass loss rate estimates that are usually quoted for this object, the wind is optically thick to the continuum at some and possibly all wavelengths. Consequently the observed variations in apparent spectral type and inferred temperature are changes in the wind and do not necessarily mean that the underlying stellar radius and interior structure are evolving on such a short timescale. To explain the evidence for simultaneous outflow and infall of material near the star, we propose a `rain' model in which blobs of gas condense in regions of lowered opacity outside the dense wind. With the apparent warming of its wind, the recent appearance of strong emission, and a decline in the mass loss rate, IRC +10420 may be about to shed its opaque wind, cross the `yellow void', and emerge as a hotter star.Comment: To appear in the Astronomical Journal, August 200

Unidentified Galactic High-Energy Sources as Ancient Pulsar Wind Nebulae in the light of new high energy observations and the new code

In a Pulsar Wind Nebula (PWN), the lifetime of inverse Compton (IC) emitting electrons exceeds the lifetime of its progenitor pulsar (as well as its shell-type remnant), but it also exceeds the age of those that emit via synchrotron radiation. Therefore, during its evolution, the PWN can remain bright in IC so that its GeV-TeV gamma-ray flux remains high for timescales much larger (for 10^5 - 10^6 yrs) than the pulsar lifetime and the X-ray PWN lifetime. In this scenario, the magnetic field in the cavity induced by the wind of the progenitor star plays a crucial role. This scenario is in line with the discovery of several unidentified or "dark" sources in the TeV gamma-ray band without X-ray counterparts; and it is also finding confirmation in the recent discoveries at GeV gamma rays. Moreover, these consequences could be also important for reinterpreting the detection of starburst galaxies in the TeV gamma-ray band when considering a leptonic origin of the gamma-ray signal. Both theoretical aspects and their observational proofs will be discussed, as well as the first results of our new modeling code.Comment: Proceedings of the 5th International Symposium on High-Energy Gamma-Ray Astronomy (Gamma2012

Pulsational instability of yellow hypergiants

Instability of population I (X=0.7, Y=0.02) massive stars against radial oscillations during the post-main sequence gravitational contraction of the helium core is investigated. Initial stellar masses are in the range from 65M_\odot to 90M_\odot. In hydrodynamic computations of self-exciting stellar oscillations we assumed that energy transfer in the envelope of the pulsating star is due to radiative heat conduction and convection. The convective heat transfer was treated in the framework of the theory of time-dependent turbulent convection. During evolutionary expansion of outer layers after hydrogen exhaustion in the stellar core the star is shown to be unstable against radial oscillations while its effective temperature is Teff > 6700K for Mzams=65M_\odot and Teff > 7200K for mzams=90M_\odot. Pulsational instability is due to the \kappa-mechanism in helium ionization zones and at lower effective temperature oscillations decay because of significantly increasing convection. The upper limit of the period of radial pulsations on this stage of evolution does not exceed 200 day. Radial oscillations of the hypergiant resume during evolutionary contraction of outer layers when the effective temperature is Teff > 7300K for Mzams=65M_\odot and Teff > 7600K for Mzams=90M_\odot. Initially radial oscillations are due to instability of the first overtone and transition to fundamental mode pulsations takes place at higher effective temperatures (Teff > 7700K for Mzams=65M_\odot and Teff > 8200K for Mzams=90M_\odot). The upper limit of the period of radial oscillations of evolving blueward yellow hypergiants does not exceed 130 day. Thus, yellow hypergiants are stable against radial stellar pulsations during the major part of their evolutionary stage.Comment: 20 pages, 7 gigures. Accepted for publication in Astronomy Letter