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

Probing the Nature of the Vela X Cocoon

Vela X is a pulsar wind nebula (PWN) associated with the active pulsar B0833-45 and contained within the Vela supernova remnant (SNR). A collimated X-ray filament ("cocoon") extends south-southwest from the pulsar to the center of Vela X. VLA observations uncovered radio emission coincident with the eastern edge of the cocoon and H.E.S.S. has detected TeV $\gamma$-ray emission from this region as well. Using XMM-\textit{Newton} archival data, covering the southern portion of this feature, we analyze the X-ray properties of the cocoon. The X-ray data are best fit by an absorbed nonequilibrium plasma model with a powerlaw component. Our analysis of the thermal emission shows enhanced abundances of O, Ne, and Mg within the cocoon, indicating the presence of ejecta-rich material from the propagation of the SNR reverse shock, consistent with Vela X being a disrupted PWN. We investigate the physical processes that excite the electrons in the PWN to emit in the radio, X-ray and $\gamma$-ray bands. The radio and non-thermal X-ray emission can be explained by synchrotron emission. We model the $\gamma$-ray emission by Inverse Compton scattering of electrons off of cosmic microwave background (CMB) photons. We use a 3-component broken power law to model the synchrotron emission, finding an intrinsic break in the electron spectrum at $\sim5 \times 10^{6}$ keV and a cooling break at $\sim$ 5.5 $\times 10^{10}$ keV. This cooling break along with a magnetic field strength of 5 $\times 10^{-6}$ G indicate that the synchrotron break occurs at $\sim$1 keV.Comment: accepted for publication to ApJ

Periodic Modulations in an X-ray Flare from Sagittarius A*

We present the highly significant detection of a quasi-periodic flux modulation with a period of 22.2 min seen in the X-ray data of the Sgr A* flare of 2004 August 31. This flaring event, which lasted a total of about three hours, was detected simultaneously by EPIC on XMM-Newton and the NICMOS near-infrared camera on the HST. Given the inherent difficulty in, and the lack of readily available methods for quantifying the probability of a periodic signal detected over only several cycles in a data set where red noise can be important, we developed a general method for quantifying the likelihood that such a modulation is indeed intrinsic to the source and does not arise from background fluctuations. We here describe this Monte Carlo based method, and discuss the results obtained by its application to a other XMM-Newton data sets. Under the simplest hypothesis that we witnessed a transient event that evolved, peaked and decayed near the marginally stable orbit of the supermassive black hole, this result implies that for a mass of 3.5 x 10^{6} Msun, the central object must have an angular momentum corresponding to a spin parameter of a=0.22.Comment: 4 pages, 6 figures, submitted to ApJ

A Cosmic Ray Positron Anisotropy due to Two Middle-Aged, Nearby Pulsars?

Geminga and B0656+14 are the closest pulsars with characteristic ages in the ran ge of 100 kyr to 1 Myr. They both have spindown powers of the order 3e34 erg/s at present. The winds of these pulsars had most probably powered pulsar wind nebulae (PWNe) that broke up less than about 100 kyr after the birth of the pulsars. Assuming that leptonic particles accelerated by the pulsars were confined in th e PWNe and were released into the interstellar medium (ISM) on breakup of the PW Ne, we show that, depending on the pulsar parameters, both pulsars make a non-ne gligible contribution to the local cosmic ray (CR) positron spectrum, and they m ay be the main contributors above several GeV. The relatively small angular dist ance between Geminga and B0656+14 thus implies an anisotropy in the local CR po sitron flux at these energies. We calculate the contribution of these pulsars to the locally observed CR electr on and positron spectra depending on the pulsar birth period and the magnitude o f the local CR diffusion coefficient. We further give an estimate of the expecte d anisotropy in the local CR positron flux. Our calculations show that within the framework of our model, the local CR posit ron spectrum imposes constraints on pulsar parameters for Geminga and B0656+14, notably the pulsar period at birth, and also the local interstellar diffusion co efficient for CR leptons.Comment: accepted for publication in ApJ

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

Drivers of land use change and household determinants of sustainability in smallholder farming systems of Eastern Uganda

Smallholder farming systems in sub-Saharan Africa have undergone changes in land use, productivity and sustainability. Understanding of the drivers that have led to changes in land use in these systems and factors that influence the systems’ sustainability is useful to guide appropriate targeting of intervention strategies for improvement. We studied low input Teso farming systems in eastern Uganda from 1960 to 2001 in a place-based analysis combined with a comparative analysis of similar low input systems in southern Mali. This study showed that policy-institutional factors next to population growth have driven land use changes in the Teso systems, and that nutrient balances of farm households are useful indicators to identify their sustainability. During the period of analysis, the fraction of land under cultivation increased from 46 to 78%, and communal grazing lands nearly completely disappeared. Cropping diversified over time; cassava overtook cotton and millet in importance, and rice emerged as an alternative cash crop. Impacts of political instability, such as the collapse of cotton marketing and land management institutions, of communal labour arrangements and aggravation of cattle rustling were linked to the changes. Crop productivity in the farming systems is poor and nutrient balances differed between farm types. Balances of N, P and K were all positive for larger farms (LF) that had more cattle and derived a larger proportion of their income from off-farm activities, whereas on the medium farms (MF), small farms with cattle (SF1) and without cattle (SF2) balances were mostly negative. Sustainability of the farming system is driven by livestock, crop production, labour and access to off-farm income. Building private public partnerships around market-oriented crops can be an entry point for encouraging investment in use of external nutrient inputs to boost productivity in such African farming systems. However, intervention strategies should recognise the diversity and heterogeneity between farms to ensure efficient use of these external inputs

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

Impacts of heterogeneity in soil fertility on legume-finger millet productivity, farmers ' targeting and economic benefits

Targeting of integrated management practices for smallholder agriculture in sub-Saharan Africa is necessary due to the great heterogeneity in soil fertility. Experiments were conducted to evaluate the impacts of landscape position and field type on the biomass yield, N accumulation and N2-fixation by six legumes (cowpea, green gram, groundnut, mucuna, pigeonpea and soyabean) established with and without P during the short rain season of 2005. Residual effects of the legumes on the productivity of finger millet were assessed for two subsequent seasons in 2006 in two villages in Pallisa district, eastern Uganda. Legume biomass and N accumulation differed significantly (P <0.001) between villages, landscape position, field type and P application rate. Mucuna accumulated the most biomass (4.8–10.9 Mg ha-1) and groundnut the least (1.0–3.4 Mg ha-1) on both good and poor fields in the upper and middle landscape positions. N accumulation and amounts of N2-fixed by the legumes followed a similar trend as biomass, and was increased significantly by application of P. Grain yields of finger millet were significantly (P <0.001) higher in the first season after incorporation of legume biomass than in the second season after incorporation. Finger millet also produced significantly more grain in good fields (0.62–2.15 Mg ha-1) compared with poor fields (0.29–1.49 Mg ha-1) across the two villages. Participatory evaluation of options showed that farmers preferred growing groundnut and were not interested in growing pigeonpea and mucuna. They preferentially targeted grain legumes to good fields except for mucuna and pigeonpea which they said they would grow only in poor fields. Benefit-cost ratios indicated that legume-millet rotations without P application were only profitable on good fields in both villages. We suggest that green gram, cowpea and soyabean without P can be targeted to good fields on both upper and middle landscape positions in both villages. All legumes grown with P fertiliser on poor fields provided larger benefits than continuous cropping of millet

Archiving South African digital research data: How ready are we?

Abstract Digital data archiving and research data management have become increasingly important for institutions in South Africa, particularly after the announcement by the National Research Foundation, one of the principal South African academic research funders, recommending these actions for the research that they fund. A case study undertaken during the latter half of 2014, among the biological sciences researchers at a South African university, explored the state of data management and archiving at this institution and the readiness of researchers to engage with sharing their digital research data through repositories. It was found that while some researchers were already engaged with digital data archiving in repositories, neither researchers nor the university had implemented systematic research data management