A Feynman integral via higher normal functions

We study the Feynman integral for the three-banana graph defined as the scalar two-point self-energy at three-loop order. The Feynman integral is evaluated for all identical internal masses in two space-time dimensions. Two calculations are given for the Feynman integral; one based on an interpretation of the integral as an inhomogeneous solution of a classical Picard-Fuchs differential equation, and the other using arithmetic algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use the rather special fact that the Feynman integral is a family of regulator periods associated to a family of K3 surfaces. We show that the integral is given by a sum of elliptic trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm value is related to the regulator of a class in the motivic cohomology of the K3 family. We prove a conjecture by David Broadhurst that at a special kinematical point the Feynman integral is given by a critical value of the Hasse-Weil L-function of the K3 surface. This result is shown to be a particular case of Deligne's conjectures relating values of L-functions inside the critical strip to periods.Comment: Latex. 70 pages. 3 figures. v3: minor changes and clarifications. Version to appear in Compositio Mathematic

Prospects for India's cereal supply and demand to 2020:

The possibility of an emerging cereal gap of serious proportions by the year 2020, is a useful illustration of the kind of constructive dialogue IFPRI hopes to encourage. It responds to several quite recent developments, notably the rapid expansion of India's industrial and service sectors since the 1991 structural reforms, the improved prospects for continued growth over the next few decades, and the likelihood of rising per capita incomes that could generate substantially increased demand for livestock products. As demand for livestock products grows, livestock production could increasingly depend on cereals for feed — perhaps as much as 50 million tons by 2020, according to G.S. Bhalla, Peter Hazell, and John Kerr, authors of this 2020 discussion paper on Prospects for Balancing Cereal Needs in India to 2020. These conclusions differ somewhat from other IFPRI studies, which have generally found that growth in demand for livestock products will be lower than the current study. This divergence of views is a useful signal to policymakers to pay careful attention to trends in demand for livestock products in India in the coming years. This study and the rest of IFPRI's 2020 research have consistently pointed to the vital link between agricultural policies and prospects for production growth in the next two decades. (from Forward by Per Pinstrup-Andersen)South Asia, South Asia and Central Asia, Grain Yields India., Food supply India Forecasting., Grain as feed India Forecasting., Consumption (Economics) India., Livestock India.,

Prospects for India's cereal supply and demand to 2020:

The possibility of an emerging cereal gap of serious proportions by the year 2020, is a useful illustration of the kind of constructive dialogue IFPRI hopes to encourage. It responds to several quite recent developments, notably the rapid expansion of India's industrial and service sectors since the 1991 structural reforms, the improved prospects for continued growth over the next few decades, and the likelihood of rising per capita incomes that could generate substantially increased demand for livestock products. As demand for livestock products grows, livestock production could increasingly depend on cereals for feed — perhaps as much as 50 million tons by 2020, according to G.S. Bhalla, Peter Hazell, and John Kerr, authors of this 2020 discussion paper on Prospects for Balancing Cereal Needs in India to 2020. These conclusions differ somewhat from other IFPRI studies, which have generally found that growth in demand for livestock products will be lower than the current study. This divergence of views is a useful signal to policymakers to pay careful attention to trends in demand for livestock products in India in the coming years. This study and the rest of IFPRI's 2020 research have consistently pointed to the vital link between agricultural policies and prospects for production growth in the next two decades. (from Forward by Per Pinstrup-Andersen)Grain Yields India., Food supply India Forecasting., Grain as feed India Forecasting., Consumption (Economics) India., Livestock India.,

X-Ray Observations of Black Widow Pulsars

We describe the first X-ray observations of five short orbital period ($P_B < 1$ day), $\gamma$-ray emitting, binary millisecond pulsars. Four of these, PSRs J0023+0923, J1124$-$3653, J1810+1744, and J2256$-$1024 are `black-widow' pulsars, with degenerate companions of mass $\ll0.1 M_{\odot}$, three of which exhibit radio eclipses. The fifth source, PSR J2215+5135, is an eclipsing `redback' with a near Roche-lobe filling $\sim$0.2 solar mass non-degenerate companion. Data were taken using the \textit{Chandra X-Ray Observatory} and covered a full binary orbit for each pulsar. Two pulsars, PSRs J2215+5135 and J2256$-$1024, show significant orbital variability while PSR J1124$-$3653 shows marginal orbital variability. The lightcurves for these three pulsars have X-ray flux minima coinciding with the phases of the radio eclipses. This phenomenon is consistent with an intrabinary shock emission interpretation for the X-rays. The other two pulsars, PSRs J0023+0923 and J1810+1744, are fainter and do not demonstrate variability at a level we can detect in these data. All five spectra are fit with three separate models: a power-law model, a blackbody model, and a combined model with both power-law and blackbody components. The preferred spectral fits yield power-law indices that range from 1.3 to 3.2 and blackbody temperatures in the hundreds of eV. The spectrum for PSR J2215+5135 shows a significant hard X-ray component, with a large number of counts above 2 keV, which is additional evidence for the presence of intrabinary shock emission and is similar to what has been detected in the low-mass X-ray binary to millisecond pulsar transition object PSR J1023+0038.Comment: 8 pages, 6 figures, 2 tables, submitted to Ap

Peculiar Spin Frequency and Radio Profile Evolution of PSR J1119−-6127 Following Magnetar-like X-ray Bursts

We present the spin frequency and profile evolution of the radio pulsar J1119$-$6127 following magnetar-like X-ray bursts from the system in 2016 July. Using data from the Parkes radio telescope, we observe a smooth and fast spin-down process subsequent to the X-ray bursts resulting in a net change in the pulsar rotational frequency of $\Delta\nu\approx-4\times10^{-4}$\,Hz. During the transition, a net spin-down rate increase of $\Delta\dot\nu\approx-1\times10^{-10}$\,Hz\,s$^{-1}$ is observed, followed by a return of $\dot{\nu}$ to its original value. In addition, the radio pulsations disappeared after the X-ray bursts and reappeared about two weeks later with the flux density at 1.4\,GHz increased by a factor of five. The flux density then decreased and undershot the normal flux density followed by a slow recovery back to normal. The pulsar's integrated profile underwent dramatic and short-term changes in total intensity, polarization and position angle. Despite the complex evolution, we observe correlations between the spin-down rate, pulse profile shape and radio flux density. Strong single pulses have been detected after the X-ray bursts with their energy distributions evolving with time. The peculiar but smooth spin frequency evolution of PSR~J1119$-$6127 accompanied by systematic pulse profile and flux density changes are most likely to be a result of either reconfiguration of the surface magnetic fields or particle winds triggered by the X-ray bursts. The recovery of spin-down rate and pulse profile to normal provides us the best case to study the connection between high magnetic-field pulsars and magnetars.Comment: Accepted for publication in MNRAS on 2018 July 2

Emergence of the Shackleton Range from beneath the Antarctic Ice Sheet due to glacial erosion

This paper explores the long-term evolution of a subglacial fjord landscape in the Shackleton Range, Antarctica. We propose that prolonged ice-sheet erosion across a passive continental margin caused troughs to deepen and lower the surrounding ice-sheet surface, leaving adjacent mountains exposed. Geomorphological evidence suggests a change in the direction of regional ice flow accompanied emergence. Simple calculations suggest that isostatic compensation caused by the deepening of bounding ice-stream troughs lowered the ice-sheet surface relative to the mountains by ~800m. Use of multiple cosmogenic isotopes on bedrock and erratics (26Al, 10Be, 21Ne) provides evidence that overriding of the massif and the deepening of the adjacent troughs occurred earlier than the Quaternary. Perhaps this occurred in the mid-Miocene, as elsewhere in East Antarctica in the McMurdo Dry Valleys and the Lambert basin. The implication is that glacial erosion instigates feedback that can change ice-sheet thickness, extent, and direction of flow. Indeed, as the subglacial troughs evolve over millions of years, they increase topographic relief; and this changes the dynamics of the ice sheet. © 2013 Elsevier B.V

The Distance to the Soft Gamma Repeater SGR 1627-41

We report millimeter observations of the line of sight to the recently discovered Soft Gamma Repeater, SGR 1627-41, which has been tentatively associated with the supernova remnant SNR G337.0-0.1 Among the eight molecular clouds along the line of sight to SGR 1627-41, we show that SNR G337.0-0.1 is probably interacting with one of the most massive giant molecular clouds (GMC) in the Galaxy, at a distance of 11 kpc from the sun. Based on the high extinction to the persistent X-ray counterpart of SGR 1627-41, we present evidence for an association of this new SGR with the SNR G337.0-0.1; they both appear to be located on the near side of the GMC. This is the second SGR located near an extraordinarily massive GMC. We suggest that SGR 1627-41 is a neutron star with a high transverse velocity (~ 1,000 \kms) escaping the young (~ 5,000 years) supernova remnant G337.0-0.1Comment: 17 pages, including 2 figures. Accepted for publication in the Astrophysical Journal Letter

SHORTCUT METHOD OF SOLUTION OF GEODESIC EQUATIONS FOR SCHWARZSCHILD BLACK HOLE

It is shown how the use of the Kerr-Schild coordinate system can greatly simplify the formulation of the geodesic equation of the Schwarzschild solution. An application of this formulation to the numerical computation of the aspect of a non-rotating black hole is presented. The generalization to the case of the Kerr solution is presented too.Comment: 11 pages, 2 PostScript figures (available as uuencoded compressed tar file), uses epsfig.tex). Accepted on February 1995 for publication in Classical and Quantum Gravit