Magnetar powered GRBs: Explaining the extended emission and X-ray plateau of short GRB light curves

Extended emission (EE) is a high-energy, early time rebrightening sometimes seen in the light curves of short gamma-ray bursts (GRBs). We present the first contiguous fits to the EE tail and the later X-ray plateau, unified within a single model. Our central engine is a magnetar surrounded by a fall-back accretion disc, formed by either the merger of two compact objects or the accretion-induced collapse of a white dwarf. During the EE phase, material is accelerated to super-Keplarian velocities and ejected from the system by the rapidly rotating ($P \approx 1 - 10$ ms) and very strong ($10^{15}$ G) magnetic field in a process known as magnetic propellering. The X-ray plateau is modelled as magnetic dipole spin-down emission. We first explore the range of GRB phenomena that the propeller could potentially reproduce, using a series of template light curves to devise a classification scheme based on phenomology. We then obtain fits to the light curves of 9 GRBs with EE, simultaneously fitting both the propeller and the magnetic dipole spin-down and finding typical disc masses of a few $10^{-3}$ $M_{\odot}$ to a few $10^{-2}$ $M_{\odot}$. This is done for ballistic, viscous disc and exponential accretion rates. We find that the conversion efficiency from kinetic energy to EM emission for propellered material needs to be $\gtrsim 10\%$ and that the best fitting results come from an exponential accretion profile.Comment: 13 pages, 5 figures, accepted to MNRA

Spatial clusters of gonorrhoea in England with particular reference to the outcome of partner notification: 2012 and 2013

Background: This study explored spatial-temporal variation in diagnoses of gonorrhoea to identify and quantify endemic areas and clusters in relation to patient characteristics and outcomes of partner notification (PN) across England, UK. Methods: Endemic areas and clusters were identified using a two-stage analysis with Kulldorff’s scan statistics (SaTScan). Results Of 2,571,838 tests, 53,547 diagnoses were gonorrhoea positive (positivity = 2.08%). The proportion of diagnoses in heterosexual males was 1.5 times that in heterosexual females. Among index cases, men who have sex with men (MSM) were 8 times more likely to be diagnosed with gonorrhoea than heterosexual males (p<0.0001). After controlling for age, gender, ethnicity and deprivation rank, 4 endemic areas were identified including 11,047 diagnoses, 86% of which occurred in London. 33 clusters included 17,629 diagnoses (34% of total diagnoses in 2012 and 2013) and spanned 21 locations, some of which were dominated by heterosexually acquired infection, whilst others were MSM focused. Of the 53,547 diagnoses, 14.5% (7,775) were the result of PN. The proportion of patients who attended services as a result of PN varied from 0% to 61% within different age, gender and sexual orientation cohorts. A third of tests resulting from PN were positive for gonorrhoea. 25% of Local Authorities (n = 81, 95% CI: 20.2, 29.5) had a higher than expected proportion for female PN diagnoses as compared to 16% for males (n = 52, 95% CI: 12.0, 19.9). Conclusions: The English gonorrhoea epidemic is characterised by spatial-temporal variation. PN success varied between endemic areas and clusters. Greater emphasis should be placed on the role of PN in the control of gonorrhoea to reduce the risk of onward transmission, re-infection, and complications of infection

Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates

We analyze the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean field limit. The mean field equations for particle densities are written in terms of Ricatti equations with the steady-state current $J$ as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents $J$ are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for $J$ from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.Comment: 12 pages, 4 figure

Testing isomorphism of graded algebras

We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma

Very High Modulation Efficiency of Ultralow Threshold Current Single Quantum Well InGaAs Lasers

A record high current modulation efficiency of 5 GHz/[sqrt](mA) has been demonstrated in an ultralow threshold strained layer single quantum well InGaAs laser

Broadband modelling of short gamma-ray bursts with energy injection from magnetar spin-down and its implications for radio detectability

The magnetar model has been proposed to explain the apparent energy injection in the X-ray light curves of short gamma-ray bursts (SGRBs), but its implications across the full broadband spectrum are not well explored. We investigate the broadband modelling of four SGRBs with evidence for energy injection in their X-ray light curves, applying a physically motivated model in which a newly formed magnetar injects energy into a forward shock as it loses angular momentum along open field lines. By performing an order of magnitude search for the underlying physical parameters in the blast wave, we constrain the characteristic break frequencies of the synchrotron spectrum against their manifestations in the available multi-wavelength observations for each burst. The application of the magnetar energy injection profile restricts the successful matches to a limited family of models that are self-consistent within the magnetic dipole spin-down framework.We produce synthetic light curves that describe how the radio signatures of these SGRBs ought to have looked given the restrictions imposed by the available data, and discuss the detectability of these signatures with present-day and near-future radio telescopes. Our results show that both the Atacama Large Millimetre Array and the upgraded Very Large Array are now sensitive enough to detect the radio signature within two weeks of trigger in most SGRBs, assuming our sample is representative of the population as a whole. We also find that the upcoming Square Kilometre Array will be sensitive to depths greater than those of our lower limit predictions.Comment: 15 pages, 4 figures, 6 tables, accepted for publication in MNRA

Constraining properties of GRB magnetar central engines using the observed plateau luminosity and duration correlation

An intrinsic correlation has been identified between the luminosity and duration of plateaus in the X-ray afterglows of Gamma-Ray Bursts (GRBs; Dainotti et al. 2008), suggesting a central engine origin. The magnetar central engine model predicts an observable plateau phase, with plateau durations and luminosities being determined by the magnetic fields and spin periods of the newly formed magnetar. This paper analytically shows that the magnetar central engine model can explain, within the 1$\sigma$ uncertainties, the correlation between plateau luminosity and duration. The observed scatter in the correlation most likely originates in the spread of initial spin periods of the newly formed magnetar and provides an estimate of the maximum spin period of ~35 ms (assuming a constant mass, efficiency and beaming across the GRB sample). Additionally, by combining the observed data and simulations, we show that the magnetar emission is most likely narrowly beamed and has $\lesssim$20% efficiency in conversion of rotational energy from the magnetar into the observed plateau luminosity. The beaming angles and efficiencies obtained by this method are fully consistent with both predicted and observed values. We find that Short GRBs and Short GRBs with Extended Emission lie on the same correlation but are statistically inconsistent with being drawn from the same distribution as Long GRBs, this is consistent with them having a wider beaming angle than Long GRBs.Comment: MNRAS Accepte

A Buffer Stocks Model for Stabilizing Price of Staple Food with Considering the Expectation of Non Speculative Wholesaler

This paper is a study of price stabilization in the staple food distribution system. All stakeholders experience market risks due to some possibility causes of price volatility. Many models of price stabilization had been developed by employing several approaches such as floor-ceiling prices, buffer funds, export or import taxes, and subsidies. In the previous researches, the models were expanded to increase the purchasing price for producer and decrease the selling price for consumer. Therefore, the policy can influence the losses for non-speculative wholesaler that is reflected by the descending of selling quantity and ascending of the stocks. The objective of this model is not only to keep the expectation of both producer and consumer, but also to protect non-speculative wholesaler from the undesirable result of the stabilization policy. A nonlinear programming model was addressed to determine the instruments of intervention program. Moreover, the result shows that the wholesaler behavior affects the intervention costs. Index Terms Buffer stocks, Price stabilization, Nonlinear programming, Wholesaler behavior

Manipulating biphotonic qutrits

Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement induced non-linearities can be employed to dramatically extend the range of possible transforms on biphotonic qutrits; the three level quantum systems formed by the polarisation of two photons in the same spatio-temporal mode. We fully characterise the biphoton-photon entanglement that underpins our technique, thereby realising the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.Comment: 4 pages, 4 figure