Sequential and continuum bifurcations in degenerate elliptic equations

We examine the bifurcations to positive and sign-changing solutions of degenerate elliptic equations. In the problems we study, which do not represent Fredholm operators, we show that there is a critical parameter value at which an infinity of bifurcations occur from the trivial solution. Moreover, a bifurcation occurs at each point in some unbounded interval in parameter space. We apply our results to non-monotone eigenvalue problems, degenerate semi-linear elliptic equations, boundary value differential-algebraic equations and fully non-linear elliptic equations

Biophysical mechanisms that maintain biodiversity through trade-offs

Published onlineJournal ArticleTrade-offs are thought to arise from inevitable, biophysical limitations that prevent organisms from optimizing multiple traits simultaneously. A leading explanation for biodiversity maintenance is a theory that if the shape, or geometry, of a trade-off is right, then multiple species can coexist. Testing this theory, however, is difficult as trait data is usually too noisy to discern shape, or trade-offs necessary for the theory are not observed in vivo. To address this, we infer geometry directly from the biophysical mechanisms that cause trade-offs, deriving the geometry of two by studying nutrient uptake and metabolic properties common to all living cells. To test for their presence in vivo we isolated Escherichia coli mutants that vary in a nutrient transporter, LamB, and found evidence for both trade-offs. Consistent with data, population genetics models incorporating the trade-offs successfully predict the co-maintenance of three distinct genetic lineages, demonstrating that trade-off geometry can be deduced from fundamental principles of living cells and used to predict stable genetic polymorphisms

A search for thermal X-ray signatures in Gamma-Ray Bursts I: Swift bursts with optical supernovae

The X-ray spectra of Gamma-Ray Bursts can generally be described by an absorbed power law. The landmark discovery of thermal X-ray emission in addition to the power law in the unusual GRB 060218, followed by a similar discovery in GRB 100316D, showed that during the first thousand seconds after trigger the soft X-ray spectra can be complex. Both the origin and prevalence of such spectral components still evade understanding, particularly after the discovery of thermal X-ray emission in the classical GRB 090618. Possibly most importantly, these three objects are all associated with optical supernovae, begging the question of whether the thermal X-ray components could be a result of the GRB-SN connection, possibly in the shock breakout. We therefore performed a search for blackbody components in the early Swift X-ray spectra of 11 GRBs that have or may have associated optical supernovae, accurately recovering the thermal components reported in the literature for GRBs 060218, 090618 and 100316D. We present the discovery of a cooling blackbody in GRB 101219B/SN2010ma, and in four further GRB-SNe we find an improvement in the fit with a blackbody which we deem possible blackbody candidates due to case-specific caveats. All the possible new blackbody components we report lie at the high end of the luminosity and radius distribution. GRB 101219B appears to bridge the gap between the low-luminosity and the classical GRB-SNe with thermal emission, and following the blackbody evolution we derive an expansion velocity for this source of order 0.4c. We discuss potential origins for the thermal X-ray emission in our sample, including a cocoon model which we find can accommodate the more extreme physical parameters implied by many of our model fits.Comment: 16 pages, 6 figures, accepted for MNRA

X-ray and UV observations of V751 Cyg in an optical high state

Aims: The VY Scl system (anti-dwarf nova) V751 Cyg is examined following a claim of a super-soft spectrum in the optical low state. Methods: A serendipitous XMM-Newton X-ray observation and, 21 months later, Swift X-ray and UV observations, have provided the best such data on this source so far. These optical high-state datasets are used to study the flux and spectral variability of V751 Cyg. Results: Both the XMM-Newton and Swift data show evidence for modulation of the X-rays for the first time at the known 3.467 hr orbital period of V751 Cyg. In two Swift observations, taken ten days apart, the mean X-ray flux remained unchanged, while the UV source brightened by half a magnitude. The X-ray spectrum was not super-soft during the optical high state, but rather due to multi-temperature optically thin emission, with significant (10^{21-22} cm^-2) absorption, which was higher in the observation by Swift than that of XMM-Newton. The X-ray flux is harder at orbital minimum, suggesting that the modulation is related to absorption, perhaps linked to the azimuthally asymmetric wind absorption seen previously in H-alpha.Comment: 6 pages, 9 figures, accepted for publication in A&

Antibiotic Cycling and Antibiotic Mixing: which one best mitigates antibiotic resistance?

Published onlineJournal ArticleThis is the final version of the article. Available from Oxford University Press via the DOI in this record.Can we exploit our burgeoning understanding of molecular evolution to slow the progress of drug resistance? One role of an infection clinician is exactly that: to foresee trajectories to resistance during antibiotic treatment and to hinder that evolutionary course. But can this be done at a hospital-wide scale? Clinicians and theoreticians tried to when they proposed two conicting behavioural strategies that are expected to curb resistance evolution in the clinic, these are known as 'antibiotic cycling' and 'antibiotic mixing'. However, the accumulated data from clinical trials, now approaching 4 million patient days of treatment, is too variable for cycling or mixing to be deemed successful. The former implements the restriction and prioritisation of di_erent antibiotics at di_erent times in hospitals in a manner said to 'cycle' between them. In antibiotic mixing, appropriate antibiotics are allocated to patients but randomly.Mixing results in no correlation, in time or across patients, in the drugs used for treatment which is why theorists saw this as an optimal behavioural strategy. So while cycling and mixing were proposed as ways of controlling evolution, we show there is good reason why clinical datasets cannot choose between them: by re-examining the theoretical literature we show prior support for the theoretical optimality of mixing was misplaced. Our analysis is consistent with a pattern emerging in data: neither cycling or mixing is a priori better than the other at mitigating selection for antibiotic resistance in the clinic.REB was funded during this work by an MRC Discipline Hopping Fellowship G0802611, RPM was funded by a Conacyt PhD award, all authors were supported by EPSRC grant EP/I00503X/1 (grant holder REB)

On the X-ray variability of magnetar 1RXS J170849.0-400910

We present a long-term X-ray flux and spectral analysis for 1RXS J170849.0-400910 using Swift/XRT spanning over 8 years from 2005-2013. We also analyze two observations from Chandra and XMM in the period from 2003-2004. In this 10-yr period, 1RXS J170849.0-400910 displayed several rotational glitches. Previous studies have claimed variations in the X-ray emission associated with some of the glitches. From our analysis we find no evidence for significant X-ray flux variations and evidence for only low-level spectral variations. We also present an updated timing solution for 1RXS J170849.0-400910, from RXTE and Swift observations, which includes a previously unreported glitch at MJD 56019. We discuss the frequency and implications of radiatively quiet glitches in magnetars.Comment: 9 pages, 2 figures, accepted for publication in Ap

Direct simulation of ion beam induced stressing and amorphization of silicon

Using molecular dynamics (MD) simulation, we investigate the mechanical response of silicon to high dose ion-irradiation. We employ a realistic and efficient model to directly simulate ion beam induced amorphization. Structural properties of the amorphized sample are compared with experimental data and results of other simulation studies. We find the behavior of the irradiated material is related to the rate at which it can relax. Depending upon the ability to deform, we observe either the generation of a high compressive stress and subsequent expansion of the material, or generation of tensile stress and densification. We note that statistical material properties, such as radial distribution functions are not sufficient to differentiate between different densities of amorphous samples. For any reasonable deformation rate, we observe an expansion of the target upon amorphization in agreement with experimental observations. This is in contrast to simulations of quenching which usually result in denser structures relative to crystalline Si. We conclude that although there is substantial agreement between experimental measurements and most simulation results, the amorphous structures being investigated may have fundamental differences; the difference in density can be attributed to local defects within the amorphous network. Finally we show that annealing simulations of our amorphized samples can lead to a reduction of high energy local defects without a large scale rearrangement of the amorphous network. This supports the proposal that defects in amorphous silicon are analogous to those in crystalline silicon.Comment: 13 pages, 12 figure

An Efficient Molecular Dynamics Scheme for the Calculation of Dopant Profiles due to Ion Implantation

We present a highly efficient molecular dynamics scheme for calculating the concentration depth profile of dopants in ion irradiated materials. The scheme incorporates several methods for reducing the computational overhead, plus a rare event algorithm that allows statistically reliable results to be obtained over a range of several orders of magnitude in the dopant concentration. We give examples of using this scheme for calculating concentration profiles of dopants in crystalline silicon. Here we can predict the experimental profile over five orders of magnitude for both channeling and non-channeling implants at energies up to 100s of keV. The scheme has advantages over binary collision approximation (BCA) simulations, in that it does not rely on a large set of empirically fitted parameters. Although our scheme has a greater computational overhead than the BCA, it is far superior in the low ion energy regime, where the BCA scheme becomes invalid.Comment: 17 pages, 21 figures, 2 tables. See: http://bifrost.lanl.gov/~reed

Scattered Emission from A Relativistic Outflow and Its Application to Gamma-Ray Bursts

We investigate a scenario of photons scattering by electrons within a relativistic outflow. The outflow is composed of discrete shells with different speeds. One shell emits radiation for a short duration. Some of this radiation is scattered by the shell(s) behind. We calculate in a simple two-shell model the observed scattered flux density as a function of the observed primary flux density, the normalized arrival time delay between the two emission components, the Lorentz factor ratio of the two shells and the scattering shell's optical depth. Thomson scattering in a cold shell and inverse Compton scattering in a hot shell are both considered. The results of our calculations are applied to the Gamma-Ray Bursts and the afterglows. We find that the scattered flux from a cold slower shell is small and likely to be detected only for those bursts with very weak afterglows. A hot scattering shell could give rise to a scattered emission as bright as the X-ray shallow decay component detected in many bursts, on a condition that the isotropically equivalent total energy carried by the hot electrons is large, $\sim 10^{52-56}$ erg. The scattered emission from a faster shell could appear as a late short $\gamma$-ray/MeV flash or become part of the prompt emission depending on the delay of the ejection of the shell.Comment: 13 pages, 3 figures, MNRAS in press; a short intuitive estimation is added before detailed calculations; references update