The Swift-Hohenberg equation with a nonlocal nonlinearity

It is well known that aspects of the formation of localised states in a one-dimensional Swift--Hohenberg equation can be described by Ginzburg--Landau-type envelope equations. This paper extends these multiple scales analyses to cases where an additional nonlinear integral term, in the form of a convolution, is present. The presence of a kernel function introduces a new lengthscale into the problem, and this results in additional complexity in both the derivation of envelope equations and in the bifurcation structure. When the kernel is short-range, weakly nonlinear analysis results in envelope equations of standard type but whose coefficients are modified in complicated ways by the nonlinear nonlocal term. Nevertheless, these computations can be formulated quite generally in terms of properties of the Fourier transform of the kernel function. When the lengthscale associated with the kernel is longer, our method leads naturally to the derivation of two different, novel, envelope equations that describe aspects of the dynamics in these new regimes. The first of these contains additional bifurcations, and unexpected loops in the bifurcation diagram. The second of these captures the stretched-out nature of the homoclinic snaking curves that arises due to the nonlocal term.Comment: 28 pages, 14 figures. To appear in Physica

Friends, Neighbours and Distant Partners: Extending or Decentring Family Relationships?

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The Skn7 Response Regulator of \u3ci\u3eSaccharomyces cerevisiae\u3c/i\u3e Interacts with Hsf1 In Vivo and Is Required for the Induction of Heat Shock Genes by Oxidative Stress

The Skn7 response regulator has previously been shown to play a role in the induction of stress-responsive genes in yeast, e.g., in the induction of the thioredoxin gene in response to hydrogen peroxide. The yeast Heat Shock Factor, Hsf1, is central to the induction of another set of stress-inducible genes, namely the heat shock genes. These two regulatory trans-activators, Hsf1 and Skn7, share certain structural homologies, particularly in their DNA-binding domains and the presence of adjacent regions of coiled-coil structure, which are known to mediate protein–protein interactions. Here, we provide evidence that Hsf1 and Skn7 interact in vitro and in vivo and we show that Skn7 can bind to the same regulatory sequences as Hsf1, namely heat shock elements. Furthermore, we demonstrate that a strain deleted for the SKN7 gene and containing a temperature-sensitive mutation in Hsf1 is hypersensitive to oxidative stress. Our data suggest that Skn7 and Hsf1 cooperate to achieve maximal induction of heat shock genes in response specifically to oxidative stress. We further show that, like Hsf1, Skn7 can interact with itself and is localized to the nucleus under normal growth conditions as well as during oxidative stress

Ethics of Using Artificial Intelligence to Augment Drafting Legal Documents

This article focuses on the second step in the due diligence process. While it addresses the question of competency, it focuses more on the further steps a lawyer must take to ensure that the use of the service as part of the representation of a client is consistent with the lawyer’s other ethical obligations. While it is important to emphasize that competency requires that the lawyer must be able to assess whether the work product is comparable to what a human would produce, competency is of course a fact-depending inquiry: whether a will is competently drafted turns on the standard of care of a practitioner who drafts wills. This article focuses more on how a lawyer can determine whether it is ethical to use a competent service that augments document drafting. While addressing how ethical concerns arise across typical practice areas, it highlights a practice area where the risks for violations may be particularly acute because the need for confidentiality is high, and the potential for undetected conflicts of interest is great: patent practice. This article identifies the issues, describes the potential risks, and explains what protections a lawyer should look for in the terms of service of an automated legal document drafting site to ensure ethical representation

Superconducting Diamond on Silicon Nitride for Device Applications

Chemical vapour deposition (CVD) grown nanocrystalline diamond is an attractive material for the fabrication of devices. For some device architectures, optimisation of its growth on silicon nitride is essential. Here, the effects of three pre-growth surface treatments, often employed as cleaning methods of silicon nitride, were investigated. Such treatments provide control over the surface charge of the substrate through modification of the surface functionality, allowing for the optimisation of electrostatic diamond seeding densities. Zeta potential measurements and X-ray photoelectron spectroscopy (XPS) were used to analyse the silicon nitride surface following each treatment. Exposing silicon nitride to an oxygen plasma offered optimal surface conditions for the electrostatic self-assembly of a hydrogen-terminated diamond nanoparticle monolayer. The subsequent growth of boron-doped nanocrystalline diamond thin films on modified silicon nitride substrates under CVD conditions produced coalesced films for oxygen plasma and solvent treatments, whilst pin-holing of the diamond film was observed following RCA-1 treatment. The sharpest superconducting transition was observed for diamond grown on oxygen plasma treated silicon nitride, demonstrating it to be of the least structural disorder. Modifications to the substrate surface optimise the seeding and growth processes for the fabrication of diamond on silicon nitride devices

The long-term evolution of the spin, pulse shape, and orbit of the accretion-powered millisecond pulsar SAX J1808.4-3658

We present a 7 yr timing study of the 2.5 ms X-ray pulsar SAX J1808.4-3658, an X-ray transient with a recurrence time of ~2 yr, using data from the Rossi X-ray Timing Explorer covering 4 transient outbursts (1998-2005). We verify that the 401 Hz pulsation traces the spin frequency fundamental and not a harmonic. Substantial pulse shape variability, both stochastic and systematic, was observed during each outburst. Analysis of the systematic pulse shape changes suggests that, as an outburst dims, the X-ray "hot spot" on the pulsar surface drifts longitudinally and a second hot spot may appear. The overall pulse shape variability limits the ability to measure spin frequency evolution within a given X-ray outburst (and calls previous nudot measurements of this source into question), with typical upper limits of |nudot| < 2.5x10^{-14} Hz/s (2 sigma). However, combining data from all the outbursts shows with high (6 sigma) significance that the pulsar is undergoing long-term spin down at a rate nudot = (-5.6+/-2.0)x10^{-16} Hz/s, with most of the spin evolution occurring during X-ray quiescence. We discuss the possible contributions of magnetic propeller torques, magnetic dipole radiation, and gravitational radiation to the measured spin down, setting an upper limit of B < 1.5x10^8 G for the pulsar's surface dipole magnetic field and and Q/I < 5x10^{-9} for the fractional mass quadrupole moment. We also measured an orbital period derivative of Pdot = (3.5+/-0.2)x10^{-12} s/s. This surprising large Pdot is reminiscent of the large and quasi-cyclic orbital period variation observed in the so-called "black widow" millisecond radio pulsars, supporting speculation that SAX J1808.4-3658 may turn on as a radio pulsar during quiescence. In an appendix we derive an improved (0.15 arcsec) source position from optical data.Comment: 22 pages, 10 figures; accepted for publication in Ap

The Most Massive Black Holes in the Universe: Effects of Mergers in Massive Galaxy Clusters

Recent observations support the idea that nuclear black holes grew by gas accretion while shining as luminous quasars at high redshift, and they establish a relation of the black hole mass with the host galaxy's spheroidal stellar system. We develop an analytic model to calculate the expected impact of mergers on the masses of black holes in massive clusters of galaxies. We use the extended Press-Schechter formalism to generate Monte Carlo merger histories of halos with a mass 10^{15} h^{-1} Msun. We assume that the black hole mass function at z=2 is similar to that inferred from observations at z=0 (since quasar activity declines markedly at z<2), and we assign black holes to the progenitor halos assuming a monotonic relation between halo mass and black hole mass. We follow the dynamical evolution of subhalos within larger halos, allowing for tidal stripping, the loss of orbital energy by dynamical friction, and random orbital perturbations in gravitational encounters with subhalos, and we assume that mergers of subhalos are followed by mergers of their central black holes. Our analytic model reproduces numerical estimates of the subhalo mass function. We find that the most massive black holes in massive clusters typically grow by a factor ~ 2 by mergers after gas accretion has stopped. In our ten realizations of 10^{15} h^{-1} Msun clusters, the highest initial (z=2) black hole masses are 5-7 x 10^9 Msun, but four of the clusters contain black holes in the range 1-1.5 x 10^{10} Msun at z=0. Satellite galaxies may host black holes whose mass is comparable to, or even greater than, that of the central galaxy. Thus, black hole mergers can significantly extend the very high end of the black hole mass function.Comment: 13 pages, 7 figures, accepted for publication in The Astrophysical Journa