7,436 research outputs found
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 proteinâprotein 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 lawyerâs 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
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