691 research outputs found
Double-Copy Constructions and Unitarity Cuts
The duality between color and kinematics enables the construction of
multiloop gravity integrands directly from corresponding gauge-theory
integrands. This has led to new nontrivial insights into the structure of
gravity theories, including the discovery of enhanced ultraviolet
cancellations. To continue to gain deeper understandings and probe these new
properties, it is crucial to further improve techniques for constructing
multiloop gravity integrands. In this paper, we show by example how one can
alleviate difficulties encountered at the multiloop level by relaxing the
color-kinematics duality conditions to hold manifestly only on unitarity cuts
instead of globally on loop integrands. As an example, we use a minimal ansatz
to construct an integrand for the two-loop four-point nonsupersymmetric pure
Yang-Mills amplitude in dimensions that is compatible with these relaxed
color-kinematics duality constraints. We then immediately obtain a
corresponding gravity integrand through the double-copy procedure. Comments on
ultraviolet divergences are also included.Comment: 26 pages, 11 figures, ancillary file, RevTe
Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
We show that at tree level, on-shell gauge invariance can be used to fully
determine the first subleading soft-gluon behavior and the first two subleading
soft-graviton behaviors. Our proofs of the behaviors for n-gluon and n-graviton
tree amplitudes are valid in D dimensions and are similar to Low's proof of
universality of the first subleading behavior of photons. In contrast to
photons coupling to massive particles, in four dimensions the soft behaviors of
gluons and gravitons are corrected by loop effects. We comment on how such
corrections arise from this perspective. We also show that loop corrections in
graviton amplitudes arising from scalar loops appear only at the second soft
subleading order. This case is particularly transparent because it is not
entangled with graviton infrared singularities. Our result suggests that if we
set aside the issue of infrared singularities, soft-graviton Ward identities of
extended BMS symmetry are not anomalous through the first subleading order.Comment: RevTeX, 5 figures, 28 pages; v3 minor corrections and clarification
Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
We provide evidence in favor of the conjectured duality between color and
kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by
constructing a form of the one-loop four-point amplitude of this theory that
makes the duality manifest. Our construction is valid in any dimension. We also
describe a duality-satisfying representation for the two-loop four-point
amplitude with identical four-dimensional external helicities. We use these
results to obtain corresponding gravity integrands for a theory containing a
graviton, dilaton, and antisymmetric tensor, simply by replacing color factors
with specified diagram numerators. Using this, we give explicit forms of
ultraviolet divergences at one loop in four, six, and eight dimensions, and at
two loops in four dimensions.Comment: 35 page, 10 figures, REVTex, ancillary mathematica file containing
one-loop diagram numerators, latest version includes updated references,
corrected two-loop numerators and various clarification
Controlling the Au/Iron oxide interface to optimise plasmonic resonance for magneto-optic diagnostics
Sepsis is one of the biggest causes of child mortality across the globe accounting for 1 in 5
deaths. Often these deaths could have been prevented with faster diagnosis. This can be
achieved by developing point of care diagnostics which can be carried out in a pharmacy
or general practitioners office. One way to develop portable diagnostics such as this is the
use of the unique magnetic and optical properties possessed by anisotropic
nanoparticles. A possible method to identify sepsis is through the presence of bacterial
endotoxins. These can be detected magneto-optically by monitoring the rotational
dynamics of anisotropic nanoparticles in an external magnetic field.
Nanoparticles of hematite and cerium phosphate were synthesised and evaluated for
their use as sensors in magneto-optical diagnosis. The sensitivity of such a probe
depends upon a combination of magnetic and plasmonic properties. These are affected
by morphology, magnetic susceptibility, and surface plasmon resonance.
The hydrothermal growth mechanisms of hematite nanorods were examined and the
relationship between directing agent concentration, reaction temperature and time was
examined. The effect of 1,2 propanediamine and alkali metal phosphates acting as
directing agents were evaluated on hematite, resulting in the formation of tuneable
nanorods with aspect ratios between 3-10 and 1-7 respectively. The rotational dynamics
of these hematite particles was assessed in glycerol solution and shown to be sensitive to
changes in viscosity at different frequencies of rotation.
Cerium phosphate nanorods were prepared with a tuneable length from 78 nm to 432
nm and aspect ratios of 3-27. The magnetic susceptibility of these rods was changed
through the addition of W, Fe, Ni and Mn ions. The addition of Co ions had only a
minimum effect n the magnetic susceptibility. The particles were rotated in external
magnetic fields and were shown to be sensitive to changes in the viscosity of a solution
based on changes in phase shift.
Hematite and cerium phosphate core shell particles were produced. The cores were
coated in gold through the seed-mediated method and the morphology of the Au shell
was shown to depend heavily upon the number of gold seeds pre-deposited on the
ii
surface as well as the concentration of the gold growth solution. Using this understanding
of the growth mechanism, nanorods with smooth gold surfaces which would produce
strong plasmonic signals were synthesised
Photo induced Force Microscopy: chemical spectroscopy beyond the diffraction limit
Over the last decade remarkable advances have been made in creating spectroscopic tools to interrogate surface properties using electromagnetic radiation in the near field, achieving lateral resolutions in the nanometre range. We review recent work involving one of the most promising of these spectroscopic tools, photo induced force microscopy (PiFM), which uses mechanical detection of dipole-dipole interactions enabling nanometre resolved mapping of surface properties ranging from vibrational modes of adsorbates to plasmon resonances. We discuss the origin of contrast in PiFM images, its applications as a local probe of chemical species and for mapping local electric fields in areas as diverse as zeolite films and biometric recognition. In comparison with related techniques such as photo thermal infrared spectroscopy (PTIR) and tip enhanced Raman spectroscopy (TERS) PiFM has many advantages but perhaps its most successful application is in combination with other surface characterisation methods which provide information averaged over much greater surface areas. We discuss the most recent developments of PiFM technology which are leading to higher resolution images and are widening the range of environments in which the technique can be applied, and we consider how the field is likely to progress in the future
PiFM and XPS Studies of Porous TiO2 Films for the Photocatalytic Decomposition of Polystyrene
The rate of photocatalytic oxidation of polystyrene over 0.1 wt% copper-doped TiO2 catalyst spin coated onto a flat substrate is investigated as a function of the catalyst deposition spin speed and, hence, film thickness. Photoinduced force microscopy and photoelectron spectroscopy show no evidence of any products of the photocatalytic oxidation remaining on the surface after reaction. The oxidation reaction shows no discernible dependence on spin speed; it is close to zero order in polystyrene concentration and exhibits a ½ life almost 50 times greater than the equivalent photocatalytic oxidation of stearic acid on the same catalysts. No difference between the rate of decay of the aliphatic and aromatic hydrogens of the polymer was observed, suggesting that once a polymer chain begins oxidising, subsequent steps are relatively rapid. This is consistent with the rate-determining step being dependent on the extent of coordination to the surface, which is much more favourable with stearic acid because of its carboxylic group
The role of growth directors in controlling the morphology of hematite nanorods
The control of the growth of hematite nanoparticles from iron chloride solutions under hydrothermal conditions in the presence of two different structure promoters has been studied using a range of both structural and spectroscopic techniques including the first report of photo induced force microscopy (PiFM) to map the topographic distribution of the structure-directing agents on the developing nanoparticles. We show that the shape of the nanoparticles can be controlled using the concentration of phosphate ions up to a limit determined to be ~6 × 10−3 mol. Akaganéite (β-FeOOH) is a major component of the nanoparticles formed in the absence of structure directors but only present in the very early stages (< 8 h) of particle growth when phosphate is present. The PiFM data suggest a correlation between the areas in which phosphate ions are adsorbed and areas where akaganéite persists on the surface. In contrast, goethite (α-FeOOH) is a directly observed precursor of the hematite nanorods when 1,2-diamino propane is present. The PiFM data shows goethite in the center of the developing particles consistent with a mechanism in which the iron hydroxide re-dissolves and precipitates at the nanorod ends as hematite
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