490 research outputs found
Model validation for a noninvasive arterial stenosis detection problem
Copyright @ 2013 American Institute of Mathematical SciencesA current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use both one-dimensional pressure and shear wave experimental data from novel acoustic phantoms to validate corresponding viscoelastic mathematical models, which were developed in a concept paper [8] and refined herein. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.The National Institute of Allergy and Infectious Diseases, the Air Force Office of Scientific Research, the Deopartment of Education and the Engineering and Physical Sciences Research Council (EPSRC)
Magnetic-Moment Fragmentation and Monopole Crystallization
The Coulomb phase, with its dipolar correlations and pinch-point-scattering
patterns, is central to discussions of geometrically frustrated systems, from
water ice to binary and mixed-valence alloys, as well as numerous examples of
frustrated magnets. The emergent Coulomb phase of lattice-based systems has
been associated with divergence-free fields and the absence of long-range
order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can
emerge naturally as a persistent fluctuating background in an otherwise ordered
system. To explain this behavior, we introduce the concept of the fragmentation
of the field of magnetic moments into two parts, one giving rise to a magnetic
monopole crystal, the other a magnetic fluid with all the characteristics of an
emergent Coulomb phase. Our theory is backed up by numerical simulations, and
we discuss its importance with regard to the interpretation of a number of
experimental results
A model for predicting dissolved organic carbon distribution in a reservoir water using fluorescence spectroscopy
A number of water treatment works (WTW) in the north of England (UK) have
experienced problems in reducing the dissolved organic carbon (DOC) present in
the water to a sufficiently low level. The problems are experienced in autumn/
winter when the colour increases and the coagulant dose at the WTW needs to be
increased in order to achieve sufficient colour removal. However, the DOC
content of the water varies little throughout the year. To investigate this
further, the water was fractionated using resin adsorption techniques into its
hydrophobic (fulvic and humic acid fractions) and hydrophilic (acid and non-acid
fractions) components. The fractionation process yields useful information on
the changing concentration of each fraction but is time consuming and labour
intensive. Here, a method of rapidly determining fraction concentration was
developed using fluorescence spectroscopy. The model created used synchronous
spectra of fractionated material compared against bulk water spectra and
predicted the fraction concentrations to within 10% for a specific water. The
model was unable to predict fraction concentrations for waters from a different
watershed
Reduced dimensionality spin-orbit dynamics of CH3 + HCl reversible arrow CH4 Cl on ab initio surfaces
A reduced dimensionality quantum scattering method is extended to the study of spin-orbit nonadiabatic transitions in the CH3 + HCl reversible arrow CH4 + Cl(P-2(J)) reaction. Three two-dimensional potential energy surfaces are developed by fitting a 29 parameter double-Morse function to CCSD(T)/IB//MP2/cc-pV(T+d)Z-dk ab initio data; interaction between surfaces is described by geometry-dependent spin-orbit coupling functions fit to MCSCF/cc-pV(T+d)Z-dk ab initio data. Spectator modes are treated adiabatically via inclusion of curvilinear projected frequencies. The total scattering wave function is expanded in a vibronic basis set and close-coupled equations are solved via R-matrix propagation. Ground state thermal rate constants for forward and reverse reactions agree well with experiment. Multi-surface reaction probabilities, integral cross sections, and initial-state selected branching ratios all highlight the importance of vibrational energy in mediating nonadiabatic transition. Electronically excited state dynamics are seen to play a small but significant role as consistent with experimental conclusions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3592732
A Matrix Big Bang
The light-like linear dilaton background represents a particularly simple
time-dependent 1/2 BPS solution of critical type IIA superstring theory in ten
dimensions. Its lift to M-theory, as well as its Einstein frame metric, are
singular in the sense that the geometry is geodesically incomplete and the
Riemann tensor diverges along a light-like subspace of codimension one. We
study this background as a model for a big bang type singularity in string
theory/M-theory. We construct the dual Matrix theory description in terms of a
(1+1)-d supersymmetric Yang-Mills theory on a time-dependent world-sheet given
by the Milne orbifold of (1+1)-d Minkowski space. Our model provides a
framework in which the physics of the singularity appears to be under control.Comment: 25 pages, LaTeX; v2: discussion of singularity of Einstein frame
metric added, references adde
Lattice Supersymmetry and Topological Field Theory
It is known that certain theories with extended supersymmetry can be
discretized in such a way as to preserve an exact fermionic symmetry. In the
simplest model of this kind, we show that this residual supersymmetric
invariance is actually a BRST symmetry associated with gauge fixing an
underlying local shift symmetry. Furthermore, the starting lattice action is
then seen to be entirely a gauge fixing term. The corresponding continuum
theory is known to be a topological field theory. We look, in detail, at one
example - supersymmetric quantum mechanics which possesses two such BRST
symmetries. In this case, we show that the lattice theory can be obtained by
blocking out of the continuum in a carefully chosen background metric. Such a
procedure will not change the Ward identities corresponding to the BRST
symmetries since they correspond to topological observables. Thus, at the
quantum level, the continuum BRST symmetry is preserved in the lattice theory.
Similar conclusions are reached for the two-dimensional complex Wess-Zumino
model and imply that all the supersymmetric Ward identities are satisfied {\it
exactly} on the lattice. Numerical results supporting these conclusions are
presented.Comment: 18 pages, 2 figure
Exact Lattice Supersymmetry: the Two-Dimensional N=2 Wess-Zumino Model
We study the two-dimensional Wess-Zumino model with extended N=2
supersymmetry on the lattice. The lattice prescription we choose has the merit
of preserving {\it exactly} a single supersymmetric invariance at finite
lattice spacing . Furthermore, we construct three other transformations of
the lattice fields under which the variation of the lattice action vanishes to
where is a typical interaction coupling. These four
transformations correspond to the two Majorana supercharges of the continuum
theory. We also derive lattice Ward identities corresponding to these exact and
approximate symmetries. We use dynamical fermion simulations to check the
equality of the massgaps in the boson and fermion sectors and to check the
lattice Ward identities. At least for weak coupling we see no problems
associated with a lack of reflection positivity in the lattice action and find
good agreement with theory. At strong coupling we provide evidence that
problems associated with a lack of reflection positivity are evaded for small
enough lattice spacing.Comment: 29 pages, 10 figures. New results at strong coupling added. Minor
corrections to text and one reference added. Version to appear in Phys. Rev.
Quantum field theory on manifolds with a boundary
We discuss quantum theory of fields \phi defined on (d+1)-dimensional
manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(\phi) which
is a bilinear form in \phi defines the Gaussian measure with a covariance
(Green function) {\cal G}. We discuss a relation between the quantum field
theory with a fixed boundary condition \Phi and the theory defined by the Green
function {\cal G}. It is shown that the latter results by an average over \Phi
of the first. The QFT in (anti)de Sitter space is treated as an example. It is
shown that quantum fields on the boundary are more regular than the ones on
(anti) de Sitter space.Comment: The version to appear in Journal of Physics A, a discussion on the
relation to other works in the field is adde
Thermal phases of D1-branes on a circle from lattice super Yang-Mills
We report on the results of numerical simulations of 1+1 dimensional SU(N)
Yang-Mills theory with maximal supersymmetry at finite temperature and
compactified on a circle. For large N this system is thought to provide a dual
description of the decoupling limit of N coincident D1-branes on a circle. It
has been proposed that at large N there is a phase transition at strong
coupling related to the Gregory-Laflamme (GL) phase transition in the
holographic gravity dual. In a high temperature limit there was argued to be a
deconfinement transition associated to the spatial Polyakov loop, and it has
been proposed that this is the continuation of the strong coupling GL
transition. Investigating the theory on the lattice for SU(3) and SU(4) and
studying the time and space Polyakov loops we find evidence supporting this. In
particular at strong coupling we see the transition has the parametric
dependence on coupling predicted by gravity. We estimate the GL phase
transition temperature from the lattice data which, interestingly, is not yet
known directly in the gravity dual. Fine tuning in the lattice theory is
avoided by the use of a lattice action with exact supersymmetry.Comment: 21 pages, 8 figures. v2: References added, two figures were modified
for clarity. v3: Normalisation of lattice coupling corrected by factor of two
resulting in change of estimate for c_cri
Holographic Walking Technicolor and Stability of Techni-Branes
Techni-fermions are added as stacks of D7-anti-D7 techni-branes within the
framework of a holographic technicolor model that has been proposed as a
realization of walking technicolor. The stability of the embedding of these
branes is determined. When a sufficiently low bulk cut-off is provided the
fluctuations remain small. For a longer walking region, as would be required in
any realistic model of electroweak symmetry breaking, a larger bulk cut-off is
needed and in this case the oscillations destabilize.Comment: Latex, 25 pages, 10 figure
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