10,458 research outputs found
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast
Ultrasound Tomography has seen a revival of interest in the past decade,
especially for breast imaging, due to improvements in both ultrasound and
computing hardware. In particular, three-dimensional ultrasound tomography, a
fully tomographic method in which the medium to be imaged is surrounded by
ultrasound transducers, has become feasible. In this paper, a comprehensive
derivation and study of a robust framework for large-scale bent-ray ultrasound
tomography in 3D for a hemispherical detector array is presented. Two
ray-tracing approaches are derived and compared. More significantly, the
problem of linking the rays between emitters and receivers, which is
challenging in 3D due to the high number of degrees of freedom for the
trajectory of rays, is analysed both as a minimisation and as a root-finding
problem. The ray-linking problem is parameterised for a convex detection
surface and three robust, accurate, and efficient ray-linking algorithms are
formulated and demonstrated. To stabilise these methods, novel
adaptive-smoothing approaches are proposed that control the conditioning of the
update matrices to ensure accurate linking. The nonlinear UST problem of
estimating the sound speed was recast as a series of linearised subproblems,
each solved using the above algorithms and within a steepest descent scheme.
The whole imaging algorithm was demonstrated to be robust and accurate on
realistic data simulated using a full-wave acoustic model and an anatomical
breast phantom, and incorporating the errors due to time-of-flight picking that
would be present with measured data. This method can used to provide a
low-artefact, quantitatively accurate, 3D sound speed maps. In addition to
being useful in their own right, such 3D sound speed maps can be used to
initialise full-wave inversion methods, or as an input to photoacoustic
tomography reconstructions
On the determination of the boundary impedance from the far field pattern
We consider the Helmholtz equation in the half space and suggest two methods
for determining the boundary impedance from knowledge of the far field pattern
of the time-harmonic incident wave. We introduce a potential for which the far
field patterns in specially selected directions represent its Fourier
coefficients. The boundary impedance is then calculated from the potential by
an explicit formula or from the WKB approximation. Numerical examples are given
to demonstrate efficiency of the approaches. We also discuss the validity of
the WKB approximation in determining the impedance of an obstacle.Comment: 10 pages, 4 figure
Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations
One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology
Physics of non-Gaussian fields and the cosmological genus statistic
We report a technique to calculate the impact of distinct physical processes
inducing non-Gaussianity on the cosmological density field. A natural
decomposition of the cosmic genus statistic into an orthogonal polynomial
sequence allows complete expression of the scale-dependent evolution of the
morphology of large-scale structure, in which effects including galaxy bias,
nonlinear gravitational evolution and primordial non-Gaussianity may be
delineated. The relationship of this decomposition to previous methods for
analysing the genus statistic is briefly considered and the following
applications are made: i) the expression of certain systematics affecting
topological measurements; ii) the quantification of broad deformations from
Gaussianity that appear in the genus statistic as measured in the Horizon Run
simulation; iii) the study of the evolution of the genus curve for simulations
with primordial non-Gaussianity. These advances improve the treatment of
flux-limited galaxy catalogues for use with this measurement and further the
use of the genus statistic as a tool for exploring non-Gaussianity.Comment: AASTeX preprint, 24 pages, 8 figures, includes several improvements
suggested by anonymous reviewe
The VOLNA code for the numerical modelling of tsunami waves: generation, propagation and inundation
A novel tool for tsunami wave modelling is presented. This tool has the
potential of being used for operational purposes: indeed, the numerical code
\VOLNA is able to handle the complete life-cycle of a tsunami (generation,
propagation and run-up along the coast). The algorithm works on unstructured
triangular meshes and thus can be run in arbitrary complex domains. This paper
contains the detailed description of the finite volume scheme implemented in
the code. The numerical treatment of the wet/dry transition is explained. This
point is crucial for accurate run-up/run-down computations. Most existing
tsunami codes use semi-empirical techniques at this stage, which are not always
sufficient for tsunami hazard mitigation. Indeed the decision to evacuate
inhabitants is based on inundation maps which are produced with this type of
numerical tools. We present several realistic test cases that partially
validate our algorithm. Comparisons with analytical solutions and experimental
data are performed. Finally the main conclusions are outlined and the
perspectives for future research presented.Comment: 47 pages, 27 figures. Other author's papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
Rapid evaluation of radial basis functions
Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem. However, this method has been associated with very high computational cost, as compared to alternative methods such as finite element or multivariate spline interpolation. For example. the direct evaluation at M locations of a radial basis function interpolant with N centres requires O(M N) floating-point operations. In this paper we introduce a fast evaluation method based on the Fast Gauss Transform and suitable quadrature rules. This method has been applied to the Hardy multiquadric, the inverse multiquadric and the thin-plate spline to reduce the computational complexity of the interpolant evaluation to O(M + N) floating point operations. By using certain localisation properties of conditionally negative definite functions this method has several performance advantages against traditional hierarchical rapid summation methods which we discuss in detail
Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
This paper revisits the question of reconstructing bulk gauge fields as
boundary operators in AdS/CFT. In the presence of the wormhole dual to the
thermofield double state of two CFTs, the existence of bulk gauge fields is in
some tension with the microscopic tensor factorization of the Hilbert space. I
explain how this tension can be resolved by splitting the gauge field into
charged constituents, and I argue that this leads to a new argument for the
"principle of completeness", which states that the charge lattice of a gauge
theory coupled to gravity must be fully populated. I also claim that it leads
to a new motivation for (and a clarification of) the "weak gravity conjecture",
which I interpret as a strengthening of this principle. This setup gives a
simple example of a situation where describing low-energy bulk physics in CFT
language requires knowledge of high-energy bulk physics. This contradicts to
some extent the notion of "effective conformal field theory", but in fact is an
expected feature of the resolution of the black hole information problem. An
analogous factorization issue exists also for the gravitational field, and I
comment on several of its implications for reconstructing black hole interiors
and the emergence of spacetime more generally.Comment: 26 pages plus appendices, 8 figures. v2: minor
clarifications/corrections, references adde
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