2,962 research outputs found
Multiparameter spectral analysis for aeroelastic instability problems
This paper presents a novel application of multiparameter spectral theory to
the study of structural stability, with particular emphasis on aeroelastic
flutter. Methods of multiparameter analysis allow the development of new
solution algorithms for aeroelastic flutter problems; most significantly, a
direct solver for polynomial problems of arbitrary order and size, something
which has not before been achieved. Two major variants of this direct solver
are presented, and their computational characteristics are compared. Both are
effective for smaller problems arising in reduced-order modelling and
preliminary design optimization. Extensions and improvements to this new
conceptual framework and solution method are then discussed.Comment: 20 pages, 8 figure
Non-uniqueness in conformal formulations of the Einstein constraints
Standard methods in non-linear analysis are used to show that there exists a
parabolic branching of solutions of the Lichnerowicz-York equation with an
unscaled source. We also apply these methods to the extended conformal thin
sandwich formulation and show that if the linearised system develops a kernel
solution for sufficiently large initial data then we obtain parabolic solution
curves for the conformal factor, lapse and shift identical to those found
numerically by Pfeiffer and York. The implications of these results for
constrained evolutions are discussed.Comment: Arguments clarified and typos corrected. Matches published versio
A finite element method for fully nonlinear elliptic problems
We present a continuous finite element method for some examples of fully
nonlinear elliptic equation. A key tool is the discretisation proposed in
Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of
a linear PDE. An added benefit to making use of this discretisation method is
that a recovered (finite element) Hessian is a biproduct of the solution
process. We build on the linear basis and ultimately construct two different
methodologies for the solution of second order fully nonlinear PDEs. Benchmark
numerical results illustrate the convergence properties of the scheme for some
test problems including the Monge-Amp\`ere equation and Pucci's equation.Comment: 22 pages, 31 figure
Circuit Synthesis of Electrochemical Supercapacitor Models
This paper is concerned with the synthesis of RC electrical circuits from
physics-based supercapacitor models describing conservation and diffusion
relationships. The proposed synthesis procedure uses model discretisation,
linearisation, balanced model order reduction and passive network synthesis to
form the circuits. Circuits with different topologies are synthesized from
several physical models. This work will give greater understanding to the
physical interpretation of electrical circuits and will enable the development
of more generalised circuits, since the synthesized impedance functions are
generated by considering the physics, not from experimental fitting which may
ignore certain dynamics
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
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