arXiv subjects

Simon Shaw

Publications and source records attributed to Simon Shaw.

5 recordsLinked to original sources

arXiv2024

Machine Learning Techniques for Source Localisation in Elastic Media

Coronary Artery Disease (CAD) results from plaque deposit in a coronary artery. Early diagnosis is imperative, so a non-invasive detection method is being developed to identify acoustic signals caused by partial occlusions in the artery. The blood flow in the artery is disturbed and imposes oscillatory stresses on the artery wall. The deformations caused by the stresses can be detected at the chest surface. Therefore, by using data simulating these surface signals, which arise from randomly assigned source positions, machine learning (ML) can be utilised to predict the source of the occlusion. Seven ML algorithms were investigated, and the results from this study found that an ensemble model combining k-Nearest Neighbours and Random Forest had the best performance. The metrics used to evaluate this was the mean squared error and Euclidean distance.

eess.SP↗

arXiv2021

A Priori Analysis of a Symmetric Interior Penalty Discontinuous Galerkin Finite Element Method for a Dynamic Linear Viscoelasticity Model

The stress-strain constitutive law for viscoelastic materials such as soft tissues, metals at high temperature, and polymers, can be written as a Volterra integral equation of the second kind with a \emph{fading memory} kernel. This integral relationship yields current stress for a given strain history and can be used in the momentum balance law to derive a mathematical model for the resulting deformation. We consider such a dynamic linear viscoelastic model problem resulting from using a \textit{Dirichlet-Prony} series of decaying exponentials to provide the fading memory in the Volterra kernel. We introduce two types of \textit{internal variable} to replace the Volterra integral with a system of auxiliary ordinary differential equations and then use a spatially discontinuous symmetric interior penalty Galerkin (SIPG) finite element method and -- in time -- a Crank-Nicolson method to formulate the fully discrete problems: one for each type of internal variable. We present \textit{a priori} stability and error analyses without using Gr\"onwall's inequality, and with the result that the constants in our estimates grow linearly with time rather than exponentially. In this sense the schemes are therefore suited to simulating long time viscoelastic response and this (to our knowledge) is the first time that such high quality estimates have been presented for SIPG finite element approximation of dynamic viscoelasticty problems. We also carry out a number of numerical experiments using the FEniCS environment (e.g. \url{https://fenicsproject.org}) and explain how the codes can be obtained and the results reproduced.

math.NA↗

arXiv2020

A priori error analysis for a finite element approximation of dynamic viscoelasticity problems involving a fractional order integro-differential constitutive law

We consider a fractional order viscoelasticity problem modelled by a power-law type stress relaxation function. This viscoelastic problem is a Volterra integral equation of the second kind with a weakly singular kernel where the convolution integral corresponds to fractional order differentiation/integration. We use a spatial finite element method and a finite difference scheme in time. Due to the weak singularity, fractional order integration in time is managed approximately by linear interpolation so that we can formulate a fully discrete problem. In this paper, we present a stability bound as well as a priori error estimates. Furthermore, we carry out numerical experiments with varying regularity of exact solutions at the end.

math.NA↗

arXiv2020

Finite Element Approximation and Analysis of Viscoelastic Scalar Wave Propagation with Internal Variable Formulations

We consider linear scalar wave equations with a hereditary integral term of the kind used to model viscoelastic solids. The kernel in this Volterra integral is a sum of decaying exponentials (The so-called Maxwell, or Zener model) and this allows the introduction of one of two types of families of internal variables, each of which evolve according to an ordinary differential equation (ODE). There is one such ODE for each decaying exponential, and the introduction of these ODEs means that the Volterra integral can be removed from the governing equation. The two types of internal variable are distinguished by whether the unknown appears in the Volterra integral, or whether its time derivative appears; we call the resulting problems the displacement and velocity forms. We define fully discrete formulations for each of these forms by using continuous Galerkin finite element approximations in space and an implicit `Crank-Nicolson' type of finite difference method in time. We prove stability and a priori bounds, and (using the FEniCS environment, https://fenicsproject.org/) give some numerical results. These bounds do not require Gr\"onwall's inequality and so can be regarded to be of high quality, allowing confidence in long time integration without an a priori exponential build up of error. As far as we are aware this is the first time that these two formulations have been described together with accompanying proofs of such high quality stability and error bounds. The extension of the results to vector-valued viscoelasticity problems is straightforward and summarised at the end. The numerical results are reproducible by acquiring the python sources from https://github.com/Yongseok7717, or by running a custom built docker container (instructions are given).

math.NA↗

arXiv2004

Systematic Search for Short-transients and Pulsation Events from INTEGRAL Survey Data

The imaging instruments on board INTEGRAL have wide fields of view and high time resolution. Therefore, they are ideal instruments to search for pulsating sources and/or transient events. We are systematically searching for pulsations and transient events from known and serendipitous sources in the Galactic Plane Scan (GPS) and Galactic Center Deep Exposure (GCDE) core program data. We analyze the standard pipe-line data using ISDC Off-line Science Analysis (OSA) system, so that our results are reproducible by general guest users. In this paper, we describe our system and report preliminary results for the first year of operation.

astro-ph↗