Search results: 965
Overview
There is much active mathematical research into aeroacoustics (the study of sound in aircraft engines). This field is closely followed, and often contributed to (sometimes helpfully) by engineers in both academia and industry (e.g. Airbus, Boeing, NASA, etc). The aim of this course is to give an overview of the mathematical techniques needed to understand the current research problems, and read current papers in the area. This could lead on to several possible PhD projects, including in asymptotics, numerical analysis, and stability theory.
Aims
The application of wave theory to problems involving the generation, propagation and scattering of acoustic and other waves is of considerable relevance in many practical situations. These include, for example, underwater sound propagation, aircraft noise, remote sensing, the effect of noise in built-up areas, and a variety of medical diagnostic applications. This course would aim to provide the basic theory of wave generation, propagation and scattering, and an overview of the mathematical methods and approximations used to tackle these problems, with emphasis on applications to aeroacoustics. The ultimate aim is for students to understand the underlying mathematical tools of acoustics sufficiently to read current research publications on acoustics, and to be able to apply these techniques to current research questions within mathematics, engineering and industry.
Learning Outcomes
- Reproduce standard models and arguments for sound generation and propagation.
- Apply mathematical techniques to model sound generation and propagation in simple systems.
- Understand and apply Wiener-Hopf factorisation in the scalar case.
Approximate Syllabus
- Some general acoustic theory.
- Sound generation by turbulence and moving bodies (including the Lighthill and Ffowcs Williams Hawkings acoustic analogies).
- Scattering (including the scalar Wiener-Hopf technique applied to the Sommerfeld problem of scattering by a sharp edge)
- Long-distance sound propagation including nonlinear and viscous effects.
- Wave-guides.
- High frequencies and Ray Tracing.
Reading List
- D.G. Crighton, A.P. Dowling, J.E. Ffowcs Williams, et al, "Modern Methods in Analyticial Acoustics", Springer 1992.
- M. Howe, "Acoustics & Aerodynamic Sound", Cambridge 2015 (available online through Warwick Library).
- S.W. Rienstra & A. Hirschberg, "An Introduction to Acoustics", (available online).
Module Aims:
Modern interdisciplinary research requires the ability to understand and interpret work of a mathematical and statistical nature that is expressed in an unfamiliar specialist language, to glean from that work the important mathematical and statistical problems and directions of research, to formulate tractable problems and to collaborate in a research team with complementary skills in order to tackle the problems. A key part of the MSc training is this innovative module aimed at preparing students for such research collaborations and teamwork and at training in skills that cannot be taught in a traditional classroom environment.
Teaching:
During
a first stage, the students will learn how to capture and formulate
mathematical or statistical problems from applications. Workshops on hot
interdisciplinary research topics will be organised. In groups of 3-4
people the students engage in one area, receiving guidance in regular
meetings by research study group leader(s). The outcome will be a
project proposal including evidence of own preparatory work and a
presentation followed by a short defense.
During a second stage, the
students will carry out the proposed projects where changes to the
groups are possible subject to balanced group sizes. Guidance will still
be provided in regular meetings by the research study group leader(s)
but more independent working will be required. The outcome will be a
written report, a presentation, a poster and a webpage.
To document
progress, each group will keep a portfolio containing individual and
group elements such as workshop logs, meeting logs, and activity
reports.
Objectives:
Both stages involve team work and training in:
- discussion and study of 'good' mathematical and statistical problems,
- formulation of problems and evaluation with respect to difficulty,
- project planning and management,
- communication, internal (within the group) as well as external (presentations),
- preparation of posters and creation of web-pages to present results.
- Measures, Carathéodory's construction, integration and convergence theorems.
- Riesz representation theorem, weak* convergence and Prokhorov's theorem.
- Hardy-Littlewood maximal inequality and Rademacher’s theorem.
The second part provides an introduction to geometric measure theory. Time permitting, we will cover some of the following topics:
- Hausdorff distance.
- Hausdorff measure, rectifiable and purely unrectifiable sets.
- Sard's theorem.
- The Besicovitch projection theorem.
Overview
There is much active mathematical research into aeroacoustics (the study of sound in aircraft engines). This field is closely followed, and often contributed to (sometimes helpfully) by engineers in both academia and industry (e.g. Airbus, Boeing, NASA, etc). The aim of this course is to give an overview of the mathematical techniques needed to understand the current research problems, and read current papers in the area. This could lead on to several possible PhD projects, including in asymptotics, numerical analysis, and stability theory.
Aims
The application of wave theory to problems involving the generation, propagation and scattering of acoustic and other waves is of considerable relevance in many practical situations. These include, for example, underwater sound propagation, aircraft noise, remote sensing, the effect of noise in built-up areas, and a variety of medical diagnostic applications. This course would aim to provide the basic theory of wave generation, propagation and scattering, and an overview of the mathematical methods and approximations used to tackle these problems, with emphasis on applications to aeroacoustics. The ultimate aim is for students to understand the underlying mathematical tools of acoustics sufficiently to read current research publications on acoustics, and to be able to apply these techniques to current research questions within mathematics, engineering and industry.
Learning Outcomes
- Reproduce standard models and arguments for sound generation and propagation.
- Apply mathematical techniques to model sound generation and propagation in simple systems.
- Understand and apply Wiener-Hopf factorisation in the scalar case.
Approximate Syllabus
- Some general acoustic theory.
- Sound generation by turbulence and moving bodies (including the Lighthill and Ffowcs Williams Hawkings acoustic analogies).
- Scattering (including the scalar Wiener-Hopf technique applied to the Sommerfeld problem of scattering by a sharp edge)
- Long-distance sound propagation including nonlinear and viscous effects.
- Wave-guides.
- High frequencies and Ray Tracing.
Reading List
- D.G. Crighton, A.P. Dowling, J.E. Ffowcs Williams, et al, "Modern Methods in Analyticial Acoustics", Springer 1992.
- M. Howe, "Acoustics & Aerodynamic Sound", Cambridge 2015 (available online through Warwick Library).
- S.W. Rienstra & A. Hirschberg, "An Introduction to Acoustics", (available online).
2017 Cohort
The SSC 2 Block will give you the opportunity to undertake a project (research, audit or service evaluation) and attend a series of lectures and seminars supporting the development of your enquiry and research skills.