## Professor A Russell Davies

### Overview

Telephone: +44(0)29 208 74827

Fax: +44(0)29 208 74199

Extension: 74827

Location: M/1.17

**Research Interests**

Inverse problems in materials characterization.

Numerical inversion of integral transforms.

Mechanics of time-dependent materials.

Mathematical problems in imaging science.

Computational partial differential equations.

**Research Group**

#### Recent Significant Publications

**Anderssen RS, Davies A R, de Hoog FR**. On the Volterra integral equation relating creep and relaxation. INVERSE PROBLEMS Volume: 24 Issue: 3 Article Number: 035009 13pp Published: 2008 doi: 10.1088/0266-5611/24/3/035009

**Anderssen RS, Davies A R, de Hoog FR. **The effect of kernel perturbations when solving the interconversion convolution equation of linear viscoelasticity. APPLIED MATHEMATICS LETTERS Volume: 24 Issue: 1 Pages: 71-75 Published: 2011

**Anderssen RS, Davies A R, de Hoog FR. **On the sensitivity of interconversion between relaxation and creep. RHEOLOGICA ACTA Volume: 47 Issue: 2 Pages: 159-167 Published: 2008

**Teaching**

**Administrative Duties**

Financial Matters/Financial Plan

Management of School

Staff Appraisal and Development

Strategic Plan/Annual Report

Teaching Loads

Chair of the School Management Committee

Member of School Admissions Committee

Member of School Research Committee

Member of School Staff/Student Panel

Member of School Teaching and Learning Committee

### Publications

#### Recent papers on inverse problems

1. A.R. Davies and R.S. Anderssen. Sampling Localization in Determining the Relaxation Spectrum. J. Non-Newtonian Fluid Mech. 73, 163-179, 1997.

2. A.R. Davies and R.S. Anderssen. Sampling Localization and Duality Algorithms in Practice. J. Non-Newtonian Fluid Mech. 79, 235-253, 1998.

3. A.R. Davies and C.M Newbury. Moving average formulae for the direct recovery of the relaxation spectrum. In “ Proceeding of the XIIIth International Congress in Rheology” D M Binding, N E Hudson, J Mewis, J-M Piau, C J S Petrie, P Townsend, M H Wagner and K Walters (Eds.), British Society of Rheology, Glasgow, 2, 205-207, 2000.

4. R.J. Loy, C.M. Newbury, R.S. Anderssen and A.R. Davies. A duality proof ofsampling localization. Bulletin Aust. Math. Soc., 64. 265-269, 2001

5. R.S. Anderssen and A.R. Davies. Simple Moving Average Formulae for Estimating the Relaxation Spectrum. J. Rheology 45,1-27, 2001.

6. A.R. Davies, D. Morgan and P.R. Williams. Relating the relaxation spectrum to wave dispersion data. Journal of Non-Newtonian Fluid Mechanics 124, 25-32, 2004.

7. A.R. Davies and P.R Williams. Recent advances in differential mechanical spectroscopy. Proceedings: XVIth International Congress of Rheology, RE35 pp1-4, Korean Society of Rheology, Seoul 2004.

8. A. Nikonov, A. R. Davies and I. Emri. The determination of creep and relaxation functions from a single experiment. J. Rheol. 49 (2005) 1193-1211

9. R. S. Anderssen, A.R. Davies and F. R. de Hoog. On interconversion between creep and relaxation functions. The ANZIAM Journal, 48 (2006) C346-C363.

10 . R. S. Anderssen, A.R Davies and F. R. de Hoog. On the sensitivity of interconversion between relaxation and creep Rheologica Acta online: 10.1007/s00397-007-0223-6.

### Research

#### External Funding Since 2000

**2000-02**: The computation of complex industrial EPSRC £49,800 non-Newtonian flows -JREI

**2000-4:** Mathematical and Numerical Modelling of Leaf(UK) Confectionery Manufacture -EPSRC £38,500

**2000-3:** Complex fluids and complex flows. EPSRC £583,000 UWS/UWA Platform Grant

**2001:** Resource capital for complex fluids research HEFCW £100,000

**2002-7:** Unilever Research Consultancy Unilever £70,000

**2004-6:** SRIF2 Resource for Computational Fluid Dynamics HEFCW £650,000

#### Major Conference Talks Since 2004

Aug 2004. Relating the Relaxation Spectrum to Wave Dispersion Data. VIIIth International Workshop on Time Dependent Materials, Bled.

Jan 2005. Wobble, Creep and Relaxation: Modelling Materials with Memory. SIAM UK-IE Meeting, Cork.

April 2005. Determining Creep and Relaxation Functions from a Single Experiment. AERC 2005, Grenoble.

October 2005. On Creep and Relaxation. Vth International Conference on Mechanics of Time Dependent Materials. Nagano, Japan.

August 2006. Recent advances in Linear Viscoelasticity. IXth International Workshop on Time Dependent Materials. Portoroz.

### Postgraduate Students

#### Current

#### Graduated (Since 2000)

D.Morgan

G. Bowers

M. al Hodaly

S.L.Huang

Eman el Aidarous

### Biography

#### Qualifications

**1969 **- BSc Hons Mathematics and Physics, King’s College, London

**1971** - MSc (Mathematics), Oxford University, Balliol College

**1974** - D Phil (Mathematics), Oxford University, Balliol College

**Scholarships** - Thomas and Elizabeth Williams Scholar, 1970-73; Balliol College Graduate Award, 1971-1973

#### **Membership of
Learned Societies**

Institute of Mathematics and its Applications (MIMA, CMath)

London Mathematical Society

British Society of Rheology

SIAM

#### Appointments

**1973-75:** Atlas Research Fellow in Mathematics,
Pembroke College Oxford and SERC Rutherford-Appleton Laboratory

**1976-85:** Lecturer in Applied Mathematics, The University College of Wales, Aberystwyth

**1984:** Visiting Fellow, Centre for Mathematical Analysis, Australian National University

**1984:** Visiting Scientist, Division of Mathematics and Statistics, CSIRO, Canberra

**1984-86:** Senior Lecturer in Applied Mathematics, UCW, Aberystwyth

**1986:** Visiting Fellow, Centre for Mathematical Analysis, Australian National University

**1986-90:** Reader in Mathematics, UCW, Aberystwyth

**1990:** Visiting Fellow, Centre for Mathematical Analysis, Australian National University

**1990-to date: **Professor of Mathematics, UCW, Aberystwyth (now UWA)

**1990:** Visiting Fellow, Department of Mathematics, Melbourne University

**1998:** Visiting Scientist, CSIRO Mathematical and Information Sciences, Canberra

**2000:** Visiting Scientist, CSIRO Mathematical and Information Sciences, Canberra

**2000-2003:** Head of Department of Mathematics, UWA

**2006:** Visiting Scientist, CSIRO Mathematical and Information Sciences, Canberra

2006-to date: Head of the School of Mathematics, Cardiff University

#### Editorial Boards and Advisory Committees

**Editorial Board: **Inverse Problems (1988-92)

**Editorial Board:** Numerical Methods for Partial Differential Equations, 1992-

**Council:** British Society of Rheology (1994 - 2000)

**Scientific Committee:** Smith Institute for Industrial Mathematics and System Engineering, 2000–2006

**Scientific Committee:** KTN for Industrial Mathematics 2007-

#### Awards and Honours

**Annual Award:** British Society of Rheology 2005

**President: **Society of Industrial and Applied Mathematics, United Kingdom and Ireland m2007-2009

**Consultancies**

National Physical Laboratory, Teddington

Shell Research Limited, Thornton

RAPRA Technology, Shawbury

BICC Cables, Chester

Devro-Teepak Limited, Moodiesburn

Nestle Research Laboratory, Lausanne

Leaf UK, Southport

Unilever UK, Port Sunlight