1( 2 · I· & · 1'3.

34 /1981

'I'll! : /\11.';'IH/\l.1/\N N/\'l'l()N/\1. llNIVl : l~Sl'l'Y

OEP/\RTMENT OF /\PPLIED MATIIEM/\TICS

Annual Report, 1980

Aims and development of department

At the end of 1980 the work of the department was under investigation

by a review committee and this has encouraged all members of staff to con­

sider the past achievements of the department, its current state of health

and the direction its development should take over the next decade. Since

the department was formed, it has been conscious of the need for careful

undergraduate teaching and has concentrated mainly on showing students how mathematics can be used in different branches of the physical and biological

sciences. It has produced a Rhodes Scholar and four University Medallists

and eight of its honours or M.Sc. graduates have gone on to complete a Ph.D.

The department has not attracted many post-graduate students but its output

of research papers has been good and two members of staff have been promoted

to professorships at other universities.

One feature of the department's research has been its collaboration

with other groups in making use of mathematical methods. This tradition

is still being maintained. For many years the department has been linked

with the Mount Stromlo Observatory and there are links at present via cosmol­

ogy and research on white dwarf stars. Another important link is with the

Division of Mathematics and Statistics, CSIRO. Dr Diesendorf (OMS) and Dr

Martin have worked together to study the feasibility of power generation

from wind energy and to study the characteristics of various machines which

make use of wLnd .energy. A development of this might be an interest in the

cost and characteristics of devices for generating energy from sea waves, a

topic on which little research appears to have been done so far in Australia.

Another line of development arises from our increasing interest in

npplications of mathematics to biological problems. However, any develop­

ment is eloucll'cl by uncertainty about the future of the department, for

although we hclicve firmly that Applied Mathematics ought to be continued as

a separate discipline we have no guarantee at present that this view will prevail.

Cou rscs, course changes :rn<l enrolments

Our enrolments in first-year units decreased again and this is causing

concern, since it is liable to be reflected in our second-year enrolments in

1981. For 1980, the consolidation of the second year units into one-point

units, in place of half-point units, appeared to be an improvement and we

propose to continue this in 1981.

We wert· able to take advantage of the presence of a v1s1 tor in the department (Dr E.R. Lapwood) to put on a course on Seismology and Elasto ­

dynamics. This was for our third-year and fourth-year honours students.

Another interesting course for these students was on "Mathematical Modelling",

where the emphasis was on devising suitable mathematical equatjons for a

given problem. /\s part of the course, each student picked out a problem for h imscl f, set up :1 system of t>qtwt ions ;md worked out a solution (using

numeric~il methods :is required). The student then gave a 20-minute seminar

- 2 -34/1981

talk on his project and wrote up the results as a report. Although this unusual course required a lot of work by the lecturer in charge, it was

highly successful and the students enjoyed the challenge it presented.

J\ table of enrolments and examinatjon results ls given ut the end of the report. (Since percentage figures c:rn he mislc<.icling when only a -;m:dl

llltl!llH.'r or students is involved, thl' tahlcs show <ll"tlJ:il 1111111hers r;ithcr· th:in

percentages.) One encour:.iging feature was that we liau two very good sluucnts in the final honours year for Applied Mathematics. One of them w<.is awarded

a special grant by the Australian Institute of Nuclear Science and Engineer­ing because her honours project was of interest to the Applied Mathematics

Group at Lucas Heights (Atomic Energy Commission). Both these students obtained first-class honours.

At the end of 1979, one of our fourth-year students (P.M. Nanninga) was awarded a University Medal. (The information came too late to be incl-

uded in our 1979 report.) Two of the students were awarded Ph.D. scholar­ships at the Mount Stromlo Observatory.

Student Participation

The departmental committee met three times during the year and in addition the student representatives Met separately to elect a represent­ative on the Review Committee. Indeed the second of the committee meetings was taken up almost entirely with a discussion of the membership and functions

of the Review Committee. The Vice-Chancellor attended the meeting and explained the procedure that had been followed in reviews of other depart­

ments. In this case, the Departments of Applied Mathematics and Pure Mathematics were to be reviewed together so some modifications of the usual

procedure would be required.

The departmental committee also discussed assessment procedures and the weighting that should be given to different components of the assessment.

Another topic that was discussed in some detail was the choice of textbooks. It appeared that the book lists issued by the department were helpful, although a difficulty had arisen in connection with one book which was out of print and not being reprinted.

Staff

Professor: Reader: S/Lecturers:

Lecturer:

Temporary Lecturers:

Ter.iporary Tutor:

Research Assistant: Secretary:

A. Brown, M. /\. (Glas), Ph.D. (Can tab) J.E. Drummond, M.Sc. (NZ), B.A. (Cantab) S.M.A. Meggitt, M.A. (Oxon), M.Sc. (Natal),

Ph.D. (A.N.U.) (on study leave, July-December, 1980)

D.T. \hckramasinghe, M.A. (Cantab), .. Ph.D. (Cantab) (on leave without pay throughout year) 11.F. Petersons, M.Sc. (Syd), Ph.D. (SyJ)

~'J.P. llealy, 3.Sc. (LonJ), Ph.D. (Llrnd) D.3. Stewart-Richardson, 3.Sc. (SyJ),

M.Sc. (N.E.)

G.M. D'Este, B.Sc. (A.N.U.)

B.L. Martin, B./\. (Rice), Ph.D. (Syd) B. I-lawkins.

In addition to the full-time staff listed above, the department had

the assistance of several part-time tutors. Of these, ir C . .J. 1~11rdcn and

. ) .~'1 /I ~JK I

llr ~~-"- Ts.ing were ;1vailable throughout the year, Mr C.R. Fulford and Miss

.J .II .. Jenkinson for first semester and Mr R. Black for second semester.

nr Meggitt was gra11ted six months' study leave and has been working

al the Royal Observatory, Edinburgh. Mainly he has been studying predict­

ion s of spectra and polarisation for stars which show cyclotron radiation,

:iltho1Jgh he has a wider interest in the internal structure and atmosphere of

sta rs.

Dr Ilc:ily h;i s conti1111cd \VJ'It1ng hi s hook on qu~rntum mech;111ics ;1nd he

gave ;1 lt'cturt' course on this topic during the ye;1r. Mr D'l :stc worked on

traffic flow problems, us ing opcr;1tion research techniques, and he ha·; sub­

mitted several papers for publication. (Some of these have been accepted

but will not be published until 1981 or 1982.)

Dr Martin and Professor Brown presented papers at the A.~ZAAS meeting

in Adelaide in May. The paper by Professor Brown was on a diffusion problem

which involved the diffusion of a toxic substance into two different types

of seaweed, one commercially valuable and the other of negligible value. In

practice the two types are found tangled together and the toxic substance was

intended to kill off the non-valuable seaweed without damaging the valuable

species. This was to enable experimental work to be carried out on the

valuable species without having the results blurred by the presence of the other

species. From a mathematical point of view it was a question of finding

critical values for a non-dimensional parameter which controlled the

diffusion rate into the two types of seaweed. (This work has also been

accepted for publication but will not appear until 1981.)

Our most important visitor for the year was Dr E.R. Lapwood, Cambridge

llnivcrsity, who gave several seminars and made a valuable contribution to our

undergraduate teaching with a course of 12 lectures on elastic vibrations and

se ismology. Later in the year, Dr R.J . Y. McLeod, New Mexico State University,

visited the department for a few days and gave a seminar on a numerical

analysis problem.

The department helped to sponsor a successful one-day seminar on 11 TI1e

Applications of Mathematics in Industry". The principal organisers of the

seminar were Ors Anderssen and De Hoag (Division of Mathematics and Statistics,

CSIRO), who arranged the programme for the seminar and found a publisher for

the proceedings. Our contribution was mainly financial although members of

the department attended the seminar and made minor contributions to the dis­

cussion.

Publications

Brown, A. By-passing an awkward turning, Mathematics Gazette, 64,

(1980). (Page numbers not available.)

Healy, W.P. Path-dependent Lagrangians in relativistic electro­

dynamics, Journal of Physics, A: Mathematical and General, 13,

2 382- 2393' (1980) .

Martin, B. N1 1c-lear Knights (Canberra: Rupert Public Interest

Movcm<'n t , l 980) .

Martin, 13. Mahi 1 ising ngainst nuclear war . .!_, (6/7)' 6-11 (1980).

Social J\ltcrnativcs,

Martin, B. Sources of political power in academia. In Miller, A.H .

(ed.), Research & Development in Higher Education. Volume 3.

Freedom and Control in Higher Education (Sydney: Higher

Education Research and Development Society of Australasia, 1980),

- 4 - 34/1981 •

pp. 180-184.

Martin, B. an<l lhesendorf, M.* The capacity credit of wind power: a numerical model. Procce<lings 3rd International Sympo s ium on Win<l Energy Systems, BHRJ\ Fluid Engineering, Cranfi e ld, Bedford, England, Paper No. L3, pp. 555-564 (Aup;us t 1980).

Martin, B. and Wickramasinghe, D.T. Methods for calculating circular polarisation in magnetic white dwarfs. Proceedings

of the Astronomical Society of Australia, l· 351-352 (1979).

Martin, B. and Wickramasinghe, D.T. Solutions for radiative transfer

in magnetic atmospheres. Monthly Notices of the Royal Astronomical Society, 189, 883-895 (1979).

Petersons, 11.r. (1980).

Symmetry and Maximisation, Circuit, no. 105, p.11

Wickramasinghe, D. T. and Martin, B. Models for GD90 and G99-47. New Zealand Journal of Science, ~' 441-443 (1979).

DEPARTill:~;T OF

Subject Enrolled Sitting

or Unit

Al2 16 13

A21 54 44

A22 42 38 A31H 40 38

A32H 34 _,, .)_

B27 36 35

B28 30 29

B37H 11 11

B38H 9 9

B30H 6 6

C27 11 11

C28 10 9

C31H 5 5

C32H 3 3

C34H 2 2

C35H 5 4

C36H 1 1

C37H 5 4

Final honours

M.Sc.

- 5 - 34/1981

TI-IE . .\USTRALIAN NATIO. AL illJIVERS ITY

APPLIED ~IA TI-IBlATICS ANALYSIS OF

Wastage Failure Sitting

3 1 13

10 6 44

4 7 38 2 2 38 2 3 32

1 4 35

1 4 29

0 0 11 0 1 9

0 0 6

0 0 11 1 0 9

0 0 5

0 0 3

0 0 2

1 0 4

0 0 1 1 0 4

Enrolled (as at 30/4/80)

3

1

STUDEYf PERFORl'-IANCE

High Distinction

0 4 0 9 7

2 1 3 2 1

1 2 0 1 0 1 0 1

Sitting 3

Distinction

3 10

9 8 5

5 4 3 2 1

1 0 0 0 1 1 1 0

Results Hl 2,

• Credit Pass Fail

2 ..,

1 9 15 6 8 l .+ 7

15 .+ 2

8 9 3

5 19 4

7 13 4 4 1 0 3 1 1

3 l 0

4 - 0 ;:i

3 -+ 0 4 1 0 2 0 0

0 1 0 0 2 0 0 0 0 1 2 0

H2A 1.