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.