Australian Mathematical Society (AustMS): E-Journals
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A note on étale representations from nilpotent orbits
No full texthttp://dx.doi.org/10.1017/S000497271200033
Automorphism and outer automorphism groups of right-angled Artin groups are not relatively hyperbolic
No full texthttp://dx.doi.org/10.1017/S000497271200033
Some extremal results on the chromatic-stability index
No full texthttp://dx.doi.org/10.1017/S000497271200033
Treating cancerous cells with a continuous release of virus particles
Get PDFWe investigate a model for the treatment of a tumour through the application of a virus. In the original model it was assumed that the virus particles are released only at one time. Such a treatment strategy cannot eliminate a tumour, as the tumour-free steady-state solution is unstable except for pathological circumstances in which the tumour does not grow and/or the virus does not die. We extend the model by allowing the tumour to be treated by a continuous release of virus particles. We show that the scaled delivery rate has two threshold values: below the lower threshold the system evolves to a stable periodic solution; above the higher threshold the tumour is eradicated.
References
C. E. Engeland, J. P. W. Heidbuechel, R. P. Araujo, and A. L. Jenner. Improving immunovirotherapies: The intersection of mathematical modelling and experiments. ImmunoInformatics 6 (2022), p. 100011. doi: 10.1016/j.immuno.2022.100011
A. L. Jenner, A. C. F. Coster, P. S. Kim, and F. Frascoli. Treating cancerous cells with viruses. Lett. Biomath. 5.2 (2018), S117–S136. doi: 10.1080/23737867.2018.1440977
A. L. Jenner, F. Frascoli, C.-O. Yun, and P. S. Kim. Optimising hydrogel release profiles for viro-immunotherapy using oncolytic adenovirus expressing IL-12 and GM-CSF with immature dendritic cells. Appl. Sci. 10.8 (2020). doi: 10.3390/app10082872
J. P. Tian. The replicability of oncolytic virus: Defining conditions in tumor virotherapy. Math. Bio. Eng. 8.3 (2011), pp. 841–860. doi: 10.3934/mbe.2011.8.84
Proceedings of the 2020 Mathematics in Industry Study Group
Get PDFMISG 2020
University of Newcastle, Australia
28 January -- 1 February, 2020
This special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2020 Mathematics and Statistics in Industry Study Group (MISG 2020) held at the University of Newcastle from 28 January -- 1 February 2020. The MISG is a special interest meeting of ANZIAM, the Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) division of the Australian Mathematics Society. The MISG meetings take place annually and provide a forum where projects proposed by industry can be worked on intensively, by high profile scientists in the fields of Applied Mathematics, Statistics and Operations Research, from Australia, New Zealand and the world beyond, along with representatives from the industries proposing the projects.
The writing of these papers was coordinated by the project moderators in consultation with the coauthors and company representatives. The manuscripts were submitted to the editors, Associate Professor Mike Meylan, Professor Ngamta Thamwattana and Professor Tony Roberts, and were subsequently refereed by two expert referees. On the advice of the referees, manuscripts were accepted for publication, subject to the recommended revisions, and formally approved by the editorial committee.
At MISG 2020, six projects were presented from diverse industries, with 78 delegates participating.
Industry Partners
We gratefully acknowledge the support of our industry partners:
Lovells Springs;
Safearth;
Concrush;
Hyper Q Aerospace.
Acknowledgements
In addition to our industry partners, we gratefully acknowledge support from the following organisations:
ANZIAM;
Office of the NSW Chief Scientist \& Engineer, Department of Industry, NSW Government;
Priority Research Centre: Computer Assisted Research Mathematics and its Applications, The University of Newcastle;
Faculty of Science, The University of Newcastle.
We are also grateful to Professor Ryan Loxton from the Centre for Optimisation and Decision Science, Curtin University, for giving a public lecture on power of optimisation research in mining, energy, and agriculture industries, as part of the MISG's outreach event and acknowledge the support from the Hunter Branch of the Royal Society of NSW in promoting the public lecture. We are also grateful to Professor Mark McGuinness (Victoria University of Wellington), Professor Troy Farrell (Queensland University of Technology), Associate Professor Amie Albrecht (University of South Australia) and Dr Neville Fowkes (University of Western Australia) for their helpful advice and comments in organising the MISG 2020.
MISG2020 Organising Committee
Professor Ngamta Thamwattana (Co-Director)
Associate Professor Mike Meylan (Co-Director)
Mrs Juliane Turner (Administrative Support)
Dr David Allingham (Technical Support
Development of rigorous methods in fluid mechanics and theory of water waves
No full textAbstract of my Ph.D. Theses
My scientific supervisors
Professor Yury Stepanyants - USQ
https://staffprofile.usq.edu.au/Profile/Yury-Stepanyants
Assoc Prof Dmitry Strunin - USQ
https://staffprofile.usq.edu.au/Profile/Dmitry-Struni
Look, Knave
No full textWe examine a recursive sequence in which s_n is a literal description of what the binary expansion of the previous term s_{n−1} is not. By adapting a technique of Conway, we determine limiting behaviour of {s_n} and dynamics of a related self-map of 2^{NN}. Our main result is the existence and uniqueness of a pair of binary sequences, each the compliment-description of the other. We also take every opportunity to make puns
Asymptotics of a Gauss hypergeometric function with two large parameters: a new case
No full textAsymptotic expansions of the Gauss hypergeometric function with large parameters, as , are known for many special cases, but not for one that the author encountered in recent work on fluid mechanics: and . This paper gives the leading term for that case if is not a negative integer and is not on the branch cut , and it shows how subsequent terms can be found.
doi:10.1017/S144618111900016
One-dimensional chaotic laminar flow with competitive exothermic and endothermic reactions
No full textWe consider the numerical solution of competitive exothermic and endothermic reactions in the presence of a chaotic advection flow. The resulting behaviour is characterized by a strong dependence on the competitive reaction history. The burnt temperature is not immediately connected to simple enthalpy calculations, so there is a subtlety in the interplay between the major parameters, notably the Damköhler number, the ratio of the heats of exothermic and endothermic reactions, as well as the ratio of their respective activation energies. This paper seeks to explore the way these parameters affect the steady states of these reaction fronts and their stability.
doi:10.1017/S144618112000005
Slow-burning instabilities of Dufort-Frankel finite differencing
No full textDuFort–Frankel averaging is a tactic to stabilize Richardson’s unstable three-level leapfrog timestepping scheme. By including the next time level in the right-hand-side evaluation, it is implicit, but it can be rearranged to give an explicit updating formula, thus apparently giving the best of both worlds. Textbooks prove unconditional stability for the heat equation, and extensive use on a variety of advection–diffusion equations has produced many useful results. Nonetheless, for some problems the scheme can fail in an interesting and surprising way, leading to instability at very long times. An analysis for a simple problem involving a pair of evolution equations that describe the spread of a rabies epidemic gives insight into how this occurs. An even simpler modified diffusion equation suffers from the same instability. Finally, the rabies problem is revisited and a stable method is found for a restricted range of parameter values, although no prescriptive recipe is known which selects this particular choice.
doi:10.1017/S144618112100004