Projects per year
Personal profile
Research interests
I am an expert in using asymptotic methods to find solutions to continuous and discrete problems arising within applied mathematics.
In particular, I am interested in using exponential asymptotic techniques to explore behaviour that is invisible to classical asymptotic methods. I spend a lot of time looking at a special class of behaviour known as the Stokes Phenomenon, that only appears at exponentially small orders in an asymptotic expression. Understanding this behaviour can be an important way to describe effects that normally lie beyond the reach of common asymptotic methods.
My research largely falls into three themes:
Asymptotic Methods
 Exponential asymptotics in differential and difference equations
 Ordinary and higherorder Stokes Phenomenon
 Multiple scales techniques on discrete domains
Fluid Dynamics
 Freesurface flows and water waves
 Formation of air bubbles in viscous fluid
Discrete Systems
 Approximating solutions to discrete special functions
 Solitary wave behaviour in particle chains and lattices
 Bifurcations in discrete systems
Research student supervision
I am always looking for talented students with an interest in asymptotics, fluid dynamics, or discrete systems. I offer a range of projects, including:
 Behaviour of exponentiallysmall gravitycapillary waves
 Nearsolitary wave dynamics in chains of particles
 Asymptotic studies of discrete integrable systems
 HeleShaw flow interfaces on complicated domains
Biography
I am a Lecturer in Applied Mathematics at Macquarie University. In 2018, I was awarded an Australian Research Council Discovery Fellowship for 201921.
I studied a BEng (Hons)/BAppSci (Hons) at the Queensland University of Technology in Brisbane, writing an Honours and Masters project with Prof. Scott McCue. I moved to the University of Oxford in 2009 to study for my DPhil., under the supervision of Prof. Jon Chapman, studying exponential asymptotics in unsteady and threedimensional flows. I was awarded my doctorate in 2013.
I moved back to Australia, and worked at The University of Sydney as a postdoc with Prof. Nalini Joshi on the asymptotics of discrete integrable systems. In 2016, I was appointed as a Lecturer in Applied Mathematics at Macquarie University.
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Network
Projects

A new asymptotic toolbox for nonlinear discrete systems and particle chains
4/02/19 → 3/02/22
Project: Other


New mathematical analysis of multiphase fluid flows
Green, C. & Lustri, C.
1/01/18 → 31/12/19
Project: Other
Research Outputs
 87 Citations
 6 hIndex
 19 Article

Morphogenesis of mesoscopic surface patterns formed in polarized twophoton etching of diamond
Berhane, A. M., Baldwin, C. G., Liang, K., Moshkani, M., Lustri, C., Downes, J. E., Stampfl, C. & Mildren, R. P., 1 Mar 2021, In : Carbon. 173, p. 271285 15 p.Research output: Contribution to journal › Article
Open AccessFile 
A note on the Stokes phenomenon in flow under an elastic sheet
Lustri, C. J., Koens, L. & Pethiyagoda, R., 4 Sep 2020, In : Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 378, 2179, p. 116 16 p., 20190530.Research output: Contribution to journal › Article

Kelvin wake pattern at small Froude numbers
Pethiyagoda, R., Moroney, T. J., Lustri, C. J. & McCue, S. W., 9 Sep 2020, (Submitted) In : arXiv.org ePrint archive.Research output: Contribution to journal › Article

Nanoptera and Stokes curves in the 2periodic Fermi–Pasta–Ulam–Tsingou equation
Lustri, C. J., 15 Jan 2020, In : Physica D: Nonlinear Phenomena. 402, p. 113 13 p., 132239.Research output: Contribution to journal › Article
3 Citations (Scopus) 
Generalized solitary waves in a finitedifference Kortewegde Vries equation
Joshi, N. & Lustri, C. J., Apr 2019, In : Studies in Applied Mathematics. 142, 3, p. 359384 26 p.Research output: Contribution to journal › Article
2 Citations (Scopus)