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 higher-order Stokes Phenomenon
- Multiple scales techniques on discrete domains

Fluid Dynamics

- Free-surface 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 exponentially-small gravity-capillary waves
- Near-solitary wave dynamics in chains of particles
- Asymptotic studies of discrete integrable systems
- Hele-Shaw 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 2019-21.

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 three-dimensional 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.

## Fingerprint Fingerprint is based on mining the text of the person's scientific documents to create an index of weighted terms, which defines the key subjects of each individual researcher.

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## Projects 2017 2019

- 2 Active

## Research Output 2012 2018

- 39 Citations
- 3 h-Index
- 14 Article

## Generalized solitary waves in a finite-difference Korteweg-de Vries equation

Joshi, N. & Lustri, C. 2018 (Submitted) In : ArXiv e-prints.Research output: Contribution to journal › Article

## Nanoptera in a period-2 Toda chain

Lustri, C. J. & Porter, M. 19 Apr 2018 In : SIAM Journal on Applied Dynamical Systems. 17, 2, p. 1182–1212 31 p.Research output: Contribution to journal › Article

## Nonlinear q-Stokes phenomena for q-Painlevè I

Joshi, N., Lustri, C. & Luu, S. 2018 (Accepted/In press) In : Journal of Physics A: Mathematical and Theoretical.Research output: Contribution to journal › Article

## Selection of a Hele-Shaw bubble via exponential asymptotics

Lustri, C. J., Green, C. C. & McCue, S. W. 2018 (Submitted) In : ArXiv e-prints.Research output: Contribution to journal › Article

## Standing lattice solitons in the discrete NLS equation with saturation

Alfimov, G. L., Korobeinikov, A. S., Lustri, C. J. & Pelinovsky, D. E. 2018 (Submitted) In : ArXiv e-prints.Research output: Contribution to journal › Article