Christopher Lustri

Dr

  • 62 Citations
  • 4 h-Index
20122022
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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 Dive into the research topics where Christopher Lustri is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

Exponential Asymptotics Mathematics
Stokes Mathematics
Solitons Engineering & Materials Science
Painlevé Mathematics
Discrete Equations Mathematics
Froude number Engineering & Materials Science
Gravity waves Engineering & Materials Science
Free Surface Flow Mathematics

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Projects 2017 2022

Research Outputs 2012 2019

  • 62 Citations
  • 4 h-Index
  • 16 Article

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

Joshi, N. & Lustri, C. J., Apr 2019, In : Studies in Applied Mathematics. 142, 3, p. 359-384 26 p.

Research output: Contribution to journalArticleResearchpeer-review

Korteweg-de Vries equation
Solitary Waves
Solitons
Korteweg-de Vries Equation
Difference equation

Nanoptera and Stokes curves in the 2-periodic Fermi–Pasta–Ulam–Tsingou equation

Lustri, C. J., 25 Oct 2019, (Accepted/In press) In : Physica D: Nonlinear Phenomena. 132239.

Research output: Contribution to journalArticleResearchpeer-review

Solitons
Stokes
Exponential Asymptotics
Oscillation
oscillations

Nonlinear q-Stokes phenomena for q-Painlevé I

Joshi, N., Lustri, C. J. & Luu, S., 21 Jan 2019, In : Journal of Physics A: Mathematical and Theoretical. 52, 6, p. 1-30 30 p., 065204.

Research output: Contribution to journalArticleResearchpeer-review

Open Access
File
Painlevé
power series
Difference equations
Stokes
Power series

On asymptotics of optimal stopping times

Lustri, C. & Sofronov, G., 5 Apr 2019, (Submitted) In : arXiv e-prints. 14 p.

Research output: Contribution to journalArticleResearchpeer-review

Optimal Stopping Time
Upper bound
Asymptotic Behavior
Statistics
Optimal Stopping Problem

Standing lattice solitons in the discrete NLS equation with saturation

Alfimov, G. L., Korobeinikov, A. S., Lustri, C. J. & Pelinovsky, D. E., Sep 2019, In : Nonlinearity. 32, 9, p. 3445-3484 40 p.

Research output: Contribution to journalArticleResearchpeer-review

NLS Equation
Discrete Equations
Solitons
Discrete Nonlinear Schrödinger Equation
Saturation