Dr Isaac Towers

Undergraduate Coordinator
+61 2 5114 5050
02 6268 8786

LOCATION

Room 132a PEMS South (Bldg 26) School of Science, UNSW Canberra, Australian Defence Force Academy, PO Box 7916, Canberra BC ACT 2610, AUSTRALIA

  • ABOUT
  • PUBLICATIONS

Dr Isaac Towers is a Senior Lecturer in the School of Physical, Environmental and Mathematical Sciences at UNSW Canberra.

Current Research

  • Stochastic differential equations
  • Ecological modelling
  • Nonlinear dynamics
  • Combustion waves

PhD Opportunities and Scholarships

If you are interested in PhD research in Applied Mathematics contact: Dr Isaac Towers, i.towers@adfa.edu.au

Current Postgraduate Students

  • Chad Anderson (PhD) - Analysis of Population Dynamics subject to Environmental Changes
  • Paul Hartlipp (MPhil) - An investigation of coastal sea surface measurements for the Maritime Continent using SARAL/Altika Satellite measurements
  • Luis Mijangos Aruajo (PhD) - Genetics for Forecasting and Managing Biodiversity
  • Rashed Saifuddin (PhD) - Developing realistic models for stressed ecosystems
  • Chris Thomas (PhD) - Incorporation of spotting and intrinsic fire dynamics in a coupled atmosphere-fire modelling framework
  • Hilyati Zazali (PhD) - Stochastic bushfire spread modelling

Past Postgraduate Students

  1. Andrew Robards (MPhil) - The cost efficiency of different freight modes
  2. Dr. Zhejun Huang  (PhD) - Combustion waves in a two-stage sequential exothermic-endothermic reaction scheme
  3. Chad Anderson (MPhil) - Population Dynamics in a Stochastic Environment
  4. Tom Dose (Honours) - Discrete population dynamics with varying carrying capacity
  5. Dr. Hamizah Safuan - Mathematical Analysis of Population Growth Subject to Environmental Change (2014 Ria de Groot Prize Winner)
  6. Yang Sun (MPhil) -  Soliton Dynamics in Frequency-Modulated Lattices

 

 

Journal articles

Amirian MM; Towers IN; Jovanoski Z; Irwin AJ, 2020, 'Memory and mutualism in species sustainability: A time-fractional Lotka-Volterra model with harvesting', Heliyon, vol. 6, pp. e04816 - e04816, http://dx.doi.org/10.1016/j.heliyon.2020.e04816

Huang Z; Sidhu HS; Towers IN; Jovanoski Z; Watt S; Gubernov VV, 2020, 'Properties of nonadiabatic combustion waves in competitive exothermic reactions', Applied Mathematical Modelling, vol. 77, pp. 1216 - 1228, http://dx.doi.org/10.1016/j.apm.2019.09.010

Ang TK; Safuan HM; Sidhu HS; Jovanoski Z; Towers IN, 2019, 'Impact of Harvesting on a Bioeconomic Predator–Prey Fishery Model Subject to Environmental Toxicant', Bulletin of Mathematical Biology, vol. 81, pp. 2748 - 2767, http://dx.doi.org/10.1007/s11538-019-00627-8

Watt SD; Sidhu HS; Jovanoski Z; Towers IN; Huang Z, 2019, 'Watershed initial conditions for propagating waves in a system with bistability: A weight-function approach', Applied Mathematics Letters, vol. 91, pp. 106 - 112, http://dx.doi.org/10.1016/j.aml.2018.11.018

Huang Z; Sidhu H; Towers I; Jovanoski Z; Watt S, 2018, 'On the route to extinction in non-adiabatic flames from competitive exothermic reactions', Mathematical Modelling of Natural Phenomena, vol. 13, http://dx.doi.org/10.1051/mmnp/2018047

Huang Z; Sidhu H; Towers I; Jovanoski Z; Gubernov V, 2017, 'Stability analysis of combustion waves for competitive exothermic reactions using Evans function', Applied Mathematical Modelling, vol. 54, pp. 347 - 360, http://dx.doi.org/10.1016/j.apm.2017.09.055

Dose T; Jovanoski Z; Safuan HM; Sidhu H; Towers I, 2017, 'Dynamics of a Discrete Non-Autonomous Ricker Model', Journal of Engineering and Applied Science, vol. 12, pp. 2304 - 2309, http://dx.doi.org/10.3923/jeasci.2017.2304.2309

Saifuddin R; Jovanoski Z; Safuan HM; Towers I; Sidhu H, 2017, 'Stability of a Population in a Model with Delayed Environmental Response', Journal of Engineering and Applied Sciences, vol. 12, pp. 2299 - 2303, http://dx.doi.org/10.3923/jeasci.2017.2299.2303

Huang Z; Sidhu HS; Towers IN; Jovanoski Z; Gubernov VV, 2017, 'Properties of combustion waves in a model with competitive exothermic reactions', Journal of Mathematical Chemistry, vol. 55, pp. 1187 - 1201, http://dx.doi.org/10.1007/s10910-017-0733-0

Anderson C; Jovanoski Z; Sidhu H; Towers I, 2016, 'Logistic equation with a simple stochastic carrying capacity', ANZIAM Journal, vol. 56, pp. C431 - C445, http://dx.doi.org/10.0000/anziamj.v56i0.9386

Huang Z; Sidhu HS; Towers IN; Jovanoski Z; Gubernov VV, 2016, 'Nonadiabatic combustion waves in a two-step competitive exothermic-reaction model', Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, vol. 57, pp. C14 - C31, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/10391/0

Huang Z; Sidhu H; Towers I; Jovanoski Z; Gubernov V, 2015, 'Reaction waves in solid fuels for adiabatic competitive exothermic reactions', ANZIAM Journal, vol. 56, pp. C148 - C162, http://dx.doi.org/10.0000/anziamj.v56i0.9343

Towers IN; Jovanoski Z; Sidhu HS; Safuan H, 2015, 'On travelling wave solutions of the diffusive Leslie–Gower model', Applied Mathematics and Computation, vol. 274, pp. 362 - 371, http://dx.doi.org/10.1016/j.amc.2015.10.088

Safuan H; Sidhu H; Jovanoski Z; Towers I, 2014, 'A two-species predator-prey model in an environment enriched by a biotic resource', ANZIAM Journal, vol. 54, pp. C768 - C787, http://dx.doi.org/10.0000/anziamj.v54i0.6376

Sidhu H; Sharples J; Towers I; Gubernov V; wee W, 2013, 'Properties of reaction fronts in a non-adiabatic two stage exothermic-endothermic competitive reaction scheme', ANZIAM Journal, vol. 54, http://dx.doi.org/10.0000/anziamj.v54i0.6302

Towers I; Gubernov V; Kolobov AV; Polezhaev AA; Sidhu HS, 2013, 'Bistability of flame propagation in a model with competing exothermic reactions', Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences, vol. 469, pp. 20130315-1 - 20130315-19, http://dx.doi.org/10.1098/rspa.2013.0315

Jovanoski Z; Towers I; Sidhu HS; Mohd Safuan H, 2013, 'Exact solution of a non-autonomous logistic population model', Ecological Modelling, vol. 251, pp. 99 - 102, http://dx.doi.org/10.1016/j.ecolmodel.2012.12.016

Safuan H; Sidhu HS; Jovanoski Z; Towers I, 2013, 'Impacts of Biotic Resource Enrichment on a Predator-Prey Population', Bulletin of Mathematical Biology, vol. on-line July 2013, pp. 1798 - 1812, http://dx.doi.org/10.1007/s11538-013-9869-7

Towers I; Jovanoski Z; Sidhu HS; mohd safuan H, 2012, 'Coupled logistic carrying capacity model', The ANZIAM Journal, vol. 53, pp. C172 - C184, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/4972

Towers I; Jovanoski Z, 2012, 'Shepherded solitons', The ANZIAM Journal, vol. 53, pp. C312 - C324, http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5122

Konar S; Jovanoski Z; Towers I, 2011, 'Two-color bright solitons in a three-level atomic system in the cascade configuration', Journal of Modern Optics, vol. 58, pp. 1035 - 1040, http://dx.doi.org/10.1080/09500340.2011.591509

Konar S; Jovanoski Z; Towers I, 2011, 'Incoherent spatial optical solitons in photorefractive crystals', Optics and Laser Technology, vol. 43, pp. 1466 - 1469, http://dx.doi.org/10.1016/j.optlastec.2011.04.022

Oslington P; Towers I, 2010, 'Trade, Migration, and Inequality in a World without Factor Price Equalization', Review of International Economics, vol. 18, pp. 650 - 662, http://dx.doi.org/10.1111/j.1467-9396.2010.00902.x

Oslington PR; Towers I, 2009, 'Pushing Economies (and Students)Outside the Factor Price Equalization Zone', Journal of Economic Education, vol. 40, pp. 422 - 436, http://dx.doi.org/10.1080/00220480903238099

Towers I; Robinson G, 2009, 'A model for multiple isothermal circumstellar dust shells', Physica Scripta T, vol. 80, http://dx.doi.org/10.1088/0031-8949/80/01/015901

Robinson G; Towers I; Jovanoski Z, 2009, 'Isothermal circumstellar dust shell model for teaching', International Journal of Mathematical Education in Science and Technology, vol. 40, pp. 795 - 845, http://dx.doi.org/10.1080/00207390902825302

Towers I; Jovanoski Z, 2008, 'Application of rational Chebyshev polynomials to optical problems', The ANZIAM Journal, vol. 50, pp. C60 - C74

Jovanoski Z; Towers IN; Ansari NA, 2008, 'Domain walls and their stability', ANZIAM Journal, vol. 50

Jovanoski Z; Ansari NA; Towers I; Sammut RA, 2008, 'Exact domain-wall solitons', Physics Letters, Section A, vol. 372, pp. 610 - 612, http://dx.doi.org/10.1016/j.physleta.2007.07.068

Ansari NA; Towers I; Jovanoski Z; Sidhu HS, 2007, 'A semi-classical approach to two-frequency solitons in a three-level cascade atomic system', Optics Communications, vol. 274, pp. 66 - 73, http://dx.doi.org/10.1016/j.optcom.2007.02.019

Ansari NA; Jovanoski Z; Sidhu HS; Towers I, 2006, 'Non-Linear Interactions of Two Intense Fields with a Three-Level Atomic System', Journal of Nonlinear Optical Physics and Materials, vol. 15, pp. 401 - 414, http://dx.doi.org/10.1142/S0218863506003402

Towers I, 2005, 'Interrogating functions', International Journal of Mathematical Education in Science and Technology, vol. 36, pp. 922 - 930, http://dx.doi.org/10.1080/00207390500084948

Jovanoski Z; Towers I; Ansari NA; Sammut RA, 2005, 'Approximate analysis of circular bends in nonlinear planar waveguides', Optics Communications, vol. 244, pp. 399 - 409, http://dx.doi.org/10.1016/j.optcom.2004.09.036

Jovanoski Z; Towers I; Garth SJ; Sammut RA, 2005, 'Modes on a bent nonlinear waveguide: solutions based upon the method of perturbations', Journal of Modern Optics, vol. 52, pp. 707 - 723, http://dx.doi.org/10.1080/09500340412331283679

Towers IN; Malomed BA; Wise FW, 2003, 'Light bullets in quadratic media with normal dispersion at the second harmonic', PHYSICAL REVIEW LETTERS, vol. 90, http://dx.doi.org/10.1103/PhysRevLett.90.123902

Band YB; Towers I; Malomed BA, 2003, 'Unified semiclassical approximation for Bose-Einstein condensates: Application to a BEC in an optical potential', PHYSICAL REVIEW A, vol. 67, http://dx.doi.org/10.1103/PhysRevA.67.023602

Mihalache D; Mazilu D; Towers I; Malomed BA; Lederer F, 2003, 'Stable spatiiotemporal spinning solitons in a bimodal cubic-quintic medium', Physical Review E, vol. 67, pp. 566081 - 566089, http://dx.doi.org/10.1103/PhysRevE.67.056608

Mihalache D; Mazilu D; Towers I; Malomed BA; Lederer F, 2002, 'Stable two-dimensional spinning solitons in a bimodal cubic-quintic model with four-wave mixing', JOURNAL OF OPTICS A-PURE AND APPLIED OPTICS, vol. 4, pp. 615 - 623, http://dx.doi.org/10.1088/1464-4258/4/6/305

Towers IN; Malomed BA, 2002, 'Polychromatic solitons in a quadratic medium', PHYSICAL REVIEW E, vol. 66, http://dx.doi.org/10.1103/PhysRevE.66.046620

Mihalache D; Mazilu D; Crasovan L; Towers I; Buryak AV; Malomed BA; Torner L; Torres JP; Lederer F, 2002, 'Stable Spinning Optical Solitons in Three Dimensions', Physical Review Letters, vol. 88, pp. 1 - 4, http://dx.doi.org/10.1103/PhysRevLett.88.073902

Mihalache D; Mazilu D; Crasovan L; Towers I; Malomed BA; Buryak AV; Torner L; Lederer F, 2002, 'Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities', Physical Review E, vol. 66, pp. 1 - 7, http://dx.doi.org/10.1103/PhysRevE.66.016613

Towers I; Malomed BA, 2002, 'Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity', Journal of the Optical Society of America B - Optical Physics, vol. 19, pp. 537 - 543, http://dx.doi.org/10.1364/JOSAB.19.000537

Elyutin PV; Buryak AV; Gubernov V; Sammut RA; Towers I, 2001, 'Interaction of two one-dimensional Bose-Einstein solitons: Chaos and energy exchange', Physical Review E, vol. 64, pp. 1 - 9, http://dx.doi.org/10.1103/PhysRevE.64.016607

Towers I; Buryak AV; Sammut RA; Malomed BA; Crasovan L; Mihalache D, 2001, 'Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation', Physics Letters, Section A, vol. 288, pp. 292 - 298, http://dx.doi.org/10.1016/S0375-9601(01)00565-5

Towers I; Buryak AV; Sammut RA; Malomed BA, 2001, 'Stable localized vortex solitons', Physical Review E, vol. 63, pp. 1 - 4, http://dx.doi.org/10.1103/PhysRevE.63.055601

Malomed BA; Peng G; Chu PL; Towers I; Buryak AV; Sammut RA, 2001, 'Stable helical solitons in optical media', Pramana - Journal of Physics, vol. 57, pp. 1061 - 1078, http://dx.doi.org/10.1007/s12043-001-0014-z

Towers I; Buryak AV; Sammut RA; Malomed BA, 2000, 'Quadratic solitons resulting from double-resonance wave mixing', Journal of the Optical Society of America B - Optical Physics, vol. 17, pp. 2018 - 2025, http://dx.doi.org/10.1364/JOSAB.17.002018

Buryak AV; Towers I; Trillo S, 2000, 'Multistability, homoclinic clamping, and chaos in nonlinear quadratic distributied feedback systems', Physics Letters, Section A, vol. 267, pp. 319 - 325, http://dx.doi.org/10.1016/S0375-9601(00)00124-9

Towers I; Sammut RA; Buryak AV; Malomed BA, 1999, 'Soliton multistability as a result of double-resonance wave mixing in x(2) media', Optics Letters, vol. 24, pp. 1738 - 1740, https://www.ncbi.nlm.nih.gov/pubmed/18079920

Conference Papers

Sharples JJ; Gubernov VV; Sidhu HS; Towers IN; Kolobov AV; Polezhaev AA, 2020, 'Behaviour of combustion waves in one-step and two-step models', in 18th World IMACS Congress and MODSIM 2009 - International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings, pp. 4453 - 4459

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