Dr Isaac Towers Lecturer BSc Otago, PhD UNSW@ADFA School of Physical, Environmental and Mathematical Sciences UNSW @ ADFA Canberra   ACT   2600 AUSTRALIA Phone: +61 2 6268 8217 Fax: +61 2 6268 8786 Email: i.towers@adfa.edu.au Location: PEMS Sth, Room 132a

Research Interests:

Optics and Photonics

Biography

• BSc (Hons) in Physics, Otago University, New Zealand 1997
• PhD Applied Mathematics, UNSW @ ADFA 2001
• Postdoctoral Fellow, Engineering Faculty, Tel Aviv University 2001-2002
• Employed by UNSW@ADFA as Lecturer since 2002.

Teaching

Current teaching:

• ZPEM1303 Engineering Mathematics 1A
• ZPEM2303 Engineering Mathematics 2A
• ZINT1001 Engineering Computational Methods

Previous teaching: complex analysis, projectile motion, and differential equations.

Current Research

• Solitons and wave interaction mainly in nonlinear optics
• Nonlinear dynamics
• Circumstellar dust shell modelling
• Ginzburg-Landau equation
• Numerical techniques for partial differential equations

Figure 1. The solution of the Fisher-Kolmogorov equation with a tanh initial condition (dashed line) quickly resolves into a travelling wave with speed 2.

Circumstellar dust shell modelling
Dr Isaac Towers & Dr Garry Robinson

It is now well established that many stars are surrounded by dust particles forming circumstellar shells. These dust shells may either be the remnants of the dust cloud which formed the central star, or material ejected from the star. Through infrared spectroscopy it has been found that the dust particles consist of a core of material consisting primarily of either silicate type material, or carbon based material, although other grain species (e.g.,alumina) may be present. Surrounding the grain core may be volatile ice mantle of material, such as water-ice (H2O-ice) or carbon dioxide-ice (CO₂-ice). We are working on radiative transfer models to theoretically investigate dust shells and their behaviour.

Dust shell code and data

Dissipative solitons and the Ginzburg-Landau equation
Dr Isaac Towers

Dissipative solitions are localised structures due to a balance between energy loss and gain within a system. This self-organising behaviour leads results in rich dynamics which can used to describe such varied phenomena as laser beams, pattern formations in biology, nerve pulses, and chemical reactions.

Numerical schemes for parabolic partial differential equations
Dr Isaac Towers

This research project is to develop and implement numerical schemes which solve multi-dimensional partial differential equations (PDE). By using an appropriate set of orthogonal basis functions the goal is to create a spectral method which allows for boundary conditions at infinity while maintaining the speed of an explicit time-marching approach. Operator splitting, integrating factors and the so-called explicit exponential methods are being investigated.

Numerical schemes for simulating optical beam propagation
Dr Isaac Towers

To compliment theoretical investigations of nonlinear optical beams we develop numerical schemes to efficiently study beam propagation. A variety of techniques are being investigated to provide fast and accurate simulations.

Nonlinear superposition
Dr Zlatko Jovanoski, Prof. Rowland Sammut & Dr Isaac Towers

The dynamics of nonlinear systems are much richer than those of linear systems. (For example chaos is one consequence of nonlinearity.) But this interesting and complex behaviour is accompanied by an increase in the difficulty of solving the relevant equations. One of the reasons for this is that the principle of superposition -- which allows us to combine simple solutions to solve more complex problems -- is invalid for nonlinear problems. However Jacobi elliptic functions can be combined because of some remarkable identities they have. This project proposes to find solutions of some important nonlinear equations as linear combinations of elliptic functions.

PhD Opportunities and Scholarships

If you are interested in PhD research in Optics and Photonics:
Contact: Dr Isaac Towers, i.towers@adfa.edu.au

Further information concerning scholarships at: http://www.unsw.adfa.edu.au/pems/student/pgrescourses.html

Figure 2. Numerical solution of the Allen-Cahn equation. The initial condition evolves into a meta-stable state before spontaneously switching to another fully stable solution.

Publications

• Towers, I. N. & Jovanoski, J., Application of rational Chebyshev polynomials to optical problems, 50, C60-C74, (2008) Available at: http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1396
  
• Jovanoski, J. & Towers, I. N., Exact domain walls and their stability, ANZIAM Journal (in press).
  
• Oslington, P. & Towers, I. N., Trade, migration and inequality in a world without factor price equalisation, Review of International Economics (in press).
  
• Oslington, P. & Towers, I. N., Pushing economies (and students) outside the factor price equalization zone, Journal of Economic Education, in press.
  
• Jovanoski, Z., Ansari, N.A., Towers, I.N. & Sammut, R.A., 2008, Exact domainwall solitons, Physics Letters A, 372(5), 610-612. Available at:http://dx.doi.org/10.1016/j.physleta.2007.07.068
  
• Ansari, N.A., Towers, I., Jovanoski, Z. & Sidhu, H.S., 2007, A semi-classical approach to two-frequency solitons in
  a three-level cascade atomic system, Optics Communications, 274(1), 66-73.
  Available at:http://dx.doi.org/10.1016/j.optcom.2007.02.019
  
• Ansari, N.A., Jovanoski, Z., Sidhu, H.S. & Towers, I., 2006, Non-linear interactions of two intense fields with a three-level atomic system, Journal of Nonlinear Optical Physics & Materials, 15(4), 401-414.
  Available at:http://dx.doi.org/10.1142/S0218863506003402
  
• Jovanoski, Z., Towers,I.N., Ansari, N.A., Sammut, R.A., 2005, Approximate analysis of circular bends in nonlinear planar waveguides, Opt. Comm., 244, 399-409.
  Available at: http://dx.doi.org/10.1016/j.optcom.2004.09.036
  
• Towers, I.N., 2005, Interrogating functions, International Journal of Mathematical Education in Science and Technology 36, 922-930. Available at:
  http://www.informaworld.com/openurl?genre=article&issn=0020%2d739X&volume=36&issue=8&spage=922
  
• Jovanoski, Z., Towers, I.N., Garth, S.J. & Sammut, R.A., 2005, Modes on a bent nonlinear waveguide: solutions based upon the method of perturbations, J. Mod. Opt., 52, 707-723. Available at:
  http://www.informaworld.com/openurl?genre=article&issn=0950%2d0340&volume=52&issue=5&spage=707