UNSW@ADFA Mathematics Seminar Series 2006

 

Friday 3 November, 11:10
Place: P25 PEMS South

Joint Mathematics and Physics seminar
Mathematics and Physics Honours Students for 2006,
PLTOFF Thiansiri Luangwilai and PLTOFF Paul Andrews

Mathematical Modeling of Self-Heating in Compost Piles

by PLTOFF Thiansiri Luangwilai

Fires at industrial composting facilities, such as those storing industrial waste products like municipal solid waste (MSW) and landfills, are fairly common.   In most cases these are manageable and such incidents are not destructive enough to attract attention beyond the facilities. However, over the years there have been a few notable devastating fires at such facilities.

In each of these industrial processes there is an inherent increase in temperature as a consequence of the biological activity.   Indeed, such a temperature increase is one of the goals of the composting waste.   Elevated temperatures of the order of 70 - 90 degrees Celsius have been documented within a few months (or even a few days) of forming the compost pile.

Furthermore, fires have been reported in landfill areas worldwide.   Although the basic theory of spontaneous combustion relating to organic materials is well understood, there has been very little work undertaken with regard to the mechanism for fires involving biological self-heating.   Whilst a compost pile must be sufficiently large to allow degradation of the organic material, there is a critical size beyond which spontaneous ignition of the pile is very likely.  In this talk I will present results from my analysis of several models that describe the thermal response of cellulosic materials in compost piles. The main objective is to determine the critical sizes of these compost piles.


Infrared Signatures of Aircraft: A Theoretical investigation of the infrared signature of a Boeing 737-700.

by PLTOFF Paul Andrews

In an operational military environment a vehicle's ability to avoid detection is vital to the vehicle's survivability. A vehicle's detectability or stealthiness is dependant on the contrast between the vehicle's electromagnetic signature and that of the surrounding environment. The aim of the project is to determine the infrared signature of a Boeing 737-700 using a combination of infrared imagery, experimentation and mathematical modelling. This seminar is the final component for the honours year and provides a summary of the previous seminar, discusses the experiment developed to determine a surface's emissivity and the development of radiation models of select emission sources to describe the infrared signature of the Boeing 737-700 as seen by a theoretical missile.

 

Friday October 13, 11:10
Place: P25 PEMS South

LESSONS FROM THE JANUARY 2003 FIRES – ADVANCING BUSHFIRE RISK MANAGEMENT IN THE HIGH COUNTRY

Rick McRae, ACT Emergency Services Authority (ACT ESA) and BushfireCRC HighFire Risk Project

The alpine fires of January 2003 burnt vast tracts of forested country in Victoria, NSW and the ACT.   Much of the prior basis for bushfire risk management was found insufficient for understanding this event.   Lessons must be learnt from the event to ensure future safety of threatened communities. The BushfireCRC HighFire Risk Project will use Federal Government funds to address this.

Initially using the bushfire risk framework used across the ACT, we will address all aspects and methodically analyse shortfalls in understanding. Some of these are already evident from material collected during the fires, some will need to be researched.   A multi-disciplinary approach will be applied, spanning field data collection, modelling, analysis of fire data and risk methodologies. While much of the initial effort will of necessity be meteorological, many aspects of fire management will be integrated.

So far the approach has revealed significant risk drivers that have been poorly recognised to date. Nocturnal low-level jets frequently produce peak FFDIs between midnight and sunrise. These produce unexpectedly intense fire behaviour and require rethinking of objectives and strategies, and put crew safety at risk. Dynamic channelling was the key factor that produced the catastrophic fire behaviour seen around the ACT on 18/1/2003. Future mitigation effort will need to reflect these findings.

Significant improvements in bushfire risk management in the ACT have already emerged from initial efforts. Benefits are expected for the entire alpine region, and elsewhere in Australia.

Monday October 9, 14:40
Place: P25 PEMS South

"Continuum modelling of gigahertz nano-oscillators"

Ngamta Thamwattana
Nanomechanics Group,
School of Mathematics and Statistics,
University of Wollongong

Fullerenes and carbon nanotubes are of considerable interest throughout many scientific areas due to their unique and exceptional properties, such as low weight, high strength, flexibility, high thermal conductivity and chemical stability. These nanostructures have many potential applications in nanodevices. One aspect that has attracted much attention is the creation of nano-oscillators, which can produce frequencies in the gigahertz range, for applications such as ultra-fast optical filters and nano-antennae. While there are difficulties for micromechanical oscillators to reach gigahertz frequencies, it is possible for nanomechanical systems to achieve this. A number of studies have found that the sliding of an inner shell inside an outer shell of a multi-walled carbon nanotube can generate oscillatory frequencies up to several gigahertz. In addition, it has been observed that the shorter the inner tube the higher the frequency, leading to the introduction of a C₆₀ -nanotube oscillator, where high frequencies can be generated by oscillating a C₆₀ fullerene inside a single-walled carbon nanotube. The discovery of nanopeapods (nanotubes filled with C₆₀ fullerenes) and carbon nanotori (seamless toroidal single-walled carbon nanotubes) also poses the possibility of constructing an oscillator (orbiter) which has a C₆₀ fullerene orbiting inside a nanotorus.

In this talk, I will present the underlying mechanisms of the gigahertz nano-oscillators and some recent results derived using the Lennard-Jones potential together with the continuum approach for C₆₀ -single-walled carbon nanotube oscillators.

 

Friday September 15, 11.10
Place: P25 PEMS South

"Drifting Microgravity Flame Balls"

Rodney Weber, PEMS UNSW@ADFA

Drop-tower and space shuttle experiments have conclusively demonstrated that spherical flame structures can persist for long times; at least ninety minutes, with a diameter of 1cm and very low luminousity.

It so happens that a spherical flame model was examined many years ago by Zeldovich in the hope of constructing stable stationary solutions.  While a stationary solution was found, it turned out to be unstable to perturbations and it wasn't until the 1990's that Buckmaster and Joulin established that heat losses of any kind can act as a stabilising mechanism. In particular in Buckmaster et al (1990) two types of heat loss terms were introduced into the equations for a stationary, spherical flame structure and it was clearly shown that only with such loss terms was it possible to obtain stable spherical solutions. In the intervening years further calculations confirmed many of the details and provided a theoretical understanding of some of the observations that have been recorded in the microgravity experiments pioneered by Ronney (see http://microgravity.grc.nasa.gov/combustion/sofball/sofball_index.htm).

Recent experiments have shown multiple flame balls with interesting dynamic behaviour. Some of the observations, such as the slow drifting apart of two flame balls, can be explained by competition for fuel. After a brief overview of the observations and theory, I will show recent numerical results which, for the first time, really calculates two flame balls drifting slowly apart.

Friday August 18, 11:10
Place: P25 PEMS South

Two 20 minute seminars

1. Three methods for determining the optimal path of a vehicle through a minefield
   Dr. Geoff Mercer, PEMS UNSW@ADFA
   
   The problem of minimising the risk to a vehicle when travelling through a minefield is considered.  Often the trajectory of the vehicle is dependent on factors such as maximum travel time, fuel usage and the like which provide constraints on determining the optimal path of the vehicle.  Three different approaches to the problem are considered and compared.  Firstly, a continuous formulation of the problem is considered.  By following a calculus of variations argument this results in a system of four couple ODEs.  These are solved via a shooting method and computational difficulties encountered in this process are discussed.  Secondly, the trajectory of the vehicle is approximated by a discrete (but large) system of coupled springs and masses resulting in a large but well behaved system of ODEs to solve.  The mines are taken to have a repulsive force to the masses to model the risk minimisation and the springs provide the path smoothing and are used to satisfy the length constraint.  Numerical solutions to this system will be investigated.  Thirdly, on discretising the region of interest a discrete optimisation technique can be used to obtain the shortest path through the minefield subject to the risk minimisation and length constraints.
   
2. Swelling problems  with two moving boundaries.
   Dr. Steve Barry, PEMS UNSW@ADFA
   
   The swelling of grease and whole grains can be modelled by a nonlinear diffusion equation with two moving boundaries (a Stefan problem).
   
   In Cartesian coordinates interesting analytical  solutions  exist for some simplified cases,  but in general the solution must be solved  numerically.   In cylindrical coordinates only numerical solutions are possible and these need the Cartesian result.   This seminar develops the models of the swelling material, illustrates some of the analytic solutions, and demonstrates the numerical methods used to solve the problem in Cartesian and cylindrical coordinates.

Friday May 5, 11:10
Place: P25 PEMS South

"In Praise of Linearity (and ZPEM2301)"

Prof. Colin Pask, PEMS UNSW@ADFA

There is no doubt that much of science and mathematics leads us to nonlinear problems and they are exciting, important, difficult and trendy to study. In this talk I want to remind people that much of the world is actually "linear" and we have wonderful and powerful ways of describing linearity. Amongst other things, I will touch on the digital communications revolution, controversial dynamical theories in the era after Newton and why Minnie is a dog.

Friday April 21, 11:10
Place: P25 PEMS South

Presenter: Prof. Elsa Pastor Ferrer
Centre d'Estudis del Risc Tecnològic, Universitat Politècnica de Catalunya

Research background of the Centre for Technological Risk Studies (CERTEC), Technical University of Catalonia (Spain). First steps in forest fire research: fire retardant effectiveness assessment.


The Centre for Technological Risk Studies (CERTEC) is a Spanish organization whose objectives are research and education in the various fields of technological risk, safety and environmental protection. The research in the field of forest fires started in 2000 and is basically focused on the use of long-term fire retardants for extinction purposes. So, the CERTEC directs their efforts to develop a standard methodology to assess retardants effectiveness and to model their effects in terms of fire behaviour. Methodologies and instrumentation normally used in industrial engineering are being applied in this field and some experimental work is currently being done in different scenarios, i.e. fire laboratory, prescribed burnings and experimental field burnings. First steps in this direction will be presented within the framework of the present wildfire problem in the region of Catalonia (NE Spain).

Thursday 2 March , 10.00 am
Place: P25 PEMS South

Presenter: Dr Geoff Mercer
PEMS, UNSW@ADFA

Modelling agrichemical spray retention on plants and other problems from the 2006 Mathematics in Industry Study Group

Firstly, a brief overview of the 2006 Mathematics in Industry Study group will be presented including problems over a diverse range such as washing machine balancing, predicting mechanical properties of steel,  probabilities of large scale power outages,  soil quality and management models, tree growth modelling and water use in the coal industry.  Secondly,  a more in depth look at the problem I was involved with, namely the retention of agrichemical sprays on plants.  Factors considered include the spray trajectory, speeds and droplet sizes, the impaction and subsequent retention on the plant surface (taking into account leaf surface characteristics and  spray formulation), runoff from the leaf surface and building suitable plant models for simulations.

 

 

Dr Isaac Towers
School of PEMS
UNSW@ADFA

tel: (02) 6268 8217
email: i.towers@adfa.edu.au