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In this thesis, we look at how the Cross-Entropy (CE) method can be used to solve various optimisation and estimation problems in telecommunication systems and network planning, especially in the presence of noise. In Chapter 2, we mention what comprises optimisation problems. Various optimisation problems, such as constrained optimization and convex optimisation, are discussed. We also address noisy optimisation and how dealing effectively with noise plays a crucial role in locating a global optimal solution. A brief overview of three algorithms that have successfully been applied to noisy optimisation problems is also given. Chapter 3 explores a short overview of the methodology behind the CE method. We discuss how the CE method requires two simple iterative stages to locate an optimal "degenerate" sampling distribution, and hence an optimal solution to the optimisation problem. We also show how a simple modification of the algorithm can tackle noisy optimisation problems. Numerical experiments for solving both non-noisy and noisy multi-extremal continuous optimisation problems are conducted. Three test functions are used to investigate the performance of the CE algorithm on both non-noisy and noisy cases. The results suggest that the proposed algorithm can locate a global optimal solution accurately. Also, we show that the performance of the CE algorithm can be improved using the injection method. Chapter 4 and Chapter 5 discuss two types of the Network Planning Problem (NPP): single-type NPP and multi-type NPP. The aim is to determine which links in the system should be purchased in order to provide the highest possible service to the consumers, subject to a constraint on the total budget. We introduce various CE-based algorithms to tackle such non-linear combinatorial optimisation problem. Numerical experiments suggest that the proposed algorithms perform effectively and reliably in all test cases. Chapter 6 is concerned with estimating the blocking probabilities in circuit switched networks. We look at how Importance Sampling and Sequential Importance Sampling can be used to estimate the blocking probabilities. Here, the CE method is used to find optimal sampling parameters to be used in Importance Sampling and Sequential Importance Sampling. Numerical experiments suggest that Sequential Importance Sampling achieves a variance reduction over Importance Sampling in almost all cases at a cost of increased simulation time. Using CE further increases the efficiency of both.

Traditionally, growth and morphology studies of bacteria have focused on individual cells. When microbiologists subsequently became interested in bacterial colony growth, they investigated the dynamics of its height as well as those of its diameter. The models they proposed, however, were little more than empirical. In recent decades there has been a shift in focus, as researchers became interested instead in the morphology changes that colonies undergo when exposed to stressful environments such as nutrient and moisture limitation. As a result of this shift, models of colony growth in three dimensions have remained underdeveloped and rudimentary. My first task in this thesis was to assemble a sufficiently comprehensive data set from which diameter, height and cell-number growth trends in colonies could be properly analysed. This was achieved by studying the growth of many colonies of two bacterial species, Serratia marcescens and Esherichia coli, on high-nutrient non-selective agar, over a range of incubation temperatures, over periods ranging from two hours to one week. When graphed and analysed, colony diameter and colony height growth turned out to be most economically described as power-law in time, with exponent < 1. This contrasts with the claims of previous researchers, who had described both growth trends as linear, with diameter switching to a slower yet still linear growth after a certain time, and height growth ceasing altogether. From my results, I proposed a simple conceptual model, an extension of a model developed by Pirt in 1967. My hypothesis was that, in colonies growing on high-nutrient surfaces, diffusion was the dominant factor in colony growth. Ron Keam transformed my conceptual model into a mathematical one, from which I have developed one-dimensional and twodimensional numerical simulations. In all simulations to date, in both one and two dimensions, a power-law growth phase emerges as a consequence of nutrient-controlled growth, preceded by an “accelerating” phase during which colony growth overtakes diffusive processes, and succeeded by a slow transition towards growth cessation as nutrient becomes exhausted. In addition to successful demonstration of the power laws, the model in its final form yields realistic colony profiles and exhibits other features consistent with experimental results reported in the literature. / Whole document restricted, but available by request, use the feedback form to request access.

Ramanscattering and four-wave mixing are two fundamental nonlinear phenomena present in optical fibres with important implications for applications in fields ranging from modern telecommunications networks to biophotonics. This thesis investigates three situations when these two phenomena interact: Firstly we investigate the interplay of multiple four-wave mixing processes using coherent and incoherent pump waves in the presence of Raman scattering. We experimentally demonstrate that despite the requirements of phase-matching conditions it is possible to observe multiple phasematched and non-phasematched four-wave mixing processes. Furthermore we show that an incoherent light wave provided by amplified spontaneous emission noise can act as an effective pump wave for degenerate four-wave mixing. The main part of the thesis is occupied by the investigation of a mode-locked Raman fibre laser. The use of dissipative four-wave mixing for the passive mode-locking technique in combination with Raman scattering as the gain mechanism offers the possibility of achieving ultra-high repetition rates at very high average output powers. We experimentally demonstrate the mode-locked operation of the laser at 500 GHz and achieve an average output power of almost 1 W. Additionally we examine the key limitation of the laser which is supermode noise caused by mode-locking the laser at very high harmonics of the cavity resonance frequency. In order to gain qualitative insight into the influence of supermode noise on the laser dynamics we create a laser model which takes account of supermode noise. Furthermore we design a scheme to reduce supermode noise using additional subcavities, and evaluate the scheme using a lower repetition rate laser. We show that by including the subcavities into the setup the amount of supermode noise can be reduced by at least a factor 100. Lastly we introduce a novel method to measure the noise fluctuations of continuous wave lasers at timescales prohibiting the use of traditional noise measurement techniques. The noise is measured using a technique which transfers the fast noise from the continuous wave laser to a low repetition rate mode-locked laser which can be measured with traditional methods. We demonstrate that a continuous wave Raman fibre laser exhibits ultrafast, high contrast intensity fluctuations at timescales of tens of Gigahertz. This work has led to three publications and six conference presentations.

This thesis deals with the electromagnetic radiation that is reflected from and emitted by a clear or cloudy terrestrial atmosphere. Calculations are performed in order to estimate the radiation exitant to space in the visible, the near visible, and the two infrared windows at approximately 4 μm and 11 μm. The NOAA-9 satellite Advanced Very High Resolution Radiometer (AVHRR/2) is used as the data acquisition system. The satellite AVHRR system is described, as well as future TIROSN satellites. The pre-launch calibration of the radiometer is described in some detail. Post-launch calibration is examined using a reflectance difference method. The radiometer gains are shown to have changed by more than 20% from their pre-launch values. A LOWTRAN based atmospheric model suitable for New Zealand is developed to provide cloud free transmission values. Atmospheric scattering is shown to contribute negligibly to visible cloud measurements (for 8-bit radiometer resolution). The Channels 1 to 3 terrestrial reflectance is averaged from more than two years of satellite data. Sea-surface state is examined as a function of windspeed. A method of extracting surface temperature in rugged terrain is developed. Dual temperature measurements at 10.8 and 11.8 μm are used to estimate surface air temperature. The transfer of radiation in a single layer cloud is calculated as a function of cloud thickness, observation/illumination geometry and the effective radius of the cloud drop-distribution. The variation in drop-size is contained in an ensemble of modified-Gamma distributions whose effective radius varies from 1 to 30 μm with a fixed dispersion of 0.25. A technique is established which allows effective cloud radius to be estimated from 3.7 μm AVHRR/2 imagery. The radiation values at 0.65 μm and 11.8 μm are used to correct the 3.7 μm reflectance for variation in cloud thickness and temperature respectively. The procedure is limited to warm clouds of moderate optical depth. In addition, the inversion process generates values of cloud top height and temperature, cloud depth and column liquid water content. The method is used to observe the development of orographic cloud formed over the southern half of the North Island of New Zealand. The inversion results for this type of cloud are in agreement with aircraft measurements carried out by the New Zealand Meteorological Service and are well fitted by a simple drop-growth model.

The results of observational studies of very high energy (VHE) and ultra high energy (UHE) gamma ray emission, by various astrophysical objects, made from 1988 to 1990 with the JANZOS Cerenkov facility are presented. The active galaxy Cen A and the Galactic X-ray binary systems Vela X-1, Cen X-3, and Cir X-1 were monitored for VHE gamma ray emission above 1 TeV. No evidence was found for persistent or episodic emission from any of these objects. Upper limits on the VHE fluxes above 1 TeV of 2.1×10-11, 2.7×10-11, 3.6×10-11 and 3.5×10-11 cm-2 s-1 respectively were obtained for these objects. These limits are consistent with previous observations made by other groups. Various objects in the Magellanic Clouds were monitored for UHE gamma ray emission using the Cerenkov technique at large zenith angles. This technique has been found to be more sensitive at UHE energies -100 TeV than the conventional air shower technique. During 1990 the equipment was modified to allow a sky coverage of 7°×23° at large zenith angles. This enabled most of the extent of the Large Magellanic Cloud to be surveyed at UHE energies. An examination of the UHE database yielded no evidence for persistent emission from SN1987A and selected X-ray pulsars in the Magellanic Clouds. Upper limits on the UHE fluxes (in cm-2s-1) above the given threshold energies were obtained as follows: SMC X-1, 2.4×10-13 (>30 TeV); SN1987A, 2.3×10-13 (>65 TeV); PSR0540-693, 2.3×10-13(>65 TeV); LMC Trans, 1.5×10-13(>130 TeV); LMC X-4, 1.3×l0-l3 (>140 TeV). Evidence was found for two episodes of pulsed gamma ray emission above 65 TeV from SN1987A. On the nights of May 28 and June 23, 1990, a periodicity search using the Rayleigh test showed significant power at 18.356 ms. This is near a periodicity reported at optical wavelengths in September, 1990. The chance probability for the individual period was about 10-6 on each of the two nights. Excess events of the order of 1σ were also seen on these nights. The overall chance probability, allowing for all degrees of freedom, was found to be 0.1%. Evidence was also found for a single episode of gamma ray emission above 140 TeV from LMC X-4 on May 27, 1990. Excess events were seen with a statistical significance of 2.4 σ. A periodicity test showed maximum Rayleigh power at 13.488 s on this night. The chance probability for the individual period was 8×10-3 and the overall chance probability was found to be 0.5%. Adopting a recent estimate of the pulsar population in the Large Magellanic Cloud, an upper bound of 3×1034 erg s-1 on the luminosity of an average pulsar, at energies >65 TeV, was obtained.

Building on Kibblewhite's long term investigations of the nonlinear wave-wave interactions and the infrasonic ocean noise and the microseisms these induce, this thesis further explores the physical nature of these processes. The classical description of this interaction, which takes into account only the homogeneous component of the induced field, has been extended to include the inhomogeneous component. A complete expression for the wave induced noise spectrum is established following a geometrical analysis of the dispersion relations among interacting waves. The relative importance of these two components and their directivity properties are also calculated and discussed. It is shown that while at observation points deeper than 500 meters the effects of the inhomogeneous component can be regarded as negligible, it can cause an increase of noise level of up to 40 dB in the region near the surface of the sea. Furthermore, in contrast to the nearly omni-directional distribution of the homogeneous component of the induced acoustic field, there is a tendency for the energy associated with the inhomogeneous component to focus in the wind direction. Based upon a multilayer analysis of a visco-elastic geoacoustic model, Green's functions and the spectral transfer functions relating the surface source pressure field to the underwater noise and microseism fields are derived for both near and far field cases. A 3-dimensional presentation defined on the dispersion plane (frequency and horizontal wave number) is introduced to describe the sea bottom reflection-loss and, Green's functions, and is extended to include the inhomogeneous region for the first time. The characteristics of this 3-D presentation are explained in terms of the geoacoustic parameters. The influence of the interaction of multiple seas (and swell) on the induced acoustic field are also discussed in this thesis. All these effects are considered in the calculation of the synthetic spectra of both the noise and microseism field. When compared with measured data excellent agreement is found between the theoretical and experimental results, which provides further confirmation that the nonlinear interaction is the most important source of the infrasonic ocean noise, as well as confirming the basic validity of the procedure introduced by Kibblewhite and Ewans to derive the ocean noise spectra from microseism records.

Two motives are responsible for the investigation of cosmic rays. Firstly they provide the only source at present availabe of particles with extremely high energy. To study interactions between fundamental particles at energies greater than about 6 x 109 ev. therefore, one must turn to cosmic rays. Interest in geophysics and astrophysics provides the other motive. For example, a theory of the origin of cosmic rays must form an integral part of the astronomer's explnation of the universe. The prob1em of the origin of the cosmic radiation is still looking at satisfactory solution. Further, much information about the physics of the solar system and the earth may be obtained from a world wide distribution of cosmic ray observatories.

Traditionally, growth and morphology studies of bacteria have focused on individual cells. When microbiologists subsequently became interested in bacterial colony growth, they investigated the dynamics of its height as well as those of its diameter. The models they proposed, however, were little more than empirical. In recent decades there has been a shift in focus, as researchers became interested instead in the morphology changes that colonies undergo when exposed to stressful environments such as nutrient and moisture limitation. As a result of this shift, models of colony growth in three dimensions have remained underdeveloped and rudimentary. My first task in this thesis was to assemble a sufficiently comprehensive data set from which diameter, height and cell-number growth trends in colonies could be properly analysed. This was achieved by studying the growth of many colonies of two bacterial species, Serratia marcescens and Esherichia coli, on high-nutrient non-selective agar, over a range of incubation temperatures, over periods ranging from two hours to one week. When graphed and analysed, colony diameter and colony height growth turned out to be most economically described as power-law in time, with exponent < 1. This contrasts with the claims of previous researchers, who had described both growth trends as linear, with diameter switching to a slower yet still linear growth after a certain time, and height growth ceasing altogether. From my results, I proposed a simple conceptual model, an extension of a model developed by Pirt in 1967. My hypothesis was that, in colonies growing on high-nutrient surfaces, diffusion was the dominant factor in colony growth. Ron Keam transformed my conceptual model into a mathematical one, from which I have developed one-dimensional and twodimensional numerical simulations. In all simulations to date, in both one and two dimensions, a power-law growth phase emerges as a consequence of nutrient-controlled growth, preceded by an “accelerating” phase during which colony growth overtakes diffusive processes, and succeeded by a slow transition towards growth cessation as nutrient becomes exhausted. In addition to successful demonstration of the power laws, the model in its final form yields realistic colony profiles and exhibits other features consistent with experimental results reported in the literature. / Whole document restricted, but available by request, use the feedback form to request access.

Ramanscattering and four-wave mixing are two fundamental nonlinear phenomena present in optical fibres with important implications for applications in fields ranging from modern telecommunications networks to biophotonics. This thesis investigates three situations when these two phenomena interact: Firstly we investigate the interplay of multiple four-wave mixing processes using coherent and incoherent pump waves in the presence of Raman scattering. We experimentally demonstrate that despite the requirements of phase-matching conditions it is possible to observe multiple phasematched and non-phasematched four-wave mixing processes. Furthermore we show that an incoherent light wave provided by amplified spontaneous emission noise can act as an effective pump wave for degenerate four-wave mixing. The main part of the thesis is occupied by the investigation of a mode-locked Raman fibre laser. The use of dissipative four-wave mixing for the passive mode-locking technique in combination with Raman scattering as the gain mechanism offers the possibility of achieving ultra-high repetition rates at very high average output powers. We experimentally demonstrate the mode-locked operation of the laser at 500 GHz and achieve an average output power of almost 1 W. Additionally we examine the key limitation of the laser which is supermode noise caused by mode-locking the laser at very high harmonics of the cavity resonance frequency. In order to gain qualitative insight into the influence of supermode noise on the laser dynamics we create a laser model which takes account of supermode noise. Furthermore we design a scheme to reduce supermode noise using additional subcavities, and evaluate the scheme using a lower repetition rate laser. We show that by including the subcavities into the setup the amount of supermode noise can be reduced by at least a factor 100. Lastly we introduce a novel method to measure the noise fluctuations of continuous wave lasers at timescales prohibiting the use of traditional noise measurement techniques. The noise is measured using a technique which transfers the fast noise from the continuous wave laser to a low repetition rate mode-locked laser which can be measured with traditional methods. We demonstrate that a continuous wave Raman fibre laser exhibits ultrafast, high contrast intensity fluctuations at timescales of tens of Gigahertz. This work has led to three publications and six conference presentations.