Gene expression, which connects genomic information to functional units in living cells, has received substantial attention since the completion of The Human Genome Project. Quantitative characterization of gene expression will provide valuable information for understanding the behavior of living cells, and possibilities of building synthetic gene circuits to control or modify the behavior of naturally occurring cells. Many aspects of quantitative gene expression have been studied, including gene expression dynamics and noise in E. coli. The gene expression process itself is stochastic, and modelling approaches have been broadly used to study gene expression noise; however, stochastic gene expression models are usually large and time intensive to simulate. To speed up simulations, we have developed a systematic method to simplify gene expression models with fast and slow dynamics, and investigated when we can ignore the gene expression from the background genome when modelling the gene expression from plasmids. When modelling the noise in gene expression, one usually neglected aspect is the slow maturation process of fluorescent proteins, necessary for the protein to give out fluorescence after it is produced. By modelling, we show that the maturation steps can bring large changes to both the mean protein number and the noise in the model. An unstudied aspect of gene expression dynamics is the time dependent gene expression behavior in E. coli batch culture. Contrary to the usual assumption, we have found, in E. coli batch culture gene expression, that there is no steady state in terms of both the mean number of proteins and the noise. Negative feedback is thought to be able to reduce the noise in a system, and experiments have shown that negative feedback indeed suppresses the noise in gene expression, but the modelling shows that negative feedback will increase the noise. We have found that the increase of noise by feedback is due to the exclusion of extrinsic noise from the model, and that negative feedback will suppress the extrinsic noise while increasing the intrinsic noise. Living cells are crowded with macromolecules, which will, predicted by modelling, make the reaction constant time dependent. Our experimental observation has confirmed this prediction.

Gene expression, which connects genomic information to functional units in living cells, has received substantial attention since the completion of The Human Genome Project. Quantitative characterization of gene expression will provide valuable information for understanding the behavior of living cells, and possibilities of building synthetic gene circuits to control or modify the behavior of naturally occurring cells. Many aspects of quantitative gene expression have been studied, including gene expression dynamics and noise in E. coli. The gene expression process itself is stochastic, and modelling approaches have been broadly used to study gene expression noise; however, stochastic gene expression models are usually large and time intensive to simulate. To speed up simulations, we have developed a systematic method to simplify gene expression models with fast and slow dynamics, and investigated when we can ignore the gene expression from the background genome when modelling the gene expression from plasmids. When modelling the noise in gene expression, one usually neglected aspect is the slow maturation process of fluorescent proteins, necessary for the protein to give out fluorescence after it is produced. By modelling, we show that the maturation steps can bring large changes to both the mean protein number and the noise in the model. An unstudied aspect of gene expression dynamics is the time dependent gene expression behavior in E. coli batch culture. Contrary to the usual assumption, we have found, in E. coli batch culture gene expression, that there is no steady state in terms of both the mean number of proteins and the noise. Negative feedback is thought to be able to reduce the noise in a system, and experiments have shown that negative feedback indeed suppresses the noise in gene expression, but the modelling shows that negative feedback will increase the noise. We have found that the increase of noise by feedback is due to the exclusion of extrinsic noise from the model, and that negative feedback will suppress the extrinsic noise while increasing the intrinsic noise. Living cells are crowded with macromolecules, which will, predicted by modelling, make the reaction constant time dependent. Our experimental observation has confirmed this prediction.

We investigate the behaviour of the intensity noise in a multi-longitudinal mode Nd:YAG laser. This type of laser is a nonlinear system which exhibits complicated dynamics within the intensity noise. For example, antiphase dynamics is where there is cancellation of one or more collective modes of oscillation, which are distinct from the longitudinal modes, in the total output. Commonly lasers are studied experimentally to discriminate between models used to describe them. They are convenient since many external influences can be controlled and the oscillations of interest are low frequency (in the kHz regime) making their direct measurement relatively simple. In our laser, the collective modes of oscillation are excited by broadband ambient noise. Because the phase of the excitation is unknown, we develop the cross spectral technique to measure the antiphase dynamics directly and form a picture of the intensity noise interference for two to five mode operation. For three mode operation, we measure the contributions of the longitudinal modes to the collective modes. We also calculate power spectral densities of the individual longitudinal modes and the total intensity. We test relationships between these quantities, at the collective mode frequencies, which are derived from modal rate equation theory. For two mode operation, the theoretical relations are satisfied. For three mode operation, the relations are satisfied when the picture of interferences is taken into account. The cross spectral technique is therefore shown to be a sensitive test of the model developed by Pieroux and Mandel [T. Hill et al., Phys. Rev. A 66, 063803 (2002)]. The behaviour of the multimode laser operating near the threshold of a longitudinal mode is measured. Transitions in the cross spectrum are noted in some pairs of longitudinal modes, for an arbitrary but small pump rate above threshold of a longitudinal mode. It has been shown that longitudinal modes with a high threshold pump power may become more intense than those with a lower threshold [K. Otsuka et al., Opt. Lett. 23, 201 (1998), L. Stamatescu and M.W. Hamilton, (unpublished) (1999), N.B. Abraham et al., Phys. Rev. A 62, 013810 (2000), P.A. Khandokhin, E.A. Ovchinnikov and E.Yu. Shirokov, Phys. Rev. A 61, 053807 (2000)]. The AC noise component of the first two longitudinal modes to reach threshold, is found to exhibit similar properties to their intensity. The implications of the results of this thesis, on models used to describe the behaviour of solid state lasers, are also discussed. / Thesis (Ph.D.)--Physics, 2003.

Renewed interest in open rotor aeroengines, due to their fuel efficiency, has driven renewed interest in all aspects of the noise they generate. Noise due to the ingestion of distorted atmospheric turbulence, known as Unsteady Distortion Noise (UDN), is likely to be higher for open rotors than for conventional turbofan engines since the rotors are fully exposed to oncoming turbulence and lack ducting to attenuate the radiated sound. However, UDN has received less attention to date, particularly in wind-tunnel and flight testing programmes. In this thesis a new prediction scheme for UDN is described, which allows inclusion of many key features of real open rotors which have not previously been investigated theoretically. Detailed features of the mean flow induced by the rotor, the form of atmospheric turbulence, asymmetries due to installation features, and the effect of rotor incidence are all considered. Parameter studies are conducted in each of these cases to investigate their effect upon UDN in typical static testing and flight conditions. A thorough review of the technological issues of most relevance and previous theoretical work on all types of turbulence-blade interaction noise is first undertaken. The prediction scheme is then developed for the case in which the mean flow into the rotor is axisymmetric. This shows excellent qualitative agreement with previous findings, with increased streamtube contraction resulting in a more tonal noise spectrum. The theoretical framework involves using Rapid Distortion Theory to calculate the distortion of an isotropic turbulence field (such as given by the von Karman spectrum) by the mean flow induced by the rotor (such as given by actuator disk theory), leading to an expression for the velocity incident upon the leading edge of the rotor blades. Strip theory is then used to calculate the pressure jumps across the blades, input as the forcing term in the far-field wave equation. Models are derived for open rotor-induced flow which account for the variation of blade circulation with radius, and the presence of the rotor hub and rear blade row. An investigation of appropriate turbulence models and realistic turbulence parameters is also undertaken. A key finding is that the heights of the tonal peaks are determined by the overall magnitude of the induced streamtube contraction (dependent on the total thrust generated) whereas the precise form of distortion (affected by the detailed components of the mean flow and the form of atmospheric turbulence present) alters the resulting broadband level. The prediction scheme is formulated in such a way as to facilitate extension to the asymmetric case, which is also fully derived. The model is applied in the first instance to the case of two adjacent rotors and then to the case of a single rotor at incidence. Under flight conditions, when distortion is reduced but UDN can still contribute a significant broadband component to overall noise levels, asymmetry is found to increase broadband levels around 1 Blade Passing Frequency but reduce levels elsewhere.