The diameter of the commuting graph of a finite group with trivial centre

The commuting graph of a finite group with trivial centre is examined. It is shown that the connected components of the commuting graph have diameter at most 10

Application of theory to propeller design

The various theories concerning propeller design are discussed. The use of digital computers to obtain specific blade shapes to meet appropriate flow conditions is emphasized. The development of lifting-line and lifting surface configurations is analyzed. Ship propulsive performance and basic propeller design considerations are investigated. The characteristics of supercavitating propellers are compared with those of subcavitating propellers

Calibration of Viking imaging system pointing, image extraction, and optical navigation measure

Pointing control and knowledge accuracy of Viking Orbiter science instruments is controlled by the scan platform. Calibration of the scan platform and the imaging system was accomplished through mathematical models. The calibration procedure and results obtained for the two Viking spacecraft are described. Included are both ground and in-flight scan platform calibrations, and the additional calibrations unique to optical navigation

Medicine and the Public

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Theory of the cold collision frequency shift in 1S--2S spectroscopy of Bose-Einstein-condensed and non-condensed hydrogen

We show that a correct formulation of the cold collision frequency shift for two photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogen is consistent with experimental data. Our treatment includes transport and inhomogeneity into the theory of a non-condensed gas, which causes substantial changes in the cold collision frequency shift for the ordinary thermal gas, as a result of the very high frequency (3.9kHz) of transverse trap mode. For the condensed gas, we find substantial corrections arise from the inclusion of quasiparticles, whose number is very large because of the very low frequency (10.2Hz) of the longitudinal trap mode. These two effects together account for the apparent absence of a "factor of two" between the two possibilities. Our treatment considers only the Doppler-free measurements, but could be extended to Doppler-sensitive measurements. For Bose-condensed hydrogen, we predict a characteristic "foot" extending into higher detunings than can arise from the condensate alone, as a result of a correct treatment of the statistics of thermal quasiparticles.Comment: 16 page J Phys B format plus 6 postscript figure

Inertial Confinement Fusion Neutronics

Since fire was first harnessed one million years ago, man's appetite for energy has become ever more insatiable. As we come close to the end of the fossil fuel era, new energy sources must be found as a matter of urgency. The utilisation of renewable energy sources, such as solar and wind, to completely satisfy the world energy demands would be an ideal scenario. However, the low energy density achieved by renewables as well as local opposition to the building of renewable energy infrastructure will ensure that renewable energy sources will continue to play a relatively minor role in the supply of electricity to the grid. Hence, high energy density energy sources must be employed in order to minimize local opposition to building new power stations, while sustaining the growing energy demands. Nuclear fission is a strong candidate for meeting these high energy demands due to its reliability and safety-driven new technologies. However, nuclear waste and accidents, such as Chernobyl and Fukushima, still remains a concern for many people; thus, other high energy density technologies must utilized in conjunction with fission and renewables in order to maintain energy stability without the loss of public approval. A technology which would revolutionise power production is that of nuclear fusion. However, technological complexities and limited funding ensure that commercial fusion power plants are still at least 30 years away. In essence, fusion is a process whereby two light nuclei combine to form a larger nucleus. In order to meet binding energy requirements in the newly formed nucleus, energy is released in the form of gammas or particle kinetic energy. The ejected particles have a large amount of kinetic energy, which can be used to heat water and drive electricity generating turbines as in a conventional fossil fuel power plant. The proposed fuels for all mainstream fusion reactor concepts are deuterium, which can be extracted from sea water, and tritium, which can be manufactured on the power plant site using relatively small amounts of lithium. In order to initiate and maintain fusion reactions, the fusion fuel must be heated to approximately 100 million degrees Celsius, resulting in the fuel being in the plasma state. Until fairly recently, the quest for safe and clean energy in the form of IFE has mainly been driven by areas of research relevant to formation and the ignition of the fuel. The understanding of this physics holds the key to creating a reactor that can efficiently and effectively ignite the fuel and release more energy than is supplied. However, in recent years, as these area of physics have become more understood and the reality of fusion gain actually occurring in the near future has become more apparent, the need to understand the physics and technology issues, which are peripheral to the reactor core, has become more important. An area of research which is gaining popularity is reactor blanket technology. The blanket is a component which surrounds the fusion core whose main functionality includes: Shielding fusion reactor staff from harmful neutron radiation; absorbing the energy of the 14.1MeV neutrons emitted from the D-T reaction and using this energy to convert water into steam and drive turbines; producing tritium, via the ^{\text{6}} Li(n,α)T reaction, in order to maintain reactor tritium self-sufficiency. In order to achieve this functionality, the neutron and materials physics must be understood in greater detail. The extremely high temperatures and neutron fluxes exert forces on the reactor walls which are much higher than experienced by fission reactors. It is vital that fusion energy is to produce energy with significantly less nuclear waste than is produced in the fission industry. To achieve this, blanket materials must be chosen such that they are adequately resilient to transmutation via neutron interactions. Thus, ensuring that the blanket materials, once decommissioned, will be classified as low or medium level nuclear waste and that the amount of such waste is minimal. In addition to environmental concerns, the transmutation of nuclides in the blanket, other than lithium, is not beneficial to the mechanical properties of the material which can reduce the blanket performance. A balance must be found between the addition of impurities, such as molybdenum and niobium in steels, to improve the mechanical properties of materials and the potential nuclear waste associated with the added chemicals. Thus, the study and control of nuclide transmutations within the blanket is crucial in determining the level of success of fusion reactors. The production of tritium is an important function of the blanket, as without this function the reactor core would have no fuel to burn. In order for a fusion reactor to become commercially viable, the blanket must create at least 10% more tritium than the reactor core is burning. This is due to tritium decay, small losses of tritium to the environment and tritium retention within structural materials. The vast majority of tritium produced in the blanket is a result of neutron absorption of lithium-6, which then decays to tritium and releases an alpha particle as a by-product. As the blanket ages, the amount of lithium in blanket decreases and so does the rate of tritium production, hence a solid blanket needs to be replaced every 3-6 years in order to maintain a large enough tritium breeding rate to sustain the reactor core. The concept of utilising the neutron energy, to create electricity, and a lithium blanket, to create tritium, has been studied extensively for magnetic confinement fusion (MCF) devices. Recent advancements in ICF research have lead to the realisation that ICF blanket technology (BT) must now be developed in order to ensure the technology is well understood by the time that commercial scale ignition has been achieved experimentally. However, ICFBT is generally less developed when compared to MCFBT; MCFBT research cannot be assumed to be directly applicable to ICFBT due to the vast difference in temporal distribution of neutron radiation emitted by ICF and MCF confinement regimes which results in different transmutation rates, damage and tritium breeding rates. This thesis includes an introduction to fusion and presents background theory of fusion blanket technology. The main features include the description and benchmarking of a fusion specific depletion code named FATI (Fusion Activation and Transport Interface), the development and evaluation of control theory applied to blanket impurity removal, the study of time-dependent depletion and the development of a fusion specific energy binning format for Monte-Carlo modelling. Both fission and fusion neutronic calculations rely heavily on Monte-carlo neutron transport codes, such as MCNP. The most important and frequently used functions used within these codes is the calculation of reaction rates. Calculating reaction rates can be accomplished via the point-wise estimator approach, which is accurate but very computationally expensive, or the multi-group method, which is fast but can lack accuracy if an inappropriate energy group structure is used to bin the reaction energies. Jean-Christophe Sublet, CCFE, was planning to develop a energy group structure, to be used in conjunction with Monte-carlo calculations of fusion devices. Thus, this work was completed via a collaboration between the author and Jean-Christophe. This study concluded that a 16,000 group structure was required in order to achieve < 5% uncertainty. This study could potentially have a large impact on the group structure used in fusion activation calculations. The most commonly used group structure used for fusion activation analysis is comprised of only 175 groups. Thus, the 175 group calculations could be significantly over estimating activation. One might consider the over-estimation to be better than underestimating activation, however larger activation may result in the over-engineered radiation shields which will cost more and might have a negative effect on tritium breeding capability. To date, no transport-burnup (T-B) codes exist which have been designed specifically for fusion activation and tritium breeding studies. Codes such as MONTEBURNS, MOCUP, VESTA etc have been designed for fission applications, hence they lack some features that are absolutely necessary for fusion studies. As a result of this, and the overlooking of the need for full T-B, very few T-B studies have been undertaken. Chapter 4 describes the methodology behind the T-B linking mechanism and then goes on to describe the FATI code. The FATI ( Fusion Activation and Transport Interface) has been designed and produced by the solely by the author of this thesis. The code has many fusion specific features, which are not evident in any other documented T-B code. Some of the basic features of the code were benchmarked against the VESTA code, developed by Wim Haeck. The author created VESTA input files, which were then sent to Wim at IRSN, where the simulation was completed. the benchmarking procedure showed that the majority of the calculations performed by the FATI code matched the calculations of the well tested and validated VESTA code, within acceptable margins. Large differences in the calculation of hydrogen and helium isotopes highlighted the different methods used to approach gas production in the FATI and VESTA codes. This is another case where the underlying physics of fission and fusion neutronics differs, which then leads to alternative methods of analysis. By means of tritium production and tritium breeding calculations with the FATI code, Chapter 4 also clearly shows the importance of full T-B calculations. Non T-B calculations can underestimate the tritium self-sufficiency time by 60-70%, whilst some activation products be underestimated by up to hundreds/thousands of percent. In summary, chapters 3 and 4 of this thesis will describe and test T-B methodology which has not yet been fully implemented in the study of fusion neutronics. Non-T-B calculations tend to underestimate activation whilst insufficient group structure energy resolution tends to overestimate activation. Further studies which take the findings of chapter 3 and 4 into account will need to be completed with more realised reactor geometries in order to increase the confidence in activation and tritium breeding calculations. Due to the current shortage and cost of tritium the general consensus of fusion community is that tritium production should be maximised within future DEMO reactors. However, tritium is a highly radio-toxic and the calculations associated with the production of tritium within breeding blankets have high uncertainty. Thus, in order to ensure enough tritium is to be produced, the median tritium production level must be significantly higher than is required by tritium consumption of the reactor. This poses the risk of producing significantly more tritium than can be handled by the reactor site, thus creating a health and safety concern. In addition to this, the more tritium is produced. Chapter 5 of this thesis addresses this issue by studying the capability of a Proportional-Integral-Differential (PID) controller to manage the lithium-6, lithium-7 ratio, which can be used to stabilise tritium surplus inventory. The results clearly show that a simple controller is capable of managing the tritium production and surplus. However, calculations which include fuel cycle analysis needs to be included in the control theory model in order to fully determine the type of controller that is required