On the Applications of Cyclotomic Fields in Introductory Number Theory

In this essay, we see how prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime) can lead to elegant proofs of number theoretical concepts. We namely develop the notion of primary units in a cyclotomic field, demonstrate their equivalence to real units in this case, and show how this leads to a proof of a special case of Fermat's Last Theorem. We finally modernize Dirichlet's solution to Pell's Equation

Ab initio molecular dynamics study of the interlayer and micropore structure of aqueous montmorillonite clays

Ab initio molecular dynamics simulations have been performed to gain an understanding of the interfacial microscopic structure and reactivity of fully hydrated clay edges. The models studied include both micropore and interlayer water. We identify acidic sites through dissociation mechanisms; the resulting ions can be stabilized by both micropore and interlayer water. We find clay edges possess a complex amphoteric behavior, which depends on the face under consideration and the location of isomorphic substitution. For the neutral (110) surface, we do not observe any dissociation on the timescale accessible. The edge terminating hydroxyl groups participate in a hydrogen bonded network of water molecules that spans the interlayer between periodic images of the clay framework. With isomorphic substitutions in the tetrahedral layer of the (110) clay edge, we find the adjacent exposed apical oxygen behaves as a Br?nsted base and abstracts a proton from a nearby water molecule, which in turn removes a proton from an AlOH2 group. With isomorphic substitutions in the octahedral layer of the (110) clay edge the adjacent exposed apical oxygen atom does not abstract a proton from the water molecules, but increases the number of hydrogen bonded water molecules (from one to two). Acid treated clays are likely to have both sites protonated. The (010) surface does not have the same interfacial hydrogen bonding structure; it is much less stable and we observe dissociation of half the terminal SiOH groups (?Si-O-H??SiO-+H+) in our models. The resulting anions are stabilized by solvation from both micropore and interlayer water molecules. This suggests that, when fully hydrated, the (010) surface can act as a Br?nsted acid, even at neutral pH.Qatar National Research Fund (QNRF) of Qatar Foundation, National Priorities Research Program (grant number 09-26-01-048). Our work made use of the facilities of HECToR, the UK's national high-performance computing service, which is provided by UoE HPCx Ltd at the University of Edinburgh, Cray Inc and NAG Ltd, and funded by the Office of Science and Technology through EPSRC's High End Computing Programme. Access to HECToR was through grants EP/F00521/1, EP/E045111/1, EP/I017763/1 and the UK Consortium on Mesoscopic Engineering Sciences (EP/L00030X/1). We also made use of High Performance Computing facilities at University College London.Scopu

Design, implementation and control of microwave plasma gasification system for syngas production

This thesis provides a solution for sustainable energy production. It applies the newest technologies of microwave plasma on a traditional method known as gasification. The simulation of this system has been achieved through a high frequency structure simulator to decide the best design of the structure. Microwave radiation at the frequency of 2.45 GHz has been applied to ionise argon gas and convert it into plasma. It has been proven that plasma can be self-initiated with an appropriate electric field applied. This microwave-induced plasma is the heart and soul of the Liverpool John Moores University's gasification system. It is coupled to a gasification chamber to gasify the feedstock placed inside and extract its energy as synthesis gas (i.e. hydrogen and carbon monoxide). Feedstock used in this study is carbon based material including pieces of wood and palm date seeds. This work is novel as no other work upto the date of this thesis completion has studied the different variables affecting plasma creation, plus the automation and the fully control of the microwave plama gasification system. Results reveal that after improvement of the microwave-induced plasma by automated control, it was possible to increase the synthesis gas production to 25.7% hydrogen and more than 57.6% carbon monoxide. This study has included the effects of some parameters on the plasma created, thus on its efficiency. These parameters are; the power of the microwave radiation, the reflected power from the system, the flow rate of argon and the pressure inside the gasification chamber. Other effects were taken into consideration throughout the project such as the study of the sample's moisture levels on the gas production and the use of helium gas instead of argon for plasma creation. The system has proved the benefits of applying microwave-induced plasma technology on the gasification technology. These benefits can be summarised as the reduction of the input power needed for the procedure from the range of megawatts to 1 kilowatt, and the flexibility achieved through controlling the plasma jet for an improved process

Upplevelser av kontakt med arbetsterapeuter under rehabilitering hos personer med stroke från Mellanöstern

Bakgrund: Sverige har blivit ett allt mer mångkulturellt land. Bland annat har det skett en snabb tillväxt med människor från mellanöstern. Att komma till ett nytt land som har en annan religiös och kulturell bakgrund än ens egen kan innebära att man stöter på problem och svårigheter bland annat i mötet med vård och rehabilitering vid sjukdom. Inom arbetsterapi finns det lite forskning kring bemötande mellan arbetsterapeuter och patienter med utländsk bakgrund. Med anledning av det ville vi undersöka hur stroke drabbade patienter upplever mötet med arbetsterapeuten. Syfte: Syftet är att undersöka hur personer från Mellanöstern som drabbats av stroke upplevde kontakten med arbetsterapeuter på sjukhus i Sverige. Metod: En kvalitativ studie genomfördes med semistrukturerade intervjuer med åtta personer från Mellanöstern. Analysen av intervjuerna gjordes utifrån en innehållsanalys som fokuserade på latenta och manifesta inslag. Resultat: I analysen framkom fyra subteman: Familjens roll i behandlingen, kulturella skillnader, kommunikation och förtroende för arbetsterapeuten. Dessa tillsammans bildade ett huvudtema : Vikten av att arbetsterapeuten hade en kulturell kompetens. Konklusion: Att ha stor kulturell kompetens är viktigt vid behandling av stroke drabbade personer från Mellanöstern. Det finns skillnad i synsätt beroende på kulturella och religiösa värderingar och det är viktigt att arbetsterapeuten är lyhörd har kunskap och visar respekt gentemot sina patienter

Sensitivity Analysis on the Sizing Parameters of a Series-Parallel HEV

AAC 2019, 9th IFAC Symposium on Advances in Automotive Control, ORLEANS, FRANCE, 23-/06/2019 - 27/06/2019As an alternative to power-split hybrid architectures, a simple series-parallel architecture named SPHEV 2 can be realized. In this paper, the sizing process of this architecture is briefly presented and a deeper analysis is made. Mathematical sensitivity analysis studies are conducted on the sizing parameters of the architecture in order to bring more understanding to the optimization results. Local and global sensitivities are performed to understand the influence of the sizing variables on the fuel consumption. An analysis of the sensitivities is also made

A computational study of direct CO₂ hydrogenation to methanol on Pd surfaces

The reaction mechanism of direct CO2 hydrogenation to methanol is investigated in detail on Pd (111), (100) and (110) surfaces using density functional theory (DFT), supporting investigations into emergent Pd-based catalysts. Hydrogen adsorption and surface mobility are firstly considered, with high-coordination surface sites having the largest adsorption energy and being connected by diffusion channels with low energy barriers. Surface chemisorption of CO2, forming a partially charged CO2δ−, is weakly endothermic on a Pd (111) whilst slightly exothermic on Pd (100) and (110), with adsorption enthalpies of 0.09, −0.09 and −0.19 eV, respectively; the low stability of CO2δ− on the Pd (111) surface is attributed to negative charge accumulating on the surface Pd atoms that interact directly with the CO2δ− adsorbate. Detailed consideration for sequential hydrogenation of the CO2 shows that HCOOH hydrogenation to H2COOH would be the rate determining step in the conversion to methanol, for all surfaces, with activation barriers of 1.41, 1.51, and 0.84 eV on Pd (111), (100) and (110) facets, respectively. The Pd (110) surface exhibits overall lower activation energies than the most studied Pd (111) and (100) surfaces, and therefore should be considered in more detail in future Pd catalytic studies