The progess in NMRQIP can be outlined in to four parts.1) Implementation of theoretical protocols on small number of qubits. 2) Demonstration of QIP on various NMR systems. 3) Designing and implementing the algorithms for mixed initial states. 4) Developing the techniques for coherent and decoherent control on higher number(up to 15) of qubits. This thesis contains some efforts in the direction of first three points. Quantum-state discrimination has important applications in the context of quantum communication and quantum cryptography. One of the characteristic features of quantum mechanics is that it is impossible to devise a measurement that can distinguish nonorthogonal states perfectly. However, one can distinguish them with a finite probability by an appropriate measurement strategy. In Chapter 2, we describe the implementation of a theoretical protocol of programmable quantum-state discriminator, on a two-qubit NMR System. The projective measurement is simulated by adding two experiments. This device does the unambiguous discrimination of a pair of states of the data qubit that are symmetrically located about a fixed state. The device is used to discriminate both linearly polarized states and eillipitically polarized states. The maximum probability of successful discrimination is achieved by suitably preparing the ancilla quubit. The last step of any QIP protocol is the readout. In NMR-QIP the readout is done by using density matrix tomography. It was first proposed by Ernst and co-workers that a two-dimensional method can be used to correlate input and output states. This method uses an extra (aniclla) qubit, whose transitions indicate the quantum states of the remaining qubits. The 2D spectrum of ancilla qubit represent the input and output states along F1 and F2 dimensions respectively. However the 2D method requires several t1 increments to achieve the required spectral width and resolution in the indirect dimension, hence leads to large experimental time. In chapter 3, the conventional 2D NMRQIP method is speeded-up by using Hadamard spectroscopy. The Hadamard method is used to implement various two-, three-qubit gates and qutrit gates. We also use Hadamard spectroscopy for information storage under spatial encoding and to implement a parallel search algorithm. Various slices of water sample can be spatially encoded by using a multi-frequency pulse under the field gradient. Thus the information of each slice is projected to the frequency space. Each slice represents a classical bit, where excitation and no excitation corresponds to the binary values 0 and 1 respectively. However one has to do the experiment for each binary information, by synthesizing a suitable multi-frequency pulse. In this work we show that by recording the data obtained by various Hadamard encoded multi-frequency pulses, one can suitably decode it to obtain any birnary information, without doing further experiments. Geometric phases depend only on the geometry of the path executed in the projective Hilbert space, and are therefore resilient to certain types of errors. This leads to the possibility of an intrinsically fault-tolerant quantum computation. In liquid state NMRQIP. Controlled phase shift gates are achieved by using qubit selective pulses and J evolutions, and also by using geometir phases. In order to achieve higher number of qubits in NMR, one explores dipolar couplings which are larger in magnitude, yielding strongly coupled spectra. In such systems since the Hamiltonian consists of terms, it is difficult to apply qubit selective pulses. However such systems have been used for NMRQIP by considering 2n eigen states as basis states of an n-qubit system. In chapter 4, it is shown that non-adiabatic geometric phases can be used to implement controlled phase shift gates in strongly dipolar coupled systems. A detailed theoretical explanation of non-adiabatic geometric phases in NMR is given, by using single transition operators. Using such controlled phase shift gates, the implementation of Deutsch-Jozsa and parity algorithms are demonstrated. Search algorithms play an important role in the filed of information processing. Grovers quantum search algorithm achieves polynomial speed-up over the classical search algorithm. Bruschweiler proposed a Liouville space search algorithm which achieve polymonial speed-up. This algorithm requires a weakly coupled system with a mixed initial state. In chapter 5 we modified the Bruschweiler’s algorithm, so that it can be implemented on a weakly as well as strongly coupled system. The experiments are performed on a strongly dipolar coupled four-qubit system. The experiments from four spin-1/2 nuclei of a molecule oriented in a liquid crystal matrix. Chapter 6 describes the implementation of controlled phase shift gates on a quadrupolar spin-7/2 nucleus, using non-adiabatic geometric phases. The eight energy levels of spin-7/2 nucleus, form a three qubit system. A general procedure is given, for implementing a controlled phase shift gate on a system consisting of any number of energy levels. Finally Collin’s version of three-qubit DJ algorithm using multi-frequency pulses, is implemented in the spin-7/2 system.

This thesis consists of four papers, three papers about modelling animal populations and one paper about an area integral estimate for solutions of partial differential equations on non-smooth domains. The papers are: I. Å. Brännström, Single species population models from first principles. II. Å. Brännström and D. J. T. Sumpter, Stochastic analogues of deterministic single species population models. III. Å. Brännström and D. J. T. Sumpter, Coupled map lattice approximations for spatially explicit individual-based models of ecology. IV. Å. Brännström, An area integral estimate for higher order parabolic equations. In the first paper we derive deterministic discrete single species population models with first order feedback, such as the Hassell and Beverton-Holt model, from first principles. The derivations build on the site based method of Sumpter & Broomhead (2001) and Johansson & Sumpter (2003). A three parameter generalisation of the Beverton-Holtmodel is also derived, and one of the parameters is shown to correspond directly to the underlying distribution of individuals. The second paper is about constructing stochastic population models that incorporate a given deterministic skeleton. Using the Ricker model as an example, we construct several stochastic analogues and fit them to data using the method of maximum likelihood. The results show that an accurate stochastic population model is most important when the dynamics are periodic or chaotic, and that the two most common ways of constructing stochastic analogues, using additive normally distributed noise or multiplicative lognormally distributed noise, give models that fit the data well. The latter is also motivated on theoretical grounds. In the third paper we approximate a spatially explicit individual-based model with a stochastic coupledmap lattice. The approximation effectively disentangles the deterministic and stochastic components of the model. Based on this approximation we argue that the stable population dynamics seen for short dispersal ranges is a consequence of increased stochasticity from local interactions and dispersal. Finally, the fourth paper contains a proof that for solutions of higher order real homogeneous constant coefficient parabolic operators on Lipschitz cylinders, the area integral dominates the maximal function in the L2-norm.

Photonic crystals (PhCs) are periodic dielectric structures that exhibit a photonic bandgap, i.e., a range of wavelength for which light propagation is forbidden. The special band structure related dispersion properties offer a realm of novel functionalities and interesting physical phenomena. PhCs have been manufactured using semiconductors and other material technologies. However, InP-based materials are the main choice for active devices at optical communication wavelengths. This thesis focuses on two-dimensional PhCs in the InP/GaInAsP/InP material system and addresses their fabrication technology and their physical properties covering both material issues and light propagation aspects. Ar/Cl2 chemically assisted ion beam etching was used to etch the photonic crystals. The etching characteristics including feature size dependent etching phenomena were experimentally determined and the underlying etching mechanisms are explained. For the etched PhC holes, aspect ratios around 20 were achieved, with a maximum etch depth of 5 microns for a hole diameter of 300 nm. Optical losses in photonic crystal devices were addressed both in terms of vertical confinement and hole shape and depth. The work also demonstrated that dry etching has a major impact on the properties of the photonic crystal material. The surface Fermi level at the etched hole sidewalls was found to be pinned at 0.12 eV below the conduction band minimum. This is shown to have important consequences on carrier transport. It is also found that, for an InGaAsP quantum well, the surface recombination velocity increases (non-linearly) by more than one order of magnitude as the etch duration is increased, providing evidence for accumulation of sidewall damage. A model based on sputtering theory is developed to qualitatively explain the development of damage. The physics of dispersive phenomena in PhC structures is investigated experimentally and theoretically. Negative refraction was experimentally demonstrated at optical wavelengths, and applied for light focusing. Fourier optics was used to experimentally explore the issue of coupling to Bloch modes inside the PhC slab and to experimentally determine the curvature of the band structure. Finally, dispersive phenomena were used in coupled-cavity waveguides to achieve a slow light regime with a group index of more than 180 and a group velocity dispersion up to 10^7 times that of a conventional fiber. / QC 20100712

The fluid flow and tracer transport in a single rock fracture during shear processes has been an important issue in rock mechanics and is investigated in this thesis using Finite Element Method (FEM) and streamline particle tracking method, considering evolutions of aperture and transmissivity with shear displacement histories under different normal stresses, based on laboratory tests. The distributions of fracture aperture and its evolution during shear were calculated from the initial aperture fields, based on the laser-scanned surface roughness features of replicas of rock fracture specimens, and shear dilations measured during the coupled shear-flow-tracer tests in laboratory performed using a newly developed testing apparatus in Nagasaki University, Nagasaki, Japan. Three rock fractures of granite with different roughness characteristics were used as parent samples from which nine plaster replicas were made and coupled shear-flow tests was performed under three normal loading conditions (two levels of constant normal loading (CNL) and one constant normal stiffness (CNS) conditions). In order to visualize the tracer transport, transparent acrylic upper parts and plaster lower parts of the fracture specimens were manufactured from an artificially created tensile fracture of sandstone and the coupled shear-flow tests with fluid visualization was performed using a dye tracer injected from upstream and a CCD camera to record the dye movement. A special algorithm for treating the contact areas as zero-aperture elements was used to produce more accurate flow field simulations by using FEM, which is important for continued simulations of particle transport, but was often not properly treated in literature. The simulation results agreed well with the flow rate data obtained from the laboratory tests, showing that complex histories of fracture aperture and tortuous flow channels with changing normal stresses and increasing shear displacements, which were also captured by the coupled shear-flow tests of fracture specimens with visualization of the fluid flow. From the obtained flow velocity fields, the particle transport was predicted by the streamline particle tracking method with calculated flow velocity fields (vectors) from the flow simulations, obtaining results such as flow velocity profiles, total flow rates, particle travel time, breakthrough curves and the Péclet number, Pe, respectively. The fluid flow in the vertical 2-D cross-sections of a rock fracture was also simulated by solving both Navier-Stokes (NS) and Reynolds equations, and the particle transport was predicted by streamline particle tracking method. The results obtained using NS and Reynolds equations were compared to illustrate the degree of the validity of the Reynolds equation for general applications in practice since the later is mush more computationally efficient for large scale problems. The flow simulation results show that the total flow rate and the flow velocity predicted by NS equations are quite different from that as predicted by the Reynolds equation. The results show that a roughly 5-10 % overestimation on the flow rate is produced when the Reynolds equation is used, and the ideal parabolic velocity profiles defined by the local cubic law, when Reynolds equation is used, is no longer valid, especially when the roughness feature of the fracture surfaces changes with shear. These deviations of flow rate and flow velocity profiles across the fracture aperture have a significant impact on the particle transport behavior and the associated properties, such as the travel time and Péclet number. The deviations increase with increasing flow velocity and become more significant when fracture aperture geometry changes with shear. The scientific findings from these studies provided new insights to the physical behavior of fluid flow and mass transport in rock fractures which is the scientific basis for many rock mechanics problems at the fundamental level, and with special importance to rock engineering problems such as geothermal energy extraction (where flow rate in fractures dominates the productivity of a geothermal energy reservoir) and nuclear waste repositories (where radioactive nuclides transport through fractures dominates the final safety evaluations) in fractured rocks. / Vätskeflödet och spårämnestransporten i en enskild bergsspricka under skjuvningsprocesser har varit ett viktigt ämne inom bergmekanik. I denna avhandling undersöks ämnet med hjälp av finita element metoden (FEM) och en strömlinjebaserad partikelspårningsmetod. Hänsyn tas till utveckling av öppningar och transmissivitet med skjuvningens förflyttningshistoria under olika normala belastningar baserat på laboratorietester. Fördelningen av spricköppningar och deras utveckling under skjuvning beräknades från de initiala öppningsfälten baserat på det laserscannade provets ytas grovhetskännetecken sam tskjuvningsöppningar uppmätta under de kopplade skjuvning-flöde-spårämneslaboratorietesterna som utförts med nyutvecklad testapparatur i Nagasaki Universitet i Nagasaki, Japan. Tre bergssprickor i granit med olika grovhetskarakteristika användes som utgångsprover från vilka nio gipskopior gjordes. Kopplade skjuvning-flödes tester utfördes sedan under tre normala belastningstillstånd (två nivåer med konstant normal last (KNL) och en konstant normal styvhetstillstånd (KNS). För att visualisera spårämnestransporten tillverkades en transparent övre del av sprickproverna av akryl och en nedre del av gipsbaserat på en kostgjord spänningsspricka i sandsten och de kopplade skjuvning-flödes testerna med vätskevisualisering utfördes med färgspårämne injekterat uppströms och en CCD kamera monterad ovanför för att registrera färgens rörelse. En särskild algoritm användes för att behandla kontaktytorna som nollöppningsämnen användes för att åstadkomma mer exakta flödesfältssimuleringar med FEM. Detta är viktigt för kontinuerliga simuleringar av partikelflöden men uppmärksammas oftast inte tillräckligt i litteraturen. Simuleringsresultaten överensstämde väl med de flödesnivådata som erhölls från laboratorietesterna vilket visade att komplexa historier av spricköppningar och invecklade flöden överensstämde med ändrade normala belastningar och ökande skjuvningsförflyttningar, vilket även fångades av de kopplade skjuvning-flödestesterna av sprickproverna genom visualisering av vätskeflödet. Från de erhållna flödesfälten förutsågs partikeltransporten genom en strömlinjebaserad partikelspårningsmetod med kalkylerade flödeshastighetsfält (vektorer) från flödessimuleringarna genom vilka resultat som flödeshastighetsprofiler, totala flödesnivåer,partikeltransporttid, genombrottskurvor samt Pécletnumret, Pe, erhölls. Vätskeflödet i det vertikala tvådimensionella tvärsnittet av en bergsspricka simulerades även genom att både Navier-Stokes (NS) och Reynoldsekvationerna löstes och partikeltransporten förutsågs genom den strömlinjebaserade partikelspårningsmetoden. Resultaten som erhöllsmed NS och Reynoldsekvationerna jämfördes för att illustrera graden av tillförlitlighet för Reynoldsekvationen för allmänna tillämpningar i praktiken då den senare är betydligt mer beräkningseffektiv för storskaliga problem. Resultaten från flödessimuleringarna visar att den totala flödesnivån och den totala flödeshastigheten förutsedda med NS ekvationer är helt annorlunda motsvarande värden som förutsågs med Reynoldsekvationen. Resultaten visar att en ca 5-10 % för hög uppskattning av flödesnivån erhålls då Reynoldsekvationen används och de ideala parabola hastighetsprofilerna, som definieras av den lokala kubiklagen när Reynoldsekvationen används, inte längre är giltiga särskilt när sprickytornas grovhetskarakteristika ändras med skjuvning. De här avvikelserna i flödesnivå och flödeshastighetsprofiler längs med spricköppningen har en betydande påverkan på partikeltransportuppträdande och de tillhörande egenskaperna såsom rörelsetid och Pécletnummer. Avvikelserna ökar med ökande flödeshastighet och blir mer signifikanta när spricköppningarnas geometri ändras med skjuvning. Forskningsresultaten från dessa studier gav nya insikter i de fysiska uppträdandet av vätskeflöde och masstransporter i bergssprickor vilket är den vetenskapliga basen för många bergmekanikproblem på grundläggande nivå och som har särskild vikt för bergstekniksproblem såsom geotermisk energiutvinning (där flödesnivå i sprickor dominerar produktiviteten för en geotermisk energikälla) och kärnavfallsförvaringsplatser (där transporten av radioaktiva nuklider genom sprickor dominerar den slutgiltigasäkerhetsutvärderingen) i sprickigt berg. / QC 20100803

Gelfill (GF) is made of tailings, water, binder and chemical additives (Fillset, sodium silicate gel). The components of GF are combined and mixed on the surface and transported (by gravity and/or pumping) to the underground mine workings, where the GF can be used for both underground mine support and tailings storage. Thermal (T), hydraulic (H), and mechanical (M) properties are important performance criteria of GF. The understanding of these engineering properties and their evolution with time are still limited due to the fact that GF is a new cemented backfill material. In this thesis, the evolution of the thermal, hydraulic, mechanical, and microstructural properties of small GF samples are determined. Various binder contents of Portland cement type I (PCI) are used. The GF is cured for 3, 7, 28, 90, and 120 days. It is found that the thermal, hydraulic and mechanical properties are time-dependent or affected by the degree of binder hydration index. Furthermore, a relationship is found between the compressive strength and the saturated hydraulic conductivity of the GF samples. The unsaturated hydraulic properties of GF samples have also been investigated. The outcomes show that unsaturated hydraulic conductivity is influenced by the degree of binder hydration index and binder content, especially at low suction ranges. Simple functions are proposed to predict the evolution of air-entry values (AEVs), residual water content, and fitting parameters from the van Genuchten model with the degree of hydration index (α). Furthermore, two columns are built to simulate the coupled thermo-hydro-mechanical (THM) behaviour of GF under drained and undrained conditions. The obtained results from the GF columns are compared with the small samples. It is observed that the mechanical properties, hydraulic properties (suction and water content), and temperature development are strongly coupled. The magnitude of these THM coupling factors is affected by the size of the GF. The findings also show that the mechanical, hydraulic and thermal properties of the GF columns are different from samples cured in plastic moulds.

The performance of commercial Radio Frequency Identification (RFID) tags is primarily limited by present techniques used for tag antenna design. Currently, industry techniques rely on identifying the RFID tag application (books, clothing, etc.) and then building antenna prototypes of different configurations in order to satisfy minimum read range requirements. However, these techniques inherently lack an electromagnetic basis and are unable to provide a low cost solution to the tag antenna design process. RFID tag performance characteristics (read-range, chip-antenna impedance matching, surrounding environment) can be very complex, and a thorough understanding of the RFID tag antenna design may be gained through an electromagnetic approach in order to reduce the tag antenna size and the overall cost of the RFID system. The research presented in this thesis addresses RFID tag antenna design process for passive RFID tags. With the growing number of applications (inventory, supply-chain, pharmaceuticals, etc), the proposed RFID antenna design process demonstrates procedures to design tag antennas for such applications. Electrical/geometrical properties of the antennas designed were investigated with the help of computer electromagnetic simulations in order to achieve optimal tag performance criteria such as read range, chip-impedance matching, antenna efficiency, etc. Experimental results were performed on the proposed antenna designs to compliment computer simulations and analytical modelling.

The BRIght Target Explorer (BRITE) constellation is revolutionary in the sense that the same scientific objectives can be achieved smaller (cm3 versus m3 ) and lighter (< 10kg versus 1, 000kg). It is a space astronomy mission, observing the variations in the apparent brightness of stars. The work presented herein focuses on the assembly, integration and test of the instrument used on-board six nanosatellites that form the constellation. The instrument is composed of an optical telescope equipped with a Charge Coupled Device (CCD) imager and a dedicated computer. This thesis provides a particular in-depth look into the inner workings of CCD. Methods used to characterize the instrument CCD in terms of its bias level stability, gain factor determination, saturation, dark current and readout noise level evaluation are provided. These methodologies are not limited to CCDs and they provide the basis for anyone who wishes to characterize any type of imager for scientic applications.

The BRIght Target Explorer (BRITE) constellation is revolutionary in the sense that the same scientific objectives can be achieved smaller (cm3 versus m3 ) and lighter (< 10kg versus 1, 000kg). It is a space astronomy mission, observing the variations in the apparent brightness of stars. The work presented herein focuses on the assembly, integration and test of the instrument used on-board six nanosatellites that form the constellation. The instrument is composed of an optical telescope equipped with a Charge Coupled Device (CCD) imager and a dedicated computer. This thesis provides a particular in-depth look into the inner workings of CCD. Methods used to characterize the instrument CCD in terms of its bias level stability, gain factor determination, saturation, dark current and readout noise level evaluation are provided. These methodologies are not limited to CCDs and they provide the basis for anyone who wishes to characterize any type of imager for scientic applications.

Optical response of an active medium can substantially be modified when coherent superpositions of states are excited, that is, when systems display quantum coherence and interference. This has led to fascinating applications in atomic and molecular systems. Examples include coherent population trapping, lasing without inversion, electromagnetically induced transparency, cooperative spontaneous emission, and quantum entanglement. We study quantum coherence effects in several quantum optical systems and find interesting applications. We show that quantum coherence can lead to transient Raman lasing and lasing without inversion in short wavelength spectral regions--extreme ultraviolet and x-ray--without the requirement of incoherent pumping. For example, we demonstrate transient Raman lasing at 58.4 nm in Helium atom and transient lasing without inversion at 6.1 nm in Helium-like Boron (triply-ionized Boron). We also investigate dynamical properties of a collective superradiant state prepared by absorption of a single photon when the size of the sample is larger than the radiation wavelength. We show that for large number of atoms such a state, to a good approximation, decays exponentially with a rate proportional to the number of atoms. We also find that the collective frequency shift resulting from repeated emission and reabsorption of short-lived virtual photons is proportional to the number of species in the sample. Furthermore, we examine how a position-dependent excitation phase affects the evolution of entanglement between two dipole-coupled qubits. It turns out that the coherence induced by position-dependent excitation phase slows down the otherwise fast decay of the two-qubit entanglement. We also show that it is possible to entangle two spatially separated and uncoupled qubits via interaction with correlated photons in a cavity quantum electrodynamics setup. Finally, we analyze how quantum coherence can be used to generate continuous-variable entanglement in quantum-beat lasers in steady state and propose possible implementation in quantum lithography.

Gelfill (GF) is made of tailings, water, binder and chemical additives (Fillset, sodium silicate gel). The components of GF are combined and mixed on the surface and transported (by gravity and/or pumping) to the underground mine workings, where the GF can be used for both underground mine support and tailings storage. Thermal (T), hydraulic (H), and mechanical (M) properties are important performance criteria of GF. The understanding of these engineering properties and their evolution with time are still limited due to the fact that GF is a new cemented backfill material. In this thesis, the evolution of the thermal, hydraulic, mechanical, and microstructural properties of small GF samples are determined. Various binder contents of Portland cement type I (PCI) are used. The GF is cured for 3, 7, 28, 90, and 120 days. It is found that the thermal, hydraulic and mechanical properties are time-dependent or affected by the degree of binder hydration index. Furthermore, a relationship is found between the compressive strength and the saturated hydraulic conductivity of the GF samples. The unsaturated hydraulic properties of GF samples have also been investigated. The outcomes show that unsaturated hydraulic conductivity is influenced by the degree of binder hydration index and binder content, especially at low suction ranges. Simple functions are proposed to predict the evolution of air-entry values (AEVs), residual water content, and fitting parameters from the van Genuchten model with the degree of hydration index (α). Furthermore, two columns are built to simulate the coupled thermo-hydro-mechanical (THM) behaviour of GF under drained and undrained conditions. The obtained results from the GF columns are compared with the small samples. It is observed that the mechanical properties, hydraulic properties (suction and water content), and temperature development are strongly coupled. The magnitude of these THM coupling factors is affected by the size of the GF. The findings also show that the mechanical, hydraulic and thermal properties of the GF columns are different from samples cured in plastic moulds.