We explore the optical parametric amplifier, an optical device where a pump field creates a pair of lower-frequency fields: signal and idler. The pump field is usually treated classically, but this thesis focuses on scenarios where the pump must be treated quantum mechanically. One of these scenarios is the growing field of nonlinear interferometry, where the fundamental sensitivity of a probed relative phase can beat the classical bounds and reach the maximum limit allowed by quantum mechanics, the Heisenberg limit. Indeed, we show that a fully quantum nonlinear interferometer displays a Heisenberg scaling in terms of the mean number of input pump photons. This result goes beyond the well-accepted Heisenberg scaling with respect to the down-converted photons inside the interferometer, which predicts unphysical phase sensitivities starting at a particular input pump energy. Our theoretical findings are particularly useful when designing a nonlinear interferometer with bright pump fields or optimized optical parametric amplifiers for quantum metrology and quantum imaging applications. The quantum nature of the pump field may also play a central role concerning other physical phenomena, like Hawking radiation in the context of black holes. As suggested by several authors, both the optical parametric amplifier and Hawking radiation comprise the creation of fundamental particle pairs. Thus, if the optical parametric amplifier is fully treated quantum mechanically, we may get insight into an open problem in modern physics, namely the black hole information paradox. According to this paradox, the information stored in a black hole can be destroyed once the black hole has evaporated by emitting Hawking radiation, contradicting quantum mechanics. Despite the experimental efforts to build systems that reproduce event horizons and gravitational effects in the laboratory, the evaporation of black holes due to the emission of Hawking radiation remains a challenging task. In this thesis, we experimentally investigate the impact of an evolving pump field in an optical parametric amplifier by optimizing a parametric down-conversion process. We measure the pump and signal photon number properties, finding that the pump field gets chaotic and the signal coherent when the pump displays some sizeable depletion. We arrive at similar conclusions about the pump field from its measured Wigner function. Our experiment is the first step towards a successful experiment that could suggest that information in the black hole is not destroyed but encoded in the emitted Hawking radiation starting at some point in the black hole evolution. We finally discuss further experimental improvements to investigate the parallel between the optical parametric amplifier and Hawking radiation.

An efficient way of analyzing survival clinical data such as cancer data is a great concern to health experts. In this study, we investigate and propose an efficient way of handling survival clinical data. Simulation studies were conducted to compare performances of various forms of survival model techniques using an R package ``survsim". Models performance was conducted with varying sample sizes as small ($n5000$). For small and mild samples, the performance of the semi-parametric outperform or approximate the performance of the parametric model. However, for large samples, the parametric model outperforms the semi-parametric model. We compared the effectiveness and reliability of our proposed techniques using a real clinical data of mild sample size. Finally, systematic steps on how to model and explain the proposed techniques on real survival clinical data was provided.

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Parametric design has proven to be a powerful tool for structural engineers to find innovativesolutions to complex problems more effectively compared to conventional methods. Theflexibility off parametric design is immense since all types of structures depend on a range ofparameters that can be isolated, controlled and altered.In this thesis a parametric model was built with the software Grasshopper to manage thedesign process of a common type of foundation improvement. The technique has beensuccessfully used by Tyréns AB on several 19th century buildings in Stockholm in the pastdecade. The buildings were settling due to decay of the original wooden piles. To stop furthersettlements steel piles are drilled from under the building down to the bedrock. In thebasement of the buildings new and thick reinforced concrete slabs are cast which are connectedto the ground walls with concrete corbels.The available area for the installation of these corbels, the minimum distances between thecorbels and the dimensions of each corbel are all contributing factors that limit the number ofpossible design configurations. The dimensions of the concrete corbels affect the maximumload capacity which will determine their quantity and position. The corbels have to carry thevarying line loads and point loads acting on the ground walls from the structure above.With the plug-in finite element software Karamba, reaction forces in each pile were calculatedwhich also affected the possible designs.A well-functioning and adaptable parametric model presented logical results where decreasingheight of the concrete slab was affecting the capacity of each corbel which in turn generated alarger number of corbels. The model offered both manual control and automatic optimizationwhere real time variations of loads and reactions were shown depending on the changingdesign.In the optimization process which was based on genetic algorithm a cost function to deal withthe numerous contributing parameters was designed.Verification of important results increased the confidence in the model in most cases but thelack of trust in the calculated moments of each shell element created limitations. The thesisdoes not include a complete finite element analysis of the structures generated by theparametric model. However, it presents a simple export process to the third party softwareFEM-Design for verification.The role of the model was therefore not to work as a complete solution but as a powerful andeasy-to-use design tool for the structural designer to get instant feedback of chosen corbelplacements. The model offered a simplified way of achieving more slender and economicstructures both financially as well as environmentally.Parametric design was shown to be successful for solving structural problems if the model wasbased on appropriate engineering judgements.

A study is presented of the instability mechanisms of a damped axisymmetric circular disk of uniform thickness rotating about its axis with constant angular velocity and subjected to various transverse space-fixed loading systems. The natural frequencies of spinning floppy disks are obtained for various nodal diameters and nodal circles with a numerical and an approximate method. Exploiting the fact that in most physical applications the thickness of the disk is small compared with its outer radius, we use their ratio to define a small parameter. Because the nonlinearities appearing in the governing partial-differential equations are cubic, we use the Galerkin procedure to reduce the problem into a finite number of coupled weakly nonlinear second-order equations. The coefficients of the nonlinear terms in the reduced equations are calculated for a wide range of the lowest modes and for different rotational speeds. We have studied the primary resonance of a pair of orthogonal modes under a space-fixed constant loading, the principal parametric resonance of a pair of orthogonal modes when the disk is subject to a massive loading system, and the combination parametric resonance of two pairs of orthogonal modes when the excitation is a linear spring. Considering the case of a spring moving periodically along the radius of the disk, we show how its frequency can be coupled to the rotational speed of the disk and lead to a principal parametric resonance. In each of these cases, we have used the method of multiple scales to determine the equations governing the modulation of the amplitudes and phases of the interacting modes. The equilibrium solutions of the modulation equations are determined and their stability is studied. / Master of Science

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No description available.

I den här avhandlingen visas hur lasrar och optiska parametriska oscillatorer (OPO:er) kan styras spektralt med hjälp av volymbraggitter. Volymbraggitter utgörs av ett periodiskt varierande brytningsindex som skrivits i ett fototermorefraktivt glas. Gittret reflekterar därmed en specifik våglängd som bestäms av perioden hos modulationen, och kan tillverkas med smal bandbredd och hög reflektans beroende på modulationens längd och styrka. En teoretisk modell har utvecklats för reflektiva volymbraggitters egenskaper om den infallande strålen har en större vinkelspridning än gittrets vinkeltolerans. Detta kan bl.a. inträffa i en laserkavitet där gittret används vid snett infall, och en teoretisk beskrivning är därför ett viktigt redskap för att kunna designa sådana lasrar. Spektral kontroll av ett antal fasta tillståndslasrar med hjälp av volymbraggitter har i försök påvisats, och lasern har därvid både kunnat avstämmas spektralt samtidigt som en avsmalnad spektral bandbredd erhållits. Lasern kan göras väldigt enkel genom att byta ut en av kavitetsspeglarna mot gittret. Tack vare gittrets goda spektrala urvalsmekanism kan lasern låsas var som helst i förstärkningsspektrumet. De tekniker och lasrar som demonstrerats experimentellt är följande: Lasring i en enda longitudinell mod erhölls både för en diodpumpad ErYb:glas-laser vid 1553 nm med ca 10 mW:s effekt och 90 kHz linjebredd samt för en diodpumpad Nd:GdVO4-laser vid 1066 nm med 0.85 W:s effekt. Lasrarnas våglängd kunde avstämmas över större delen av gittrets bandbredd på ca. 30 GHz. Genom att bygga Nd:GdVO4-lasern med en monolitisk kavitet kunde även en spektralt synnerligen stabil laser erhållas med under 40 MHz bandbredd. Tillämpningar för dessa lasrar finns både inom spektroskopi samt som källor för intrakavitetsfördubbling till synliga våglängder. Genom att använda gittret som inkopplingsspegel går det även att framställa lasrar med en väldigt låg kvantdefekt, som därför får minskad värmeutveckling i lasermediet. Detta medger i sin tur att lasrar med höga medeleffekter kan konstrueras, som kan användas bl.a. för olika former av materialbearbetning. I detta arbete har lasrar med låg kvantdefekt byggts med Yb:KYW som laserkristall; både en laser vid 998 nm på 3.6 W som diodpumpades vid 982 nm och med en bandbredd på 10 GHz, samt en laser vid 990 nm på 70 mW som pumpades av en Ti:safir-laser vid 980 nm. Om volymbraggittret används vid snett infall kan den reflekterade våglängden avstämmas genom att gittret roteras. Denna princip användes i en diodpumpad Yb:KYW-laser till att erhålla en brett avstämbar laservåglängd mellan 996 nm och 1048 nm med en maximal effekt på 3 W och med 10 GHz bandbredd. Genom att placera gittret i en retroreflektor kunde avstämningen göras utan att kaviteten behövde linjeras om. En laser som denna kan exempelvis användas för olika typer av materialkarakterisering och spektroskopi. Med optiska parametriska oscillatorer (OPO:er) kan laserljus omvandlas till nya våglängder. Därmed kan OPO:er användas som koherenta ljuskällor där inga effektiva lasrar existerar. OPO-processen kan göras effektiv om en pulsad pump används, och den genererade våglängden kan enkelt styras med hjälp av periodiskt polade (PP) icke-linjära kristaller, såsom PP-KTiOPO4, som användes i detta arbete. En nackdel med OPO:er är att i allmänhet är den genererade signalen tämligen spektralt bredbandig. Signalens bandbredd kan dock avsmalnas betydligt om ett spektralt filter såsom ett volymbraggitter används. Genom att byta ut en av speglarna i OPO-kaviteten mot gittret kan utformningen av OPO:n göras väldigt enkel. I en OPO med en signalvåglängd på 975 nm kunde en avsmalning av bandbredden till 50 GHz påvisas med hjälp av ett braggitter. Detta motsvarar 20 gångers minskning jämfört med om en konventionell spegel används. Som mest erhölls en pulsenergi på 0.34 mJ i signalen. Genom att rotera gittret kunde våglängden avstämmas 21 THz. För att förenkla avstämningen konstruerades även en OPO med gittret i en retroreflektor, samtidigt som kaviteten var av ringtyp. I denna OPO vid en våglängd på 760 nm och med en pulsenergi i signalen på upp till 0.42 mJ erhölls en bandbredd på 130 GHz och ett avstämningsområde på 2.6 THz. Slutligen har en OPO vid 1 µm konstruerats med ett gitter med en transversellt varierande period, s.k. chirp. Därigenom kan våglängden avstämmas väldigt enkelt genom att bara flytta gittret transversellt. En tillämpning av dessa OPO:er är såsom ljuskällor i olika typer av laserbaserade sensorer, i vilka en specifik och stabil våglängd erfordras. Dessutom kan de smalbandiga OPO:erna användas som första steg i ickelinjära processer i flera steg. Smal bandbredd är då viktig för effektiviteten i den påföljande ickelinjära omvandlingen i nästa steg. / The object of this thesis is to explore the usage of reflective volume Bragg gratings in photo-thermo-refractive glass for spectral control of solid-state lasers and optical parametric oscillators, to build tunable and narrowband coherent light-sources. In order to provide a design tool for use of reflective volume Bragg gratings in laser cavities, a theory was developed that describes the performance of the gratings if the incident beam has finite width with an angular spectrum that is comparable to the grating's angular acceptance bandwidth. Spectral control was demonstrated in a number of cw solid-state lasers, in terms of narrow bandwidth and tunable wavelength, by use of a volume Bragg grating. The design could be made very simple by replacing one of the cavity mirrors with the grating. Thanks to the grating's strong spectral selectivity, the lasers could be locked anywhere in the gain spectrum, while the laser bandwidth was substantially narrowed. In particular, the following lasers were demonstrated: Single-longitudinal-mode lasing in ErYb:glass at 1553 nm with 90 kHz linewidth and in Nd:GdVO4 at 1066 nm with a linewidth below 40 MHz. Very low quantum defect in Yb:KYW lasers, diode-pumped at 982 nm and lasing at 998 nm with 10 GHz bandwidth, as well as Ti:sapphire-pumped at 980 nm and lasing at 990 nm. An Yb:KYW laser that was widely tunable from 996 nm to 1048 nm with 10 GHz bandwidth. In nanosecond pulsed optical parametric oscillators (OPOs) based on periodically poled KTiOPO4, narrowband operation and a tunable wavelength were demonstrated with a volume Bragg grating as a cavity mirror. At a signal wavelength of 975 nm, the bandwidth was 50 GHz, a reduction by 20 times compared to using a conventional mirror. A tuning range of 21 THz was also demonstrated. In another OPO at a signal wavelength of 760 nm, a ring-cavity design was demonstrated to provide convenient tuning. A tuning range of 2.6 THz and a bandwidth of 130 GHz was shown. Also, narrowband operation and tuning in an OPO around 1 µm was demonstrated by use of a transversely chirped Bragg grating. / QC 20100813

The process of design is time consuming and result oriented. There is always a better scope for any design that reduces the time with better precision. Considering this as a major factor during design process, two of the vital parts of the aircraft conceptual design are taken into account where a lot of time can be saved. Major components considered in this work are fairings for the lift generating surfaces and cockpit windshield. In this work the major inference is to reduce the time spent on the initial conceptual design. The two components designed in this work are fairings and windshield. The fairing design in this work provides a flexible template which can be used for various fuselage and wing configurations for transport aircrafts. The windshield is classified into two types in this work, flat and blend windshield. Both the type of windshields can be implemented on appropriate fuselage. Both the components are designed to be implemented in single pilot as well as double pilot aircrafts. They also have parameters which can be modified according to the user requirement. The changes in the parameters provide the change in shape, size and volume of the components. The software used for this is CATIA V5. The process is carried out using two automation methods available in CATIA namely Power-Copy and Knowledge pattern. A comparison between the effectiveness of two automation methods used in this work is performed.

This thesis investigates a method for tackling the verification of parametric systems, systems whose behaviour may depend on the value of one or more parameters. The range of allowable values for such parameters may, in general, be large or unknown. This results in a large number of instances of a system that require verification, one instance for each allowable combination of parameter values. When one or more parameters are unbounded, the family of systems that require verification becomes infinite. Computer protocols are one example of such parametric systems. They may have parameters such as the maximum sequence number or the maximum number of retransmissions. Traditional protocol verification approaches usually only analyse and verify properties of a parametric system for a small range of parameter values. It is impossible to verify in this way every concrete instance of an infinite family of systems. Also, the number of reachable states tends to increase dramatically with increasing parameter values, and thus the well known state explosion phenomenon also limits the range of parameters for which the system can be analysed. In this thesis, we concentrate on the parametric verification of the Stop-and-Wait Protocol (SWP), an elementary flow control protocol. We have used Coloured Petri Nets (CPNs) to model the SWP, operating over an in-order but lossy medium, with two unbounded parameters: the maximum sequence number; and the maximum number of retransmissions. A novel method has been used for symbolically representing the parametric reachability graph of our parametric SWP CPN model. This parametric reachability graph captures exactly the infinite family of reachability graphs resulting from the infinite family of SWP CPNs. The parametric reachability graph is represented symbolically as a set of closed-form algebraic expressions for the nodes and arcs of the reachability graph, expressed in terms of the two parameters. By analysing the reachability graphs of the SWP CPN model for small parameter values, structural regularities in the reachability graphs were identified and exploited to develop the appropriate algebraic expressions for the parametric reachability graph. These expressions can be analysed and manipulated directly, thus the properties that are verified from these expressions are verified for all instances of the system. Several properties of the SWP that are able to be verified directly from the parametric reachability graph have been identified. These include a proof of the size of the parametric reachability graph in terms of both parameters, absence of deadlocks (undesired terminal states), absence of livelocks (undesirable cycles of behaviour from which the protocol cannot escape), absence of dead transitions (actions that can never occur) and the upper bounds on the content of the underlying communication channel. These are verified from the algebraic expressions and thus hold for all parameter values. Significantly, language analysis is also carried out on the parametric SWP. The parametric reachability graph is translated into a parametric Finite State Automaton (FSA), capturing symbolically the infinite set of protocol languages (i.e. sequences of user observable events) by means of similar algebraic expressions to those of the parametric reachability graph. Standard FSA reduction techniques were applied in a symbolic fashion directly to the parametric FSA, firstly to obtain a deterministic representation of the parametric FSA, then to obtain an equivalent minimised FSA. It was found that the determinisation procedure removed the effect of the maximum number of retransmissions parameter, and the minimisation procedure removed the effect of the maximum sequence number parameter. Conformance of all instances of the SWP over both parameters to its desired service language is proved. The development of algebraic expressions to represent the infinite class of Stop-and-Wait Protocols, and the verification of properties (including language analysis) directly from these algebraic expressions, has demonstrated the potential of this method for the verification of more general parametric systems. This thesis provides a significant contribution toward the development of a general parametric verification methodology.