Em aproveitamentos hídricos, onde podem estar envolvidas elevadas alturas de água armazenada, o vertedouro é a estrutura hidráulica responsável por conduzir com segurança o escoamento que excede a capacidade de armazenamento do reservatório. Neste aspecto, é necessário considerar o processo de dissipação de energia a fim de proteger o pé da barragem e a própria estrutura do vertedouro contra a ação erosiva da água. Este fluxo que é descarregado é usualmente amortecido por um colchão d’água, o qual é delimitado em uma bacia de dissipação projetada com intuito de resistir aos esforços impostos pelo escoamento. Em grandes barramentos, a utilização de um vertedouro tipo salto esqui, que é caracterizado por um defletor de fluxo no final de sua calha, possibilita que não haja necessidade de revestir o leito próximo do pé da barragem, pois a incidência do jato lançado ocorre distante deste local. Desta maneira, a dissipação da energia é efetuada sobre o próprio leito do rio, sendo formada uma fossa de erosão, contudo, dependendo da resistência do leito e de suas características anisotrópicas, os padrões de recirculação do fluxo podem fazer a fossa evoluir para uma situação nociva. Por isso, desde a fase de projeto desse tipo de vertedouro, monitoramento e previsões da progressão da fossa são essenciais. Então, conforme proposta deste trabalho, abordou-se cada fenômeno que influencia no potencial erosivo do jato, como a turbulência em sua emissão e o grau de difusão do mesmo no colchão d’água. Assim, com ensaios sobre modelo físico, foi possível desenvolver duas metodologias, aplicáveis tanto para a verificação da erosão de material granular na superfície de leitos, quanto para o interior de leitos rochosos fissurados, cujas forças atuantes em um bloco de rocha isolado, podem vencer seu peso submerso e o destacar da matriz. / In hydroelectric plants, which may be involved elevated heights of stored water, the dam spillway is responsible for safely flow the water that exceeds the storage capacity of the reservoir. In this respect, it is necessary to consider the process of energy dissipation in order to protect the base of the dam and the spillway structure itself against the erosive action of the water. This stream discharged is usually cushioned by a waterbed, which is bounded into a stilling basin designed with the purpose of resist the efforts imposed by the flow. In large dams, the use of a ski jump spillway type, which is characterized by a flow deflector at the end of its chute, allows no need lining the bed near the foot of the dam, since the impact of the jet is launched away this location. Thus, the energy dissipation is performed on the riverbed itself, generating a scour hole, however, depending on the resistance of the bed and its anisotropic features, patterns of flow recirculation can evolve the pit into a harmful state. For this reason, since the design phase of this type of spillway, monitoring and predicting the progression of the pit are essential. Then, according to the proposal of this work, it was dealt with each phenomenon that influences the erosive potential of the jet, as the turbulence at its issue on the air, and the level of its diffusion of on waterbed. Based on physical model tests, it was possible to develop two methodologies, applicable both for verifying erosion of granular material from the surface of the bottom, as for analyze the interior of a fissured bedrock, which the forces acting on an isolated block of rock can overcome its submerged weight and uplift it off the matrix.

Den surrealistiska thrillern I´m thinking of ending things av Charlie Kaufman hade premiär på Netflix hösten 2020. Långfilmens narrativ är en utspelad fantasi och innehåller flera inslag som framställs och kan betraktas som verklighetsfrånvända. Syftet med uppsatsen var att undersöka hur overkligheten framställs genom filmklippning och hur kamerapositionering används för att skapa ett fantasi-perspektiv. Klipp-metoder diskuterade av bland annat Bordwell och Thompson, Karen Pearlman och Walter Murch ligger till grund för en audiovisuell analys. Resultatet visar att några av valda sekvenser bryter mot konventionella klippmetoder för att generera konflikt i betraktarens förväntningar. Temporala förvrängningar används för att skapa illusion och fungerar även väl för att skildra fantasi/dröm. / I´m thinking of ending things by Charlie Kaufman premiered on Netflix in the fall of 2020. The featurefilm is a surrealistic thriller who´s narrative is played out like a fantasy containing several elements deviating from reality. The purpose of the essay was to investigate how unreality is portrayled trough the film editing and how camera work is used to create a fantasy perspective. Editing methods discussed by Bordwell and Thompson, Karen Pearlman and Walter Murch, among others, form the basis for an audiovisual analysis. The result shows that several of the selected sequences violate conventional editing to generate conflict of expectations. The use of temporal distortions works as a tool for illusion and to portray dream/fantasy.

Title: Myodynamics of the support phase during different take-off tasks in human locomotion Objectives: Six types of take-off movement were analyzed in terms of support limb kinematics, take-off dynamics and muscle activation, in order to identify differences in motor control. Methods: 14 male athletes (22.6 ± 4.4 years; 182.4 ± 5.3 cm; 74.7 ± 6.2 kg) took part in laboratory experiment. Each athlete performed six different take-off movements (running, acceleration - first and second step, long jump take-off, high jump take-off and take-off to the hurdle). System Qualisys was used to analyze kinematics of the support limb. Dynamic of the suport phase was measured with Kistler 9281 EA force- plate. ME6000 apparatus was used to measure the muscle activation. Results were processed and statistically evaluated in Matlab (MathWorks, Inc) environment. Pair ANOVA, T-test and Friedmann test were performed to identify differences between take-off movements. regression analysis was introduced to find the relationship between parameters. Results: Significant differences in take-off dynamics are realized with not so significant differences in kinematic and electromyographic parameters. high jump and long jump take-offs acted most specifically in comparison with other types of take-offs. Two typically...

Master of Science / Department of Chemistry / Mark Hollingsworth / The crystal structures of the inclusion compounds 1,6-diisocyanohexane/urea and 1,6-dicyanohexane/urea were refined at several temperatures from X-ray data. These urea inclusion compounds are commensurate structures with host:guest ratios of 6:1. In contrast with the ordinary helical topology of the urea host, these structures have stacked loop topologies of the host hydrogen bonds and crystallize in space group P21/n. At room temperature, both structures are distorted along [001] from hexagonal metric symmetry. As in earlier studies of 1-chloro-6-cyanohexane/urea, cooling 1,6-diisocyanohexane/urea gives rise to an exothermic phase transition (Hº = -856 cal mol 1, Sº = -5 cal mol-1 K-1) at 175 K that results in the cooperative translation of guest molecules by 5.5 Å along the channel axis. In the low temperature form, 1,6-diisocyanohexane/urea is distorted along [100], much like X(CH2)6Y, where X, Y = Br, Cl. Although the crystal structure of 1,6-dicyanohexane/urea is essentially isomorphous with that of the high temperature form of 1,6-diisocyanohexane/urea, it does not undergo an equivalent phase transition at low temperatures. Both of these systems exhibit dynamic disorder between two gauche conformers of the guest, which have mean planes of the alkyl chains lying within 1º of [100] (major conformer) and approximately 14º from [001] (minor conformer). The temperature dependence of site occupancy factors for the disordered sites yielded enthalpy differences between major and minor sites in 1,6-diisocyanohexane/urea and 1,6-dicyanohexane/urea of 216 and 127 cal mol 1, respectively. Since the low temperature form of 1,6-diisocyanohexane/urea is distorted along [100], this is favored at low temperatures by an increased concentration of the major conformer, which predominates in 1,6-dibromohexane/urea and congeners. In 1,6-diisocyanohexane/urea, the phase transition to the low temperature form occurs at a threshold concentration for the major conformer of 67%. With its shallower temperature dependence, 1,6-dicyanohexane/urea should not reach this threshold population until approximately 92 K, at which temperature the system cannot overcome the barrier for cooperative translation of guests along the channel axis.

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Chih-Hang Wu / In recent years the stock markets have shown tremendous volatility with significant spikes and drops in the stock prices. Within the past decade, there have been numerous jumps in the market; one key example was on September 17, 2001 when the Dow industrial average dropped 684 points following the 9-11 attacks on the United States. These evident jumps in the markets show the inaccuracy of the Black-Scholes model for pricing options. Merton provided the first research to appease this problem in 1976 when he extended the Black-Scholes model to include jumps in the market. In recent years, Kou has shown that the distribution of the jump sizes used in Merton’s model does not efficiently model the actual movements of the markets. Consequently, Kou modified Merton’s model changing the jump size distribution from a normal distribution to the double exponential distribution. Kou’s research utilizes mathematical equations to estimate the value of an American put option where the underlying stocks follow a jump-diffusion process. The research contained within this thesis extends on Kou’s research using Monte Carlo simulation (MCS) coupled with least-squares regression to price this type of American option. Utilizing MCS provides a continuous exercise and pricing region which is a distinct difference, and advantage, between MCS and other analytical techniques. The aim of this research is to investigate whether or not MCS is an efficient means to pricing American put options where the underlying stock undergoes a jump-diffusion process. This thesis also extends the simulation to utilize copulas in the pricing of baskets, which contains several of the aforementioned type of American options. The use of copulas creates a joint distribution from two independent distributions and provides an efficient means of modeling multiple options and the correlation between them. The research contained within this thesis shows that MCS provides a means of accurately pricing American put options where the underlying stock follows a jump-diffusion. It also shows that it can be extended to use copulas to price baskets of options with jump-diffusion. Numerical examples are presented for both portions to exemplify the excellent results obtained by using MCS for pricing options in both single dimension problems as well as multidimensional problems.

Value-at-Risk (VaR) model fails to predict financial risk accurately especially during financial crises. This is mainly due to the model’s inability to calibrate new market information and the fact that the risk measure is characterised by poor tail risk quantification. An alternative approach which comprises of the Expected Shortfall measure and the Lognormal Jump-Diffusion (LJD) model has been developed to address the aforementioned shortcomings of VaR. This model is called the Simulated-Expected-Shortfall (SES) model. The Maximum Likelihood Estimation (MLE) approach is used in determining the parameters of the LJD model since it’s more reliable and authenticable when compared to other nonconventional parameters estimation approaches mentioned in other literature studies. These parameters are then plugged into the LJD model, which is simulated multiple times in generating the new loss dataset used in the developed model. This SES model is statistically conservative when compared to peers which means it’s more reliable in predicting financial risk especially during a financial crisis. / Statistics / M.Sc. (Statistics)

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Different generalized Newtonian fluids (where the normal stresses were neglected) were considered in this study. Analytical expressions were derived for time independent, fully developed velocity profiles of Herschel-Bulkley fluids (including the simplifications thereof: Newtonian, power law and Bingham plastic fluids) and Casson fluids through open channel sections. Both flow through cylindrical pipes (Hagen-Poiseuille flow) and parallel plates (plane Poiseuille flow) were brought under consideration. Equations were derived for the wall shear stresses in terms of the average channel velocities. These expressions for plane Poiseuille flow were then utilized in the modelling of flow through homogeneous, isotropic porous media. Flow through parallel plates was extended and a possibility of a moving lower wall (plane Couette-Poiseuille flow) was included for Herschel-Bulkley fluids (and the simplifications thereof). The velocity of the wall was assumed to be opposite to the pressure gradient (thus in the streamwise direction) yielding three different possible flow scenarios. These equations were again revisited in the study on flow over porous structures. Averaging of the microscopic momentum transport equation was carried out by means of volume averaging over an REV (Representative Elementary Volume). Flow through parallel plates enclosing a homogeneous porous medium (assumed homogeneous up to the external boundary) was studied at the hand of Brinkman’s equation. It was as- sumed (also for non-Newtonian fluids) that the term dominating outside the external boundary layer area is directly proportional to the superficial velocity that is, since only the viscous flow regime was considered, referred to as the ‘Darcy’ velocity if the diffusive Brinkman term is completely neglected. For a shear thinning or shear thickening fluid, the excess superficial velocity term was included in the proportionality coefficient that is constant for a particular fluid traversing a particular porous medium subjected to a specific pressure gradient. For such fluids only the inverse functions could be solved. If the ‘Darcy’ velocity is not reached within the considered domain, Gauss’s hypergeo- metric function had to be utilized. For Newtonian and Bingham plastic fluids, direct solutions were obtained. The effect of the constant yield stress was embedded in the proportionality coefficient. For linear flow, the proportionality coefficient consists of both a Darcy and a Forch- heimer term applicable to the viscous and inertial flow regimes respectively. Secondary averaging for different types of porous media was accomplished by using an RUC (Representative Unit Cell) to estimate average interstitial properties. Only homoge- neous, isotropic media were considered. Expressions for the apparent permeability as well as the passability in the Forchheimer regime (also sometimes referred to as the non-Darcian permeability) were derived for the various fluid types. Finally fluid flow in a domain consisting of an open channel adjacent to an infinite porous domain is considered. The analytically derived velocity profiles for both plane Couette- Poiseuille flow and the Brinkman equation were matched by assuming continuity in the shear stress at the porosity jump between the two domains. An in-house code was developed to simulate such a composite domain numerically. The difference between the analytically assumed constant apparent permeability in a macro- scopic boundary layer region as opposed to a dependency of the varying superficial velocity was discussed. This code included the possibility to alter the construction of the domain and to simulate axisymmetrical flow in a cylinder. / AFRIKAANSE OPSOMMING: Verskeie veralgemeende Newtoniese vloeistowwe (waarvan die normaalspannings ignoreer- baar is) word in hierdie studie beskou. Analitiese uitdrukkings vir tyd-onafhanklike, ten volle ontwikkelde snelheidsprofiele vir Herschel-Bulkley vloeistowwe (wat die vereen- voudigde weergawes daarvan insluit: Newtoniese, magswet- en Bingham-plastiek vloei- stowwe), sowel as Casson vloeistowwe, is afgelei vir vloei deur ‘n oop kanaal. Beide vloei deur silindriese pype (Hagen-Poiseuille vloei) en parallelle plate (vlak-Poiseuille vloei) is oorweeg. Vergelykings vir die skuifspannings op ‘n wand in terme van die gemiddelde snelhede is afgelei. Hierdie uitdrukking wat vir vlak-Poiseuille vloei verkry is, is in die modellering van vloei deur homogene, isotropiese poreuse media ook gebruik. Vloei deur parallelle plate is uitgebrei en die moontlikheid van ‘n bewegende onderste wand (vlak-Couette-Poiseuille vloei) is ondersoek vir Herschel-Bulkley vloeistowwe (en die vereenvoudigings daarvan). Dit word aangeneem dat die snelheid van die wand in die teenoorgestelde rigting as die drukgradiënt georiënteer is (dus in die stroomgewyse rigting) wat dan tot drie verskillende moontlike vloeigevalle lei. Hierdie vergelykings is weer in die studie van vloei oor poreuse strukture gebruik. Die gemiddelde van die mikroskopiese momentum transportvergelyking is bereken oor die volume van ‘n REV (“Representative Elementary Volume”). Vloei deur parallelle plate wat ‘n homogene poreuse medium omsluit (waar die medium homogeen aanvaar word tot by die eksterne grens) is bestudeer aan die hand van Brinkman se vergelyking. Daar is aanvaar (ook vir nie-Newtoniese vloeistowwe) dat die dominante term buite die eksterne grenslaaggebied direk eweredig is aan die oppervlaksnelheid en, aangesien slegs vloei in die viskeuse gebied oorweeg word, daarna verwys word as die “Darcy”- snelheid, indien die diffusiewe Brinkman-term heeltemal weglaatbaar is. Vir ‘n span-ningsverdunnende of -verdikkende vloeistof, word die oortollige oppervlaksnelheidsterm ingesluit by die proporsionaliteitskoëffisiënt wat konstant is vir ‘n spesifieke vloeistof wat deur ‘n sekere poreuse medium, onderhewig aan ‘n spesifieke drukgradiënt, vloei. Vir sulke vloeistowwe kon slegs die inverse funksies opgelos word. As die “Darcy”- snelheid nie binne die betrokke gebied bereik word nie, is daar van Gauss se hipergeometriese funksie gebruik gemaak. Vir Newtoniese en Bingham-plastiek vloeistowwe is egter direkte oplossings verkry. Die effek van die konstante toegeespanning is ingebed in die proporsionaliteitskoëffisiënt. Vir lineêre vloei bestaan die proporsionaliteitskoëffisiënt uit beide ‘n Darcy- en ‘n Forch- heimer-term wat van toepassing is in die viskeuse- en traagheidsvloeigebiede onder- skeidelik. Sekondˆere gemiddeldes vir verskillende tipes poreuse media is verkry; deur gebruik te maak van ‘n RUC (“Representative Unit Cell”) kan interstisiële gemiddelde eienskappe geskat word. Slegs homogene, isotrope media is in oorweging gebring. Uit- drukkings vir die o¨enskynlike deurlaatbaarheid sowel as die deurdringbaarheid in die Forchheimer-gebied (ook soms na verwys as die nie-Darcy deurlaatbaarheid) is afgelei vir die verskillende vloeistoftipes. Ten slotte is vloeistofvloei in ‘n gebied wat bestaan uit ‘n oop kanaal aangrensend aan ‘n oneindige poreuse domein ondersoek. Die analities-afgeleide snelheidsprofiele vir beide vlak-Couette-Poiseuille vloei en die Brinkman-vergelyking is gekoppel deur ‘n kontinu¨ıteit in die skuifspanning by die poreuse-sprong tussen die twee gebiede te aanvaar. ‘n Interne numeriese kode is ontwikkel om so ‘n saamgestelde domein numeries te simuleer. Die verskil tussen die analities konstant-aanvaarde deurlaatbaarheid in ‘n makroskopiese grenslaagstreek, eerder as ‘n afhanklikheid met die veranderende opper- vlaksnelheid, is bespreek. Hierdie kode sluit ook die moontlikheid in om die domein te herkonstrueer, asook om die simulasie van aksiaal-simmetriese vloei in ‘n silinder te ondersoek.

The jump phenomenons of many financial assets prices have been observed in many empirical papers. In this paper we extend the Heath-Jarrow-Morton model to include the jump component to derive the European-style pricing formula of the interest rate futures options. We use numerical method to simulate the options prices and analyze how each component of HJM model under jump-diffusion processes affects the interest rate futures options. Finally, we utilize LSM method which are presented by Longstaff and Schwartz to derive American options prices and compare it with European options.

The three-dimensional (3D) baroclinic response of Cayuga Lake to surface wind forcing was investigated using the fully nonhydrostatic MITgcm. The model was validated against observed temperature data using a hydrostatic 450 m (horizontal) grid and both qualitative and quantitative methods. The model correctly reproduces the basin-scale dynamics (e.g., seiche with horizontal mode-one period T1 = 80 h) with a basin-wide root-mean-square error of 1.9 C. Nonlinear internal surges were visualized to evolve due to (i) a wind-induced locally downwelled thermocline (wind duration Twind < T1/4), (ii) a basin-scale wind-induced upwelled thermocline (Twind > T1/4), (iii) internal hydraulic jumps (IHJs). Results from a 113 m grid and field observations were used to characterize the basin-scale internal wave field according to composite Froude number (G2), Wedderburn number (WN), and Lake number (LN). The typical Cayuga Lake response is a surge when ~ 1 < WN (LN) < ~ 2-12 and a surge with emergent nonlinear internal waves (NLIWs) when WN or LN < ~ 2, in agreement with published laboratory studies. An observed shock front was simulated to be an IHJ, occurring at mid-basin during strong winds when WN < 0.8. This is the first simulation of a mid-basin seiche-induced IHJ due to super critical conditions (G2 > 1) in a lake. The topographic-induced IHJs were also shown to form when the surges interact with a sill-contraction topographic feature. Both high-resolution hydrostatic and nonhydrostatic models were used to investigate the evolution, propagation and shoaling of NLIWs at medium lake-scale. A nonhydrostatic 22 m grid with lepticity λ ~ 1 ensures minimal numerical relative to physical dispersion, qualitatively reproducing observed dispersive NLIWs using ~ 2.3E+8 grid cells. Solitary waves evolve with almost unchanged wavelengths upon grid refinement from 40 m (λ ~ 2) to 22 m; suggesting model convergence to the correct solution. Corresponding hydrostatic grids were shown to produce a packet of narrower spurious solitary-like motions with different wavelengths, representing a balance between nonlinear steepening and numerical dispersion. Local gyre-like patterns and secondary transverse NLIW packets were visualized to result from wave-topography interaction, suggesting that NLIW propagation in long narrow lakes, where the bottom topography has irregularities is fundamentally 3D. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2012-12-14 12:45:21.727

In this thesis I develop a formalism for analyzing quantum optics in photonic crystal slab cavities which may be coupled, lossy, and non-orthogonal. Using a tight-binding approximation I find classical coupled-cavity quasimodes which overlap in space and frequency. These classical modes are used to develop a multiphoton basis for quantum optics with non-orthogonal photon states. I develop creation and annihilation operators with a novel commutation relation as a consequence of the nonorthogonality of the quasimodes. With these operators the effective Hamiltonian, number operator, electric field operator and quadrature operators are obtained. The quantum jump technique is applied to handle the effects of loss. This technique is compared with the master equation, and conditions for the quantum jump technique being preferable are described. The quantum jump technique is implemented numerically, allowing for time-dependent linear and X(2) non-linear pumping. I use a combination of analytic results and characteristic functions to examine the evolution of coherent and squeezed states in a single lossy quasimode. The analysis is then extended to two nonorthogonal quasimodes. States are investigated using reduced characteristic functions. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-09-27 12:00:10.281