Dissertations / Theses on the topic 'Numerical model'

Thesis (MSc)--Stellenbosch University, 2015.
ENGLISH ABSTRACT: Various numerical modelling software packages are available for predicting moored ship motions and forces. The focus of this study was to validate the numerical models QUAYSIM and WAVESCAT and how these models together form a procedure for predicting moored ship motions and forces under the impact of high and low frequency waves. The validation procedure applied in the study involved numerical modelling of a given physical model situation in which moored ship motions and forces were measured under both high and low frequency wave conditions. A physical model with built-in bathymetry was provided by the Council for Scientific and Industrial Research (CSIR) Hydraulics Laboratory in Stellenbosch. The model consisted of a moored container vessel at a jetty, with various mooring lines and fenders. A JONSWAP spectrum, which combines high and low frequency wave components, was used to simulate wave conditions for the modelling of ship motions. The wave periods and wave heights were measured at observation stations located at specific points in the basin. Other measurements such as those of the forces in the fenders and mooring lines were also determined. A multi-step approach was used to numerically predict the ship motions and forces. Firstly, the coastal processes occurring within the basin, which was set up to simulate the physical model wave behaviour, were measured to calibrate the SWAN Delft3D-WAVE model. The wave heights and periods for the respective observation stations were obtained and compared to the physical model measurements. The Delft3D-FLOW SURFBEAT model was used to calculate the low frequency waves in the coastal area. Low frequency waves are the main cause of larger ship motions and forces, therefore it is important to investigate them as part of the ship motion prediction procedure. After the waves had been computed, wave forces acting on the vessel needed to be determined for both high and low frequency waves. These wave forces were modelled with the combinations SURFBEAT/LF-STRIP (low frequency waves) and SWAN/WAVESCAT (high frequency waves). LF-STRIP provided the link between low frequency wave models and ship motion models, converting the low frequency waves into long wave forces acting on the vessel. WAVESCAT converted the high frequency waves to short wave forces. The calculated long wave forces and short wave forces served as the input required to run the ship motion model QUAYSIM to determine the movements of the moored ship as well as the restraining forces in the lines and fenders. The ship motions and forces were compared to the physical model, with the intention of possibly validating the QUAYSIM/WAVESCAT approach for predicting moored ship motions. The study provides an overview of both the setup and results of the physical and numerical model. A description of each of the numerical models SWAN, SURFBEAT, LF-STRIP, WAVESCAT and QUAYSIM is provided, along with a comparison between the physical and numerical models for each procedure. The validation procedure provided useful documentation of the quality of these numerical modelling approaches, already in use in some design projects. The numerical models WAVESCAT and QUAYSIM models of ship motion have shown to provide a good correlation between the physical model and the numerical approach. However, improvements are still required. Good comparisons were obtained for the long wave motions (horizontal movements - surge, sway and yaw). The surge and sway motions were slightly overestimated by QUAYSIM. The magnitude of the yaw was comparable but the not well represented in spectral plots.
AFRIKAANSE OPSOMMING: Daar is verskeie numeriese modellering-sagtewareprogramme beskikbaar waarmee skipbewegings en -kragte voorspel kan word. Die fokus van hierdie studie was om die numeriese modelle QUAYSIM en WAVESCAT te valideer. Saam vorm hierdie twee modelle ’n prosedure om vasgemeerde skipbewegings en -kragte veroorsaak deur lang- en kortgolfaksie te bepaal. Die validasieprosedure wat in hierdie studie gebruik is, behels ’n numeriese modelering van ’n fisiese situasie waar ’n vasgemeerde skip se bewegings en kragte onder kort- en langgolfkondisies gemeet is. ’n Fisiese model met ingeboude batimetrie is voorsien deur die Council for Scientific and Industrial Research (CSIR) se hidroliese laboratorium in Stellenbosch. Die model bestaan uit ’n vasgemeerde houerskip by ’n pier met verskeie ankerlyne en bootbuffers. ’n JONSWAPspektrum, wat kort- en langgolfkomponente kombineer, is gebruik om golfomstandighede vir die modellering van skipbewegings te simuleer. Golfperiodes en golfhoogtes is by spesifieke waarnemingstasies in die gesimuleerde hawe-area gemeet. Verdere opmetings, soos dié van die kragte in die bootbuffers en ankerlyne, is ook gedoen. ’n Stap-vir-stap benadering is gevolg om die skipbewegings numeries te voorspel. Eerstens is die kusprosesse wat in die gesimuleerde hawe plaasvind, gekalibreer met die numeriese paket SWAN Delft3D-WAVE. Die golfhoogtes en golfperiodes vir elke waarnemingstasie is bereken en vergelyk met die fisiese model se opmetings. Die SURFBEAT-module van Delft3D-FLOW is gebruik om die lae-frekwensie golwe in die kusarea te bereken. Lae-frekwensie golwe is die hoofoorsaak van skipbewegings en daarom is dit belangrik om dit te ondersoek gedurende die voorspellingsprosedure van skipbewegings. Na die golwe bereken is, moes die kragte wat beide kort en lang golwe op die skip uitoefen ook bereken word. Hierdie golfkragte is gemodelleer deur middel van die kombinasies SURFBEAT/LFSTRIP (langgolwe) en SWAN/WAVESCAT (kortgolwe). LF-STRIP het die skakel tussen golfmodelle en skipbewegingsmodelle verskaf en die lae-frekwensie golwe omgeskakel in langgolfkragte wat op die skip uitgeoefen is. WAVESCAT het die hoë-frekwensiegolwe omgeskakel in kortgolfkragte wat op die skip uitgeoefen is. Die berekende langgolf- en kortgolfkragte is ingevoer op die skipbewegingsmodel QUAYSIM om die skipbewegings en inperkingskragte in die bootbuffers en ankerlyne te bepaal sodat dit vergelyk kon word met die fisiese model, met die doel om moontlik die QUAYSIM/WAVESCAT-prosedure om gemeerde skipbewegings te voorspel te valideer. Die studie verskaf ’n oorsig van die opstel en resultate van die fisiese en numeriese modelle. Elk van die numeriese modelle SWAN, SURFBEAT, LF-STRIP, WAVESCAT en QUAYSIM word beskryf en vergelykings word getref tussen die numeriese en fisiese modelle vir elke prosedure. Die validasieprosedure verskaf nuttige dokumentasie van die kwaliteit van hierdie numeriese modeleringsprosedures wat reeds in sekere ontwerpprojekte gebruik word. Die numeriese WAVESCAT en QUAYSIM modelle van skipbewegings het ’n goeie korrelasie tussen die fisiese model en die numeriese benadering gelewer. Verbeteringe is wel steeds nodig. Goeie vergelykings is verkry vir langgolfbewegings (horisontale bewegings – stuwing (“surge”), swaai (“sway”) en gier (“yaw”)). Die stu- en swaaibewegings was effens oorskat met QUAYSIM. Die grootte van die gier was wel vergelykbaar maar is nie grafies goed uitgebeeld nie.

In the present study, a finite volume method is employed to modelthe advection-diffusion phenomenon during a pure substance meltingprocess. The exercise is limited to a benchmark problem consisting ofthe 2D melting from a vertical wall of a PCM driven by natural convectionin the melt. Numerical results, mainly the temporal evolutionof average Nusselt number at the hot wall and the average liquid fraction,are validated by available literature data and the effect of thermalinertia in the heat transfer is considered as well. Finally, motivatedby recent publications and the model presented here, possible new researchtopics are proposed.

In this thesis, we produce a rigorous and quantitative analysis of the errors introduced by finite difference schemes into strong constraint 4D-Variational (4D-Var) data assimilation. Strong constraint 4D-Var data assimilation is a method that solves a particular kind of inverse problem; given a set of observations and a numerical model for a physical system together with a priori information on the initial condition, estimate an improved initial condition for the numerical model, known as the analysis vector. This method has many forms of error affecting the accuracy of the analysis vector, and is derived under the assumption that the numerical model is perfect, when in reality this is not true. Therefore it is important to assess whether this assumption is realistic and if not, how the method should be modified to account for model error. Here we analyse how the errors introduced by finite difference schemes used as the numerical model, affect the accuracy of the analysis vector. Initially the 1D linear advection equation is considered as our physical system. All forms of error, other than those introduced by finite difference schemes, are initially removed. The error introduced by `representative schemes' is considered in terms of numerical dissipation and numerical dispersion. A spectral approach is successfully implemented to analyse the impact on the analysis vector, examining the effects on unresolvable wavenumber components and the l2-norm of the error. Subsequently, a similar also successful analysis is conducted when observation errors are re-introduced to the problem. We then explore how the results can be extended to weak constraint 4D-Var. The 2D linear advection equation is then considered as our physical system, demonstrating how the results from the 1D problem extend to 2D. The linearised shallow water equations extend the problem further, highlighting the difficulties associated with analysing a coupled system of PDEs.

Although only our species has achieved high level of mathematical reasoning, numerical abilities are not a human prerogative and in last decades comparative research showed that several animal species display rudimentary numerical capacities (Agrillo & Beran, 2013). The ability to discriminate between quantities provide multiple benefits in different ecological contexts. For instance, numerical abilities can be useful to select the larger amount of food (Hunt et al., 2008), to reduce the probability of being spotted by predators by getting protection within the largest group of social companions (Cresswell, 1994) and to decide whether attack another group based on the assessment of the relative number of intruders (Benson-Amram et al., 2011). In particular, the discovery in recent years that even simple organisms, such as fish, possess numerical abilities similar to primates has made possible the use of fish as an animal model to study numerical cognition in the absence of language. To date, different studies have shown that fish are able to select the larger shoal of conspecifics (Agrillo et al., 2008) and can be trained to discriminate between groups of figures differing in numerosity both when allowed to use number and continuous quantities and when only number was available (Agrillo et al., 2009, 2010). Fish can also make a spontaneous use of numerical information with apparently the same effort required to discriminate continuous quantities (Dadda et al., 2009). These abilities seem to be partially inborn as one-day old fish are already able to discriminate between small groups of peers (Bisazza et al., 2010). Nonetheless several questions about numerical abilities in fish are still unanswered. For instance, it is unclear whether numerical systems are the same among different species, whether numerical acuity may be affected by different factors, such as cooperation among individuals and the presence of items in motion or whether newborn fish could be trained to discriminate between sets of items. The aim of the present study was to fill this gap. In particular, the first part of the thesis deals with some of the open questions about numerical cognition in adult fish; the second part is focused on the ontogeny of numerical competence. In the first study (Section 4.1) we set up a novel procedure for training fish to discriminate between sets of stimuli (groups of geometrical figures) differing in numerosity as the previous methodology used to train fish was time-consuming, suitable only for social species and potentially stressful for fish. To validate the method, we replicated two published experiments that used operant conditioning to investigate mosquitofish (Gambusia holbrooki) abilities to discriminate between small sets of items and the influence of numerical ratio and total number of figures on large number discrimination (Agrillo et al., 2009, 2010). In the new procedure a pair of stimuli differing in numerosity was introduced at the opposite ends of the experimental tank and a food reward was released in correspondence of the stimulus to be reinforced. Fish were initially trained on an easy numerical ratio (0.5) and were then tested in non-reinforced probe trials for their ability to generalize to new numerosities. The new procedure designed replicated previous results: fish proved able to discriminate up to 2 vs. 3 figures and their performance in the large number range decreased while increasing the numerical ratio though their numerical acuity seemed to have no upper limit. In addition, the new method proved to be rapid, applicable to different fish species and efficient to study discrimination learning in fish in tasks requiring visual stimuli. As a consequence, the novel protocol was adopted in all the training experiments presented in this thesis. The second study (Section 4.2) focused on a potential limit in numerical cognition research: the lack of cross-species studies using the same methodology. The question of whether all vertebrates share the same numerical systems or rather numerical abilities have appeared multiple times during evolution in response to specific selective pressures imposed by the environment, represents one of the main issues of animal cognition. Despite the large number of published data, results are inconsistent because the methodologies adopted vary across studies, making difficult any inter-specific comparison. To date no study has investigated if different fish species have the same numerical systems. This experiment represents the first inter-specific study using the same methodology in fish. Five fish species as diverse as guppies (Poecilia reticulata), zebrafish (Danio rerio), angelfish (Pterophyllum scalare), redtail splitfin (Xenotoca eiseni) and Siamese fighting fish (Betta splendens) were trained on an easy numerical ratio (0.50) and then were compared in their ability to generalize to more difficult ratios (0.67 and 0.75), or to a larger (25 vs. 50) or a smaller (2 vs. 4) total set size. Results showed interesting similarities among the species, opening the possibility of shared numerical systems among phylogenetically distantly related species, more in accord with the existence of ancient quantification systems inherited from a common ancestor than with an independent evolution of numerical abilities in different species. Another important question in the study of numerical cognition concerns the influence of contextual factors on the numerical capacities of a species. It is possible that the performance observed in a numerical task is limited to the specific context in which such abilities are observed rather than reflecting the full numerical competence of a species. To this purpose, the third (Section 5.1) and fourth (Section 5.2) studies investigated the potential influence on fish numerical acuity of factors that normally occur in nature, namely, the cooperative behavior within group and the perception of figures in motion. In natural environment grouping animals interact with each other and these repeated interactions among individuals can affect adaptive response. Recent studies have provided evidence that, in some contexts, collective actions allow to bypass the cognitive limits of a species and to solve problems that go beyond the capacity of a single individual (Krause et al., 2010, Couzin, 2009). To date, all numerical studies in non-human animals have tested subjects individually and it is not known whether collective behavior can enhance the capacity to solve numerical tasks. The third study (Section 5.1) aimed to verify whether fish in dyads were more accurate than single individuals in two different numerical discrimination tasks. In the first task, guppies were required to join the larger group of conspecifics (4 vs. 6); in the second one fish were trained to discriminate between sets of figures (0.5 ratio) and hence were tested in discriminations of increasing difficulty (0.67 and 0.75 ratios). Results showed that dyads performed better than singletons in selecting the larger group of social companions and also made better numerical discriminations of arrays of dots, showing that collective behavior may yield benefits that go beyond the single ecological context. In addition, in both conditions, the better individual of the dyad spontaneously emerged as the leader. Interestingly, the results here obtained aligned with data collected in adult humans where dyadic performance was superior than individual in a collective enumeration task (Bahrami et al., 2013), thus suggesting that cooperation similarly increases numerical acuity in two distantly related species, such as humans and fish. The motion of items is another factor that might potentially affect numerical abilities. Animals are naturally exposed to moving items (e.g., prey, predators) and hence the movement represents a relevant cue in their life. It is known that fish ability to discriminate between small and large groups of conspecifics is differently affected by the quantity of movement of social companions (Agrillo et al., 2008). However it is still unexplored whether fish can discriminate between two-dimensional figures in motion and whether their accuracy is the same in the small and large number range. For example, it has been reported that adult humans are faster and more accurate in estimating small numerosities (≤ 4) of dynamic items than large numerosities (≥ 4), supporting the hypothesis of two distinct numerical systems (Trick et al., 2003, Alston & Humphreys, 2004). To this aim, in the fourth study (Section 5.2) guppies were trained (0.5 ratio) and tested (0.75 ratio) with either static or moving stimuli. We observed a similar effect of items in motion in fish: while a 0.75 ratio was not discriminated with static stimuli in either numerical range (3 vs. 4 and 9 vs. 12), guppies were able to discriminate this ratio with items in motion but only in the small number range (3 vs. 4). To date, comparative psychologists disagree as to whether in non-human species a single system accounts for discriminations over the whole numerical range (called “Approximate number system”), or a distinct system operates over the small number range (≤4) (called “Object tracking system”). Although the results do not represent a direct evidence for the existence of a separate system in the range 1-4, the differential effect of motion reported in guppies reinforces the idea of separate cognitive systems for small and large numbers, in line with data collected in humans. Despite no direct comparisons have been made between fish and humans in this thesis, the similarities between the two species are worth noting as they raise the intriguing possibility that the foundation of our numerical abilities might be evolutionarily more ancient than previously thought, dating back at least as far as the divergence between fish and land vertebrates. The second part of the thesis focused on the development of numerical abilities using newborn guppies as a model species. Developmental studies can provide useful insights with respect to the existence of a single or multiple systems of numerical representation. For instance, exploring developmental trajectories of numerical skills in different contexts can help us to assess whether the same or distinct numerical systems are used in different tasks. Since an adequate method to study discrimination learning in newborn guppies was not available, in the fifth study (Section 6.1) we designed a procedure by taking into account the social needs of young individuals in order to minimize potential stress due to social deprivation, without interfering with the normal development of their behavioral repertoire. We investigated the development of social behavior in the first two weeks of life by using a spontaneous choice task where newborn guppies could choose between social companions and an empty compartment. Then, newborns were given the choice between their own mirror image and a group of peers to assess whether mirrors could be used as a substitute for social companions during experiments. Based on the findings of these experiments, the protocol for discrimination learning in adult fish was adapted to study shape discrimination in newborn fish. Newborn guppies proved capable to learn a simple shape discrimination after few trials and the training method was then used in the last study (Section 6.2) to investigate their numerical competence using sets of two-dimensional objects, as commonly done with adult fish. At present only Bisazza and colleagues (2010) investigated the ontogeny of numerical abilities in fish. The authors found that, at birth, the capacity of guppies to discriminate between shoals differing by one individual included all numerical contrasts in the range 1-4; young guppies proved also be able to discriminate small numerosities by using numerical information only. In Section 6.2 we investigated whether newborns could be trained to discriminate between small sets of figures. To this purpose, we set up three different experimental conditions to study the influence of continuous quantities that co-vary with numbers (cumulative surface area, density, etc.). In the first one number and continuous quantities were simultaneously available, in the second condition only numerical information was available and in the last one, numerical information was made irrelevant (3 vs. 3) and only continuous quantities were available. The result that fish discriminated only very easy numerical contrasts in the range 1-4 when both number and continuous variables were available was in contrast with the results of shoal discrimination experiments (Bisazza et al., 2010) thus suggesting that newborns’ capacity to use number is specific to social stimuli. On the whole data on guppies, both adult fish and newborns, are suggestive of the existence of multiple quantification mechanisms in fish which are domain-specific and serve to solve a limited set of problems in accordance with the hypothesis proposed by different authors (Feigenson et al., 2004; Spelke, 2000). In sum, the data collected in this thesis indicate that even fish, which are provided with a much smaller brain than warm-blooded vertebrates, can discriminate between quantities and solve complex numerical tasks, in line with evidence in other research fields which suggest that processing numerical information might not require complex neural circuits (Hope et al., 2010). This goes together with recent discovery that bony fish possess several other cognitive abilities that were previously believed to be uniquely present in species provided with large, complex brains (i.e. mammalian and avian species) (Bshary et al., 2002). For all these reasons, fish may become a proper model to study cognitive abilities and in particular numerical competence.
Sebbene solamente la nostra specie abbia raggiunto un elevato livello di competenze matematiche, le capacità numeriche non sono una prerogativa umana e negli ultimi decenni la ricerca comparata ha documentato come molte specie animali posseggano rudimentali abilità numeriche (Agrillo & Beran, 2013). La capacità di saper discriminare tra diverse quantità risulta essere vantaggiosa in diversi contesti ecologici. Per esempio, tale abilità può essere utile per scegliere la quantità maggiore di cibo (Hunt et al., 2008), per ridurre la probabilità di essere predati - ottenendo protezione dal gruppo di conspecifici più numeroso (Cresswell, 1994) - e per decidere se intraprendere interazioni aggressive contro un altro gruppo in base al numero di potenziali rivali (Benson-Amram et al., 2011). In particolare, la recente scoperta che persino organismi semplici, come i pesci, posseggono abilità numeriche simili a quelle osservate nei primati ha reso possibile l'utilizzo dei pesci come modello animale per studiare la cognizione numerica in assenza del linguaggio. Ad oggi, diversi studi hanno infatti dimostrato che i pesci sono capaci di selezionare il gruppo di conspecifici più numeroso (Agrillo et al., 2008) e possono essere addestrati a discriminare tra gruppi di figure di diversa numerosità, sia quando possono utilizzare l’informazione numerica e le variabili continue simultaneamente, sia nel caso in cui sia disponibile solamente l’informazione numerica (Agrillo et al., 2009, 2010). È stato inoltre dimostrato che i pesci sono in grado di discriminare tra quantità usando spontaneamente il numero, apparentemente con lo stesso sforzo cognitive richiesto per discriminare le variabili continue (Dadda et al., 2009). Queste capacità sembrano essere in parte innate, dal momento che gli avannotti di un giorno di vita sono già in grado di discriminare tra piccoli gruppi di conspecifici (Bisazza et al., 2010). Tuttavia diverse domande sulle abilità numeriche nei pesci sono ancora senza risposta. Ad esempio, non è chiaro se i sistemi numerici siano gli stessi fra specie differenti, se l'acuità numerica possa essere influenzata da diversi fattori, come la cooperazione tra gli individui e la presenza di oggetti in movimento o se i pesci appena nati possano essere addestrati a discriminare tra gruppi di oggetti bidimensionali. Lo scopo della presente tesi è stato pertanto quello di colmare queste lacune. In particolare, la prima parte della tesi affronta alcune delle questioni aperte sulla cognizione numerica nei pesci adulti, mentre la seconda parte è focalizzata sull’ontogenesi delle abilità numeriche. Nel primo lavoro (Sezione 4.1) è stata messa a punto una nuova procedura per addestrare i pesci a discriminare tra stimoli bidimensionali (gruppi di figure geometriche) di diversa numerosità, dal momento che il metodo precedentemente utilizzato in letteratura richiedeva tempi prolungati, era adatto solo per le specie sociali ed era potenzialmente stressante per i pesci. Per verificare la validità del metodo, sono stati replicati due esperimenti che hanno usato la procedura del condizionamento operante per indagare le capacità della gambusia (Gambusia holbrooki) di discriminare tra piccole numerosità e l’influenza del rapporto numerico e del numero totale di elementi nella discriminazione di grandi quantità (Agrillo et al., 2009, 2010). Nella nuova procedura, veniva introdotta una coppia di stimoli di diversa numerosità alle estremità della vasca sperimentale e successivamente veniva rilasciato del cibo in corrispondenza dello stimolo da rinforzare. I pesci sono stati inizialmente addestrati a distinguere un rapporto numerico relativamente semplice (0.5); successivamente nella fase di test, sono stati sottoposti a delle prove in estinzione (non veniva fornito il rinforzo alimentare) per verificare la loro capacità di generalizzare a nuove numerosità. La nuova procedura messa a punto ha replicato i risultati ottenuti con quella precedentemente utilizzata: i soggetti sono stati in grado di discriminare fino a 2 figure da 3; in presenza di grandi numerosità la prestazione diminuiva all’aumentare del rapporto numerico sebbene la loro capacità di discriminare sembri non avere un limite superiore. Il nuovo metodo si è inoltre rivelato rapido per la raccolta dei dati, applicabile a diverse specie di pesci ed efficacie per studiare l'apprendimento discriminativo in compiti che richiedono stimoli visivi. Di conseguenza, il nuovo protocollo è stato adottato in tutti gli esperimenti presentati in questa tesi che hanno usato la procedura di addestramento. Il secondo lavoro (Sezione 4.2) è incentrato su un potenziale limite della ricerca sulla cognizione numerica: la mancanza di studi inter-specifici che utilizzano la stessa metodologia. La questione se tutti i vertebrati condividano gli stessi sistemi numerici o se piuttosto le abilità numeriche siano apparse più volte durante l'evoluzione in risposta a specifiche pressioni selettive imposte dall'ambiente rappresenta uno dei temi principali della cognizione animale. Nonostante l’elevato numero di dati pubblicati, i risultati non sono coerenti dal momento che sono state utilizzate diverse metodologie di ricerca rendendo così difficile un confronto inter-specifico accurato. Ad oggi, nessuno studio ha indagato se diverse specie di pesci possiedano gli stessi sistemi numerici. Questo lavoro rappresenta il primo studio inter-specifico che utilizza la stessa metodologia nei pesci. Cinque diverse specie, la pecilia (Poecilia reticulata), lo zebrafish (Danio rerio), il pesce scalare (Pterophyllum scalare), la xenotoca (Xenotoca eiseni) ed il pesce combattente (Betta splendens), sono state inizialmente addestrate utilizzando un rapporto numerico semplice (0.50) e successivamente è stata confrontata la loro capacità di generalizzare a rapporti più difficili (0.67 e 0.75) o ad una numerosità maggiore (25 vs. 50) o minore (2 vs. 4). I risultati hanno mostrato interessanti somiglianze tra le specie, suggerendo la possibilità di sistemi numerici condivisi tra specie filogeneticamente distanti tra loro, più in accordo con l’esistenza di antichi sistemi di quantificazione ereditati da un antenato comune piuttosto che con un’evoluzione indipendente delle abilità numeriche in specie diverse. Un'altra questione importante nello studio della cognizione numerica riguarda l'influenza di fattori contestuali sulle capacità numeriche di una specie. È possibile che la prestazione osservata in un compito numerico sia limitata al contesto specifico in cui tali capacità sono state osservate piuttosto che riflettere le reali abilità numeriche della specie. Per questo motivo, il terzo (Sezione 5.1) e il quarto (Sezione 5.2) lavoro hanno studiato la potenziale influenza sull’accuratezza numerica dei pesci di fattori che normalmente si verificano in natura: il comportamento cooperativo all'interno del gruppo e la percezione di figure in movimento. In natura, gli animali che vivono in gruppo interagiscono tra di loro e queste interazioni ripetute tra gli individui possono incidere sulle scelte fatte in diversi contesti. Studi recenti hanno dimostrato che in alcune circostanze le azioni collettive permettono di aggirare i limiti cognitivi di una specie e di risolvere i problemi che vanno al di là delle capacità del singolo individuo (Krause et al., 2010, Couzin, 2009). Fino ad oggi, tutti gli studi di cognizione numerica condotti negli animali hanno preso in considerazione le prestazioni di singoli soggetti e non si sa quindi se il comportamento collettivo possa migliorare la capacità di risolvere compiti di discriminazione numerica. Lo scopo del terzo lavoro (Sezione 5.1) è stato quello di verificare se i pesci sottoposti a test in coppia fossero più accurati rispetto ai soggetti sottoposti a test individualmente in due diversi compiti di discriminazione numerica. Nel primo compito si è osservata la capacità delle pecilie di scegliere il gruppo di conspecifici più numeroso (4 vs. 6); nel secondo, invece, i pesci sono stati addestrati a discriminare tra gruppi di figure con un rapporto numerico pari a 0.5 e successivamente sono stati sottoposti a test usando confronti numerici più difficili (con rapporti pari a 0.67 e 0.75). I risultati hanno mostrato che i soggetti in coppia hanno avuto una prestazione migliore rispetto ai singoli, sia nella scelta del gruppo di conspecifici più numeroso, sia nel compito di discriminazione numerica, dimostrando quindi che il comportamento collettivo può fornire benefici che vanno al di là del singolo contesto ecologico. Inoltre, in entrambe le condizioni, il soggetto più accurato all’interno della coppia nella risoluzione del compito è emerso spontaneamente come leader. È interessante notare che i risultati ottenuti in questo lavoro sono in linea con i dati raccolti negli esseri umani adulti in cui la prestazione dei partecipanti in coppia è risultata superiore rispetto alle prestazioni individuali in un compito collettivo di discriminazione numerica (Bahrami et al., 2013). Questi dati suggeriscono quindi che la cooperazione aumenti l'acuità numerica in maniera simile in due specie filogeneticamente distanti tra di loro: gli esseri umani ed i pesci. Il movimento degli oggetti è un altro fattore che potrebbe potenzialmente influenzare l’acuità numerica. Gli animali sono infatti naturalmente esposti a degli elementi che si muovono (es. prede, predatori) e quindi il movimento rappresenta un segnale saliente nella loro vita. È stato dimostrato che la quantità di movimento dei conspecifici influenza in maniera differente la capacità dei pesci di discriminare tra piccoli (≤ 4) e grandi (≥ 4) gruppi di compagni sociali (Agrillo et al., 2008). Tuttavia non è stato ancora indagato se i pesci siano in grado di discriminare tra figure bidimensionali in movimento e se la loro accuratezza sia la stessa in presenza di piccole e grandi numerosità. Ad esempio, si è osservato che gli esseri umani adulti sono più veloci e più accurati nello stimare piccole quantità ( ≤ 4 ) di elementi in movimento piuttosto che grandi numerosità ( ≥ 4 ), supportando l'ipotesi di due sistemi numerici distinti (Trick et al., 2003, Alston & Humphreys, 2004). A tal fine, nel quarto lavoro (Sezione 5.2) esemplari di pecilia sono stati addestrati (con rapporto numerico 0.5) e sottoposti a test (con rapporto 0.67) con stimoli statici o in movimento. Si è osservato che gli elementi in movimento avevano un effetto simile a quello riportato nella nostra specie: mentre i soggetti a cui erano stati presentati gli stimoli statici non sono stati in grado di discriminate il rapporto pari a 0.67, sia in presenza di piccole che di grandi numerosità (3 vs. 4 e 9 vs. 12), i soggetti a cui erano stati presentati gli stimoli in movimento hanno saputo discriminare questo rapporto ma solo in presenza di piccole numerosità (3 vs 4). Ad oggi, nell’ambito della psicologia comparata c’è un dibattito sul fatto che gli animali posseggano un unico sistema di discriminazione per tutta la scala numerica (chiamato “Approximate number system”), oppure posseggano anche un sistema distinto coinvolto solo nella discriminazione di piccole numerosità (≤ 4) (chiamato “Object tracking system”). Sebbene i risultati ottenuti non rappresentino una prova diretta dell'esistenza di un sistema separato per la discriminazione numerica nell'intervallo 1-4 , il fatto che il movimento influenzi in maniera differente la discriminazione di piccole e grandi quantità nelle pecilie rafforza l'idea di sistemi cognitivi separati per piccoli e grandi numeri, in linea con i dati raccolti negli esseri umani. Nonostante in questa tesi non siano stati effettuati confronti diretti tra pesci e umani, è interessante notare le somiglianze osservate tra le due specie in quanto sollevano la possibilità che le nostre abilità numeriche abbiano un’origine più antica di quanto si pensi, che risalirebbe alla divergenza tra la linea evolutiva dei pesci e quella dei vertebrati terrestri . La seconda parte della tesi è incentrata sullo sviluppo delle abilità numeriche utilizzando gli avannotti di pecilia come specie modello. Gli studi sullo sviluppo delle abilità cognitive possono fornire indicazioni utili per quanto riguarda l'esistenza di un unico o più sistemi di rappresentazione numerica. Ad esempio, studiare lo sviluppo delle capacità numeriche in contesti diversi può aiutarci a capire se gli stessi sistemi numerici sono utilizzati in compiti diversi o piuttosto se vengono usati sistemi differenti. Dal momento che in letteratura non è presente un metodo adeguato per studiare l'apprendimento discriminativo in esemplari giovani di pecilia, nel quinto lavoro (Sezione 6.1) abbiamo messo a punto una procedura tenendo conto delle esigenze sociali dei giovani individui, al fine di ridurre al minimo il potenziale stress dovuto alla deprivazione sociale, senza interferire con il normale sviluppo del loro repertorio comportamentale. Pertanto, inizialmente abbiamo studiato lo sviluppo del comportamento sociale nelle prime due settimane di vita utilizzando un test di scelta spontanea dove gli avannotti potevano scegliere tra un compartimento contenente dei compagni sociali e uno compartimento vuoto. Successivamente veniva data ai giovani soggetti la possibilità di scegliere tra la propria immagine riflessa e un gruppo di coetanei per valutare se gli specchi potessero essere usati come sostituto dei compagni sociali durante gli esperimenti. Sulla base dei risultati ottenuti, è stato adattato il protocollo per l'apprendimento discriminativo usato nei pesci adulti per studiare la capacità degli avannotti di discriminare tra figure. I soggetti si sono dimostrati in grado di imparare una semplice discriminazione tra figure geometriche dopo poche prove; il metodo di addestramento è stato allora utilizzato nell’ultimo lavoro (Sezione 6.2) per studiare le loro capacità numeriche usando insiemi di figure bidimensionali, come viene comunemente fatto con i pesci adulti. Ad oggi, solamente Bisazza e collaboratori (2010) hanno studiato lo sviluppo ontogenetico delle abilità numeriche nei pesci. Gli autori hanno dimostrato che la capacità alla nascita delle pecilie di discriminare tra gruppi di conspecifici di diversa numerosità include tutti i confronti numerici nell’intervallo 1-4; i giovani soggetti hanno dimostrato inoltre di sapere discriminare piccole numerosità usando solamente l’informazione numerica. Nella Sezione 6.2 si è andato a verificare se gli avannotti di pecilia possono essere addestrati a discriminare tra insiemi di figure. A tal fine, sono state messe a punto tre condizioni sperimentali per studiare l'influenza delle variabili continue che co-variano con la numerosità (area complessiva degli stimoli, densità, ecc.). Nella prima condizione sia il numero che le variabili continue erano simultaneamente disponibili, nella seconda, solo l’informazione numerica era disponibile e, nell’ultima condizione l’informazione numerica è stata resa irrilevante (3 vs. 3) ed erano disponibili solo le variabili continue. Il risultato che i soggetti hanno saputo discriminare solo i confronti numerici facili nell’intervallo 1-4 quando sia il numero che le variabili continue erano disponibili è in contrasto con i dati ottenuti negli esperimenti di scelta spontanea (Bisazza et al., 2010), suggerendo che la capacità dei giovani pesci di utilizzare l’informazione numerica sia limitata agli stimoli sociali. Nel complesso i dati raccolti nella pecilia, sia in soggetti adulti che negli avannotti, suggeriscono l'esistenza nei pesci di molteplici meccanismi di discriminazione di quantità coinvolti nella risoluzione di problemi specifici, in accordo con l’ipotesi proposta in precedenza da diversi autori (Feigenson et al., 2004; Spelke, 2000). In sintesi, i dati raccolti in questa tesi indicano che anche i pesci, pur essendo dotati di un cervello molto più piccolo dei vertebrati a sangue caldo, possono discriminare tra quantità e risolvere compiti numerici complessi, in linea con altri ambiti di ricerca che suggeriscono come l’elaborazione dell’informazione numerica potrebbe non richiedere circuiti neurali complessi (Hope et al., 2010). Questo va di pari passo con la recente scoperta che i teleostei possiedono diverse abilità cognitive che in precedenza si ritenevano essere unicamente presenti nelle specie dotate di cervelli più grandi e complessi (es: mammiferi e specie di uccelli) (Bshary et al., 2002). Alla luce dei risultati presentati in questa tesi, è possibile affermare che i pesci costituiscono un modello adeguato per lo studio delle capacità cognitive ed in particolare di quelle numeriche.

Beneath many glaciers and ice sheets, hydrology influences or controls a variety of basal processes. Glaciohydraulic supercooling is a process whereby water freezes englacially or subglacially because its internal temperature is below the bulk freezing temperature. Water supercools when it is at its freezing point and flows from an area of higher pressure (lower ambient temperature) to an area of lower pressure (higher ambient temperature) without equilibrating its internal energy. The process is dependent on the configuration of the water flow path relative to the pressure gradient driving flow. I formulate the governing equations of mass, linear momentum, and internal energy for time-dependent clear water flow based on previous work (Clarke, 2003; Spring & Hutter, 1981, 1982). Because field evidence and steady-state theory point to water distributing laterally across the bed, I modify this theory to account for an aperture that is much wider than deep, which I refer to as a sheet. Ice accretion terms are formulated with porosity because accreting ice has residual porosity. Ice intrusion into such a water sheet is not described in the literature, and I formulate intrusion based on previous work as well as ideas gained from subglacial cavity formation. In addition, I modify the clear water equations to include erosion and deposition of sediment along the glacier bed and incorporation of sediment into the accreted ice. Furthermore, water may leave the ice-bed interface and flow through the glacier pore space because subglacial water pressure is relatively high when supercooling occurs. To this end, I develop an englacial waterflow model that incorporates changes in ice porosity based on creep closure and ice melt or accretion. Simulations reveal behavior that cannot be inferred from simplified models. For example, while total ice accretion is comparable to field estimates, locations of simulated ice accretion along the ice-bed interface conflict with steady state models, which tend to overpredict accretion amounts. Simulations also indicate that much sediment deposition occurs prior to water being supercooled. Sediment deposition tends to smooth subglacial topography rather than enhance it. Additional results and implications of numerical simulations are discussed.
Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate

The ability to represent the transport and fate of an oil slick at the sea surface is a formidable task. By using an accurate numerical representation of oil evolution and movement in seawater, the possibility to asses and reduce the oil-spill pollution risk can be greatly improved. The blowing of the wind on the sea surface generates ocean waves, which give rise to transport of pollutants by wave-induced velocities that are known as Stokes’ Drift velocities. The Stokes’ Drift transport associated to a random gravity wave field is a function of the wave Energy Spectra that statistically fully describe it and that can be provided by a wave numerical model. Therefore, in order to perform an accurate numerical simulation of the oil motion in seawater, a coupling of the oil-spill model with a wave forecasting model is needed. In this Thesis work, the coupling of the MEDSLIK-II oil-spill numerical model with the SWAN wind-wave numerical model has been performed and tested. In order to improve the knowledge of the wind-wave model and its numerical performances, a preliminary sensitivity study to different SWAN model configuration has been carried out. The SWAN model results have been compared with the ISPRA directional buoys located at Venezia, Ancona and Monopoli and the best model settings have been detected. Then, high resolution currents provided by a relocatable model (SURF) have been used to force both the wave and the oil-spill models and its coupling with the SWAN model has been tested. The trajectories of four drifters have been simulated by using JONSWAP parametric spectra or SWAN directional-frequency energy output spectra and results have been compared with the real paths traveled by the drifters.

Sedimenting suspensions exist in a varity of natural phenomena and industrial applications. It is already observed in experiments that the dilute fibre suspensions experience a concentration instability under gravity at low Reynolds numbers. Initially well-mixed suspensions become inhomogeneous and anisotropic due to this instability. This project is focused on the development and validation of numerical models to understand the instability in a dilute fibre suspension by means of the mixture model and the point-particle model. For periodic boundary condition, we use a linear stability analysis to show that inertia and hydro dynamic translational diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. However, numerical simulations indicate a weak wavenumber selection even at zero Reynolds number. Numerical simulations also show that the induced flow may either die or saturate on a finite amplitude. The characterof this long time behaviour is dictated by the wavenumber, the presence or absence of the translational diusivity, rotational diffusivity, and the fluid inertia on particle motions. Moreover, the most unstable wavenumber decreases with time and the maximum amplitude increases. The smallest wavenumber obtains the largest amplitude at steady state. For a vessel bounded by sidewalls, the near-wall convection is an upward back flow in the very beginning, due to the combined effects of the steric-depleted layer and a hydrodynamiclly-depleted region near the wall. However, the evolution of the near-wall convection at later times depends on the aspect ratio of the bres, the translational diffusivity and the initial perturbations. The steric-depleted layer in the mixture model can be neglected for large widths. Multiple streamers are obtained due to the sidewalls, implying that the sidewalls can generate a wavelength which is smaller than the channel width. The suspension ends up with a single streamer on one side of the container, consistent with the results of the cases with periodic boundary condition but different from the experimental results. This might be due to the absence of the botton wall in the mixture model. Moreover, the global structure evolution of a suspension is dependent on the width of the vessel and the amplitude ofthe initial perturbations.

QC 20140207

Massive stars usually form groups such as OB associations. Their fast stellar winds sweep up collectively the surrounding insterstellar medium (ISM) to generate superbubbles. Observations suggest that superbubble evolution on the surrounding ISM can be very irregular. Numerical simulations considering these conditions could help to understand the evolution of these superbubbles and to clarify the dynamics of these objects as well as the difference between observed X-ray luminosities and the predicted ones by the standard model (Weaver et al. 1977).

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric and Planetary Sciences, 1985.
Microfiche copy available in Archives and Science.
Bibliography: leaves 80-81.
by Haim Nelken.
M.S.

A large fraction of the current cost of wastewater treatment is from the treatment and disposal of wastewater sludge. Improved design, energy efficiency, and performance of dewatering facilities could significantly decrease transport and disposal costs. Dewatering facilities are designed based on field experience, trial and error, pilot plant testing, and/or full scale testing. Design is generally time-consuming and expensive. A full-scale test typically consists_ of side-by-side operation of 4 to 5 full-scale dewatering units for several weeks to more than 6 months. Theoretical modeling of the physics of dewatering units such as the belt filter press, based on laboratory determined sludge properties, would better predict dewatering performance. This research developed a numerical computer model of the physics of gravity sedimentation. The model simulated the gravity sedimentation portion of the belt filter press. The model was developed from a physically-based numerical computer model of cake filtration by Wells (1990). As opposed to the cake filtration model, the inertial and gravity terms were retained in the gravity sedimentation model. Although in the cake filtration model, the inertial terms were shown to be negligible, according to Dixon, Souter, and Buchanan (1985), inertial effects in gravity sedimentation cannot generally be ignored. The region where inertia is important is the narrow interface between suspension and sediment. In the cake filtration model the gravity term was negligible due to the relatively large magnitude of the applied pressure; but in the gravity sedimentation model, since there was no applied pressure, it was necessary to consider the effect of gravity. _ Two final governing equations were developed - solid continuity and total momentum with continuity ("momentum"). ·The finite difference equations used a "space-staggered" mesh. The solid continuity equation was solved using an explicit formulation, with a forward difference in time and central difference in space. The "momentum" equation used a fully implicit formulation with a forward difference in time. The modeler could choose either a central difference or forward difference in space. Non-linear terms were linearized. Boundary Conditions and constitutive relationships were determined. Numerical errors in the numerical model were analyzed. The model was calibrated to known data and verified with additional data. The model was extremely sensitive to the constitutive relationships used, but relatively unaffected by the At or the use of central difference or forward difference for the spatial derivative term in the "momentum" equation. Correlations of the calibrated model to data with a low initial concentration show that the constitutive parameters approximate the data, but not very well. Model runs with low initial concentration required the addition of artificial viscosity to remain stable. The gravity term was always significant, whereas the inertial terms were many orders of magnitude less than gravity. However, the lower the initial concentration, the larger the inertial terms. In addition to the belt filter press, the model can also be applied to cake filtration and design of gravity sedimentation tanks as well.

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

Model Predictive Control (MPC) is an application of control that is highly popular due to its sensible approach and its ease of implementation. These qualities give MPC an advantage over Linear Quadratic (LQ) control, even though LQ will result in the optimal result where feasible. Recent advancements have resulted in greater computational power, which has given rise to the development of more complicated MPC algorithms, but there are instances when the complexity of the calculations involved will result in the amount of computations involved or ill-conditioning of the problem.

Předkládaná práce je zaměřena na numerické modelování spalování tuhých paliv na roštu metodami výpočtové dynamiky tekutin (CFD). Jelikož výsledky CFD simulací roštového spalování závisí na kvalitě vstupních dat, která zahrnují i údaje o teplotě, hmotnostním toku a chemickém složení spalin vystupujících z lože, pozornost je věnována především procesům, probíhajícím v loži během spalování na roštu. Velká část práce je věnována vývoji spolehlivého modelu spalování v sypaných ložích, jelikož může napomoci zkvalitnit výsledky simulací i rozšířit znalosti principů spalování tuhých paliv v sypaných ložích. V rámci práce byl vyvinut jednorozměrný nestacionární model spalování v experimentálním reaktoru a implementován do počítačového programu GRATECAL 1.3 včetně grafického uživatelského rozhraní. Zvláštní důraz byl kladen na konzervativnost modelu. Proto byla vyvinuta metoda pro kontrolu hmotnostní a energetické bilance systému a následně aplikována v řadě studií, v rámci nichž byly odhaleny některé chyby týkající se definic zdrojových členů, které byly převzaty z literatury a opraveny. Pomocí modelu byla provedena analýza šíření čela sušení a reakce hoření koksu po výšce lože pšeničné slámy. Na základě výsledků těchto analýz bylo doporučeno zahrnout i modelování změny porozity částic paliva, aby šířka reakční zóny byla predikována korektně v případě, že je uvažována změna porozity celého lože. Rovněž vyvinutá bilanční metoda byla použita k analýze vlivu kritérií konvergence na hmotnostní a energetickou nerovnováhu simulovaného systému. Bylo zjištěno, že škálovaná rezidua rovnic všech veličin by měla poklesnout aspoň na hodnotu $10^{-6}$, aby bylo dosaženo nízké hmotnostní a energetické nerovnováhy a tudíž uspokojivě přesných výsledků ze simulací v loži. Druhá část práce je věnována vývoji a implementaci knihovny uživatelem definovaných funkcí pro komerční CFD nástroj ANSYS FLUENT, které slouží k propojení modelu lože s modelem komory reálné spalovací jednotky, aby byla umožněna dynamická změna okrajových podmínek na vstupu do komory v závislosti na výstupech ze simulací v loži. Vytvořené rozhraní pro propojení těchto dvou modelů je dostatečně obecné pro aplikaci na širokou škálu modelů roštových kotlů. Popsané výsledky přispívají k lepšímu porozumění numerickému modelování spalování na roštu, a to zejména ve fázi sestavování numerického modelu a nastavení parametrů řešiče pro kontrolu konvergence.

Hydrocephalus is a clinical conditon where the brain tissue is deformed by the expanding ventricules. In this thesis, the mechanical deformation of a hydrocephalic brain is studied using a biomechanical model, where the material properties of the tissue are described by a viscoelastic model. A set of governing equations is derived when the motion is quasi-static motion and deformation is small. Then, finite element method is used for spatial discretization, and finite difference and trapezoidal rule are used for time-stepping. Moreover, the computational meshes are generated from medical images of patient's brain using level set method and a program called DistMesh. Numerical stability of the time-stepping scheme is also studied.

Several numerical studies are conducted to investigate several aspect of the brain with hydrocephalus. The state of stress of the tissue is found to be compressive everywhere in the brain. The viscoelastic properties of the brain are investigated and found to be dominated by elastic response. Lastly, the displacement made by the ventricular wall as it expands and shrinks is found to be non-uniform.

In many water resources and hydrological projects, it is not always possible to get access to in-situ long-term time series weather measurements, especially for ungauged catchments. Even with gauged catchments, it is common that only rain gauge and river level data are available; other weather variables such as solar radiation, wind speed, surface temperature, surface air pressure and relative humidity are usually missing and if available are generally not in continuous form. These weather variables are basic building blocks of the global hydrological cycle that includes evapotranspiration (ET 0) and runoff estimation. The ET 0 and runoff can be estimated from the Penman-Monteith equation and rainfall runoff modeling respectively. This thesis explored a potential application of downscaled global reanalysis weather data using Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model 5 (MMS). MMS is able to downscale the global weather data down to a much finer resolution in space and time for use in local hydrological investigations. The exploration of downscaling the ERA-40 reanalysis data to the Brue catchment in Southwest England and the assessment of the relevant weather variables in comparison with those measured at the ground was described in the thesis. However, there is a problem in using these selected weather variables in hydrological processes due to uncertainties obtained from the mesoscale modelling. Therefore, this thesis focused on the improvement of the weather variables from the dynamical downscaling and statistical modeling. The improvement of dynamic downscaling with the MMS cumulus parameterization schemes (CPSs) by changing the horizontal and vertical resolutions are presented in this thesis for rainfall estimation. Meanwhile, the error correction with statistical models is an attempt to hybridize MMS with two regression models ( the multiple linear regression (MLR) and the nonlinear regression (NLR)) and two artificial intelligence systems (the artificial neural networks (ANNs) and the support vector machines (SVMs)). This exploration is to tackle the errors between the MMS downscaled and observed data in addition to other MMS derived hydro- meteorological parameters. The hold-out validation with a forward selection method was employed as an input variable selection procedure to examine the model generalization errors in these statistical models. Upon the implementation of the error correction technique of weather variables, a comparative study of runoff simulation via the PDM model was completed between the MMS downscaled, corrected and observed data. This thesis also presents a sensitivity analysis of six weather variables to ET 0 estimation and runoff simulation through various combinations of the Penrnan-Monteith equation and Probability Distributed Model (PDM}inputs. Finally, by this assessment of several case studies in this thesis, it has shown that the enhanced MMS modeling scheme with the correction approaches substantially improves the forecasted weather variables over the study area which is important for the hydrological processes.

A method for predicting unsteady, subsonic aeroelastic responses has been developed. The technique accounts for aerodynamic nonlinearities associated with angles of attack, vortex-dominated flow, static deformations, and unsteady behavior. The angle of attack is limited only by the occurrence of stall or vortex bursting near the wing. The fluid and the wing together are treated as a single dynamical system, and the equations of motion for the structure and flowfield are integrated simultaneously and interactively in the time domain. The method employs an iterative scheme based on a predictor-corrector technique. The aerodynamic loads are computed by the general unsteady vortex-lattice method and are determined simultaneously with the motion of the wing. Because the unsteady vortex-lattice method predicts the wake as part of the solution, the history of the motion is taken into account; hysteresis is predicted. Two models are used to demonstrate the technique: a rigid wing on an elastic support experiencing plunge and pitch about the elastic axis, and an elastic wing rigidly supported at the root chord experiencing spanwise bending and twisting. The method can be readily extended to account for structural nonlinearities and/or substitute aerodynamic load models. The time domain solution coupled with the unsteady vortex-lattice method provides the capability of graphically depicting wing and wake motion.
Ph. D.

In bats, the directivity patterns for reception are shaped by the surface geometry of the pinnae. Since many bat species are capable of large ear deformations, these beampatterns can be time-variant. To investigate this time-variance using numerical methods, a digital model that is capable of representing the pinna geometry during the entire deformation cycle has been developed.

Due to large deformations and occlusions, some of the surfaces relevant to sound diffraction may not be visible and the geometry of the entire pinna has to be computed from limited data. This has been achieved by combining a complete digital model of the pinna in one position with time-variant sparse sets of three dimensional landmark data. The landmark positions were estimated using stereo vision methods. A finite element model based on elasticity was constructed from CT scans of the pinna post mortem. This elastic model was deformed to provide a good fit to the positions of the landmarks and retain values of smoothness and surface energy comparable to life. This model was able to handle ratios of data to degrees of freedom around 1:5000 and still effect life-like deformations with an acceptable goodness of fit.
Master of Science

A variation on a numerical model of the motor protein myosin V presentedin a paper by Craig and Linke (2009) is developed. An alternative potential is proposed. All aspects of the model development arederived in detail and tested. Two model tests are created and used toconfirm the correctness of the developed model. A simulation demonstratesthat the developed model is able to produce a myosin V step. Adidactical transposition is presented in the form of a compendium, in which a numerical model of myosin V by Craig and Linke (2009) isdescribed. The didactical transposition is developed using a methodologyof didactical engineering. The didactical study indicated thatthe content was well recieved by the target group of eight individualsin respect to the scientific complexity and that it evokes motivation forlearning. The study also indicated that unsuccessful areas of the didacticaltransposition existed.
En variation av en numerisk modell av motorproteinet myosin V presenteradav Craig och Linke (2009) utvecklas. En alternativ potential föreslås. Alla aspekter av modellutvecklingen härleds i detalj och testas.Två modelltester skapas och används för att bekräfta riktigheteni den utvecklade modellen. En simulering demonstrerar att myosin Vkan ta ett steg i den utvecklade modellen.En didaktisk transposition presenteras i form av ett kompendium,där en numerisk modell av myosin V av Craig och Linke (2009) beskrivs.Metodologiskt utvecklas den didaktiska transpositionen medhjälp av didaktisk ingenjörskonst. Den didaktiska studien indikeradeatt innehållet togs emot väl av målgruppen bestående av åtta personeri hänseende till vetenskaplig komplexitet och att det väckte motivationför lärande. Studien indikerade även att misslyckade områden av dendidaktiska transpositionen förekom.

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In this thesis we revisit numerical methods for the simulation of the Heston model’sEuropean call. Specifically, we study the Euler, the Kahl-Jackel an two versions of theexact algorithm schemes. To perform this task, firstly we present a literature reviewwhich brings stochastic calculus, the Black-Scholes (BS) model and its limitations,the stochastic volatility methods and why they resolve the issues of the BS model,and the peculiarities of the numerical methods. We provide recommendations whenwe acknowledge that the reader might need more specifics and might need to divedeeper into a given topic. We introduce the methods aforementioned providing all ourimplementations in R language within a package.

A Lagrangian finite-element model of the plunge phase of the friction stir welding process was developed to better understand the plunge. The effects of both modeling and experimental parameters were explored. Experimental friction stir plunges were made in AA 7075-T6 at a plunge rate of 0.724 mm/s with spindle speeds ranging from 400 to 800 rpm. Comparable plunges were modeled in Forge2005. Various simulation parameters were explored to assess the effect on temperature prediction. These included the heat transfer coefficient between the tool and workpiece (from 0 to 2000 W/m-K), mesh size (node counts from 1,200 to 8,000), and material model (five different constitutive relationships). Simulated and measured workpiece temperatures were compared to evaluate model quality. As spindle speed increases, there is a statistically significant increase in measured temperature. However, over the range of spindle speeds studied, this difference is only about 10% of the measured temperature increase. Both the model and the simulation show a similar influence of spindle speed on temperature. The tool-workpiece heat transfer coefficient has a minor influence (<25% temperature change) on simulated peak temperature. Mesh size has a moderate influence (<40% temperature change) on simulated peak temperature, but a mesh size of 3000 nodes is sufficient. The material model has a high influence (>60% temperature change) on simulated peak temperature. Overall, the simulated temperature rise error was reduced from 300% to 50%. It is believed that this can be best improved in the future by developing improved material models.

In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called ``nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans isomerization. For both cases, we studied the dependence of the de-excitation on the nuclear configuration and potential energy of the molecule. We constructed a numerical model to solve the time-dependent Schr\"{o}dinger Equation for two coupled wave functions. Our algorithm takes full advantage of the sparseness of the numerical system, leading to a final set of equations that is solved recursively using nothing more than the Tridiagonal Algorithm. We observed that the most effective de-excitation occurred when the molecule transitioned from a stable equilibrium configuration to an unstable equilibrium configuration. This same mechanism is known to drive fast electronic transitions in the adiabatic frame. We concluded that while the adiabatic and diabatic frames are strongly opposed physically, the mathematical mechanism driving electronic transitions in the two frames is in some sense the same.

lnSAR has been proved its unprecedented ability and merits of monitoring ground deformation on large scale with centimeter to millimeter scale accuracy. However, several factors affect the reliability and accuracy of its applications. Among them, atmospheric artifacts due to spatial and temporal variations of atmosphere state often pose noise to interferograms. Therefore, atmospheric artifacts m itigalion remains one of the biggest challenges to be addressed in the In SAR community. State-of-the-art research works have revealed atmospheric artifacts can be partially compensated with empirical models, temporal-spatial filtering approach in lnSAR time series, pointwise GPS zenith path delay and numerical weather prediction models. In this thesis, firstly, we further develop a covariance weighted linear empirical model correction method. Secondly, a realistic LOS direction integration approach based on global reanalysis data is employed and comprehensively compared with the conventional method that integrates along zenith direction. Finally, the realistic integration method is applied to local WRF numerical forecast model data. l'vbreover, detailed comparisons between different global reanalysis data and local WRF model are assessed. In terms of empirical models correcting methods, many publications have studied correcting stratified tropospheric phase delay by assuming a linear model between them and topography. However, most of these studies ha\19 not considered the effect of turbulent atmospheric artefacts when adjusting the linear model to data. In this thesis, an improved technique that minimizes the influence of turbulent atmosphere in the model adjustment has been presented. In the proposed algorithm, the model is adjusted to the phase differences of pixels instead of using the unwrapped phase of each pixel. In addition, the different phase differences are weighted as a function of its APS covariance estimated from an empirical variogram to reduce in the model adjustment the impact of pixel pairs with significant turbulent atmosphere. The performance of the proposed method has been validated with both simulated and real Sentinel-1 SAR data in Tenerife island, Spain. Considering methods using meteorological observations to mitigate APS, an accurate realistic com puling strategy utilizing global atmospheric reanalysis data has been implemented. With the approach, the realistic LOS path along satellite and the monitored points is considered, rather than converting from zenith path delay. Com pared with zenith delay based method, the biggest advantage is that it can avoid errors caused by anisotropic atmospheric behaviour. The accurate integration method is validated with Sentinel-1 data in three test sites: Tenerife island, Spain, Almeria, Spain and Crete island, Greece. Compared to conventional zenith method, the realistic integration method shows great improvement. A variety of global reanalysis data are available from different weather forecasting organizations, such as ERA-Interim, ERAS, MERRA2. In this study, the realistic integration mitigation method is assessed on these different reanalysis data. The results show that these data are feasible to mitigate APS to some extent in most cases. The assessment also demonstrates that the ERAS performs the best statistically, compared to other global reanalysis data. l'vbreover, as local numerical weather forecast models have the ability to predict high spatial resolution atmospheric parameters, by using which, it has the potential to achieve APS mitigation. In this thesis, the realistic integration method is also employed on the local WRF model data in Tenerife and Almeria test s ites. However, it turns out that the WRF model performs worse than the original global reanalysis data.
Las técnicas lnSAR han demostrado su capacidad sin precedentes y méritos para el monitoreo de la deformaci6n del suelo a gran escala con una precisión centimétrica o incluso milimétrica. Sin embargo, varios factores afectan la fiabilidad y precisión de sus aplicaciones. Entre ellos, los artefactos atmosféricos debidos a variaciones espaciales y temporales del estado de la atm6sfera a menudo añaden ruido a los interferogramas. Por lo tanto, la mitigación de los artefactos atmosféricos sigue siendo uno de los mayores desafíos a abordar en la comunidad lnSAR. Los trabajos de investigaci6n de vanguardia han revelado que los artefactos atmosféricos se pueden compensar parcialmente con modelos empíricos, enfoque de filtrado temporal-espacial en series temporales lnSAR, retardo puntual del camino cenital con GPS y modelos numéricos de predicción meteorológica. En esta tesis, en primer lugar, desarrollamos un método de corrección de modelo empírico lineal ponderado por covarianza. En segundo lugar, se emplea un enfoque realista de integracion de dirección LOS basado en datos de reanálisis global y se compara exhaustivamente con el método convencional que se integra a lo largo de la dirección cenital. Finalmente, el método de integraci6n realista se aplica a los datos del modelo de pronóstico numérico WRF local. Ademas, se evalúan las comparaciones detalladas entre diferentes datos de reanálisis global y el modelo WRF local. En términos de métodos de corrección con modelos empíricos, muchas publicaciones han estudiado la corrección del retraso estratificado de la fase troposférica asumiendo un modelo lineal entre ellos y la topografía. Sin embargo, la mayoría de estos estudios no han considerado el efecto de los artefactos atmosféricos turbulentos al ajustar el modelo lineal a los datos. En esta tesis, se ha presentado una técnica mejorada que minimiza la influencia de la atm6sfera turbulenta en el ajuste del modelo. En el algoritmo propuesto, el modelo se ajusta a las diferencias de fase de los pixeles en lugar de utilizar la fase sin desenrollar de cada pixel. Además, las diferentes diferencias de fase se ponderan en función de su covarianza APS estimada a partir de un variograma empírico para reducir en el ajuste del modelo el impacto de los pares de pixeles con una atm6sfera turbulenta significativa. El rendimiento del método propuesto ha sido validado con datos SAR Sentinel-1 simulados y reales en la isla de Tenerife, España. Teniendo en cuenta los métodos que utilizan observaciones meteorológicas para mitigar APS, se ha implementado una estrategia de computación realista y precisa que utiliza datos de reanálisis atmosférico global. Con el enfoque, se considera el camino realista de LOS a lo largo del satélite y los puntos monitoreados, en lugar de convertirlos desde el retardo de la ruta cenital. En comparación con el método basado en la demora cenital, la mayor ventaja es que puede evitar errores causados por el comportamiento atmosférico anisotrópico. El método de integración preciso se valida con los datos de Sentinel-1 en tres sitios de prueba: la isla de Tenerife, España, Almería, España y la isla de Creta, Grecia. En comparación con el método cenital convencional, el método de integración realista muestra una gran mejora.

>Magister Scientiae - MSc
Warrant pricing has become very crucial in the present market scenario. See, for example, M. Hanke and K. Potzelberger, Consistent pricing of warrants and traded options, Review Financial Economics 11(1) (2002) 63-77 where the authors indicate that warrants issuance affects the stock price process of the issuing company. This change in the stock price process leads to subsequent changes in the prices of options written on the issuing company's stocks. Another notable work is W.G. Zhang, W.L. Xiao and C.X. He, Equity warrant pricing model under Fractional Brownian motion and an empirical study, Expert System with Applications 36(2) (2009) 3056-3065 where the authors construct equity warrants pricing model under Fractional Brownian motion and deduce the European options pricing formula with a simple method. We study this paper in details in this mini-thesis. We also study some of the mathematical models on warrant pricing using the Black-Scholes framework. The relationship between the price of the warrants and the price of the call accounts for the dilution effect is also studied mathematically. Finally we do some numerical simulations to derive the value of warrants.

Models of the fate and transport of river plumes and the bacteria they carry into lakes are developed. They are needed to enable informed decisions about beach closures to avoid economic losses, and to help design water intakes and operate combined sewer overflow schemes to obviate exposure of the public to potential pathogens. This study advances our understanding of river plumes dynamics in coastal waters by means of field studies and numerical techniques. Extensive field measurements were carried out in the swimming seasons of 2006 and 2007 on the Grand River plume as it enters Lake Michigan. They included simultaneous aerial photography, measurements of lake physical properties, the addition of artificial tracers to track the plume, and bacterial sampling. Our observed results show more flow classes than included in previous studies (e.g. CORMIX). Onshore wind can have a significant effect on the plume and whether it impacts the shoreline. A new classification scheme based on the relative magnitude of plume-crossflow length scale and Richardson number based on the wind speed is devised. Previous studies on lateral spreading are complemented with a new relationship in the near field. The plume thickness decreased rapidly with distance from the river mouth and a new non-dimensional relationship to predict thickness is developed. Empirical near field models for surface buoyant plumes are reviewed and a near field trajectory and dilution model for large aspect ratio surface discharge channels is devised. Bacterial reductions due to dilution were generally small (less than 10:1) up to 4.5 km from the river mouth. E. coli decay rates were significantly affected by solar radiation and ranged from 0.2 to 2.2 day-1 which were within the range of previous studies in Lake Michigan. Total coliform survived longer than E. coli suggesting different die-off mechanisms. Mathematical models of the bacterial transport are developed that employ a nested modeling scheme to represent the 3D hydrodynamic processes of surface river discharges in the Great Lakes. A particle tracking model is used that provides the capability to track a decaying tracer and better quantify mixing due to turbulent diffusion. Particle tracking models have considerable advantages over gradient diffusion models in simulating bacterial behavior nearshore that results in an improved representation of bacteria diffusion, decay and transport. Due to the complexity and wide variation of the time and length scale of the hydrodynamic and turbulent processes in the near field (where plume mixing is dominated by initial momentum and buoyancy) and far field (where plume mixing is dominated by ambient turbulence), a coupling technique is adapted. The far field random walk particle tracking model incorporates the empirical near field model. It simulates the transport, diffusion and decay of bacteria as discrete particles and employs the near field output as the source and transports the particles based on ambient currents predicted by the 3D hydrodynamic model. The coupled model improves dilution predictions in the near field. The new techniques advance our knowledge of the nearshore fate and transport of bacteria in the Great Lakes and can be ultimately applied to the NOAA Great Lakes Coastal Forecasting System to provide a reliable prediction tool for bacterial transport in recreational waters.

Realistic predictions of service life of steel catenary risers (SCR) require an accurate characterization of seafloor stiffness in the region where the riser contacts the seafloor, the so-called touchdown zone. This thesis presents the initial stage of development of a simplified seafloor support model. This model simulates the seafloor-pipe interaction as a flexible pipe supported on a bed of springs. Constants for the soil springs were derived from finite element studies performed in a separate, parallel investigation. These supports are comprised of elasto-plastic springs with spring constants being a function of soil stiffness and strength, and the geometry of the trench within the touchdown zone. Deflections and bending stresses in the pipe are computed based on a finite element method and a finite difference formulation developed in this research project. The finite difference algorithm has capabilities for analyzing linear springs, non-linear springs, and springs having a tension cut-off. The latter feature simulates the effect of a pipe pulling out of contact with the soil. The model is used to perform parametric studies to assess the effects of soil stiffness, soil strength, trench geometry, amplitude of pipe displacements, pipe stiffness, and length of touchdown zone on pipe deflections and bending stresses. In conclusions, the seafloor stiffness (as characterized by the three spring parameters), the magnitude of pipe displacement, and the length of the touchdown zone all influence bending stresses in the pipe. Also, the tension cutoff effect, i.e., the pipe pulling away from the soil, can have a very large effect on bending stresses in the pipe. Neglecting this effect can lead to serious over-estimate of stress levels and excessive conservatism in design.

This thesis is concerned with the numerical simulation of Newtonian and viscoelastic free-surface flows. This work is novel in advance of hybrid finite volume and free-surface techniques, and in the study of particular industrial flows. The presence of free-surfaces in a number of complex industrial flows, gives rise to instabilities during processing. Consequently, these instabilities impose certain limitations on processing windows and final product quantity. Accordingly, an important aspect of the current work is to investigate these instabilities, with a view to suggesting possible remedies for suppression. A transient semi-implicit Taylor-Galerkin/pressure-correction time-stepping framework is employed, accommodating both finite element (FE) and finite volume (FV) schemes. FE discretisation is used for the momentum-continuity equations, whilst the constitutive equations are resolved through finite volume cell-vertex approximation. To quantify the accuracy, stability and consistency of the proposed FV method, we have chosen a model sink-flow problem, that has an analytical solution. Our interest is to explore the consequences of utilising conventional cell-vertex methodology for an Oldroyd-B model and to demonstrate deficiencies in the presence of complex source terms. In this manner, a consistent approach is derived. The first complex problem addressed is that of industrial reverse-roller coating for Newtonian viscous flows. The evolving position of the free-surface, whose position is unknown a priori, is computed using kinematic boundary adjustment with mesh-stretching algorithms. The problem is analysed first to steady-state, prior to transient considerations. We have found pressure maxima to arise in the nip region, that subsequently produce elevated levels of lift on the foil. In addition, we have investigated the influence of these elevated forces (lift) on the foil, by adjusting nip-width in time. Variation in nip-gap width introduces temporal foil-vibration. This is found to have a significant impact upon pressure and lift on the foil. Such temporal changes in nip-width, also generated free-surface instabilities that act upon the coating layer (film-thickness). A second problem studied is that associated with filament-stretching flows. The long-time, large extensional deformations and break-up of Newtonian fluids is analysed, based on an axisymmetric, time-dependent half-length model. The simulation is performed between two plates, which depart at an exponentially increasing rate. Due to the presence of rigid-end-plates and imposed pinning boundary conditions, the radius of the filament varies along its length. Ultimately, this leads to filament break-up. Various remeshing schemes have been introduced. A cost-effective approach is proposed, that suppresses premature filament breakup and maintains accuracy and stability within the computer predictions up to large Hencky-strain levels. Finally, attention is turned to filament-stretching for viscoelastic fluids. Here, we have recourse to the hybrid FE/FV approach and a coupled/decoupled algorithm is outlined. Various aspects of the problem are addressed and results are compared against those for Newtonian fluids, considering a full-length model. With regard to upwinding discretisation, we have contrasted performance of both LDB and LAX-Wendroff schemes. An optimum choice has emerged that captures stress field accurately in the vicinity of the free-surface.

Face seals failures are one of the main reasons for non-productive time in Schlumberger's down hole tools. The root causes for such failures are not well understood yet. Moreover, these failures are happening in very di erent operating conditions; a face seal on a ESP will work continually for years, a face seal on a logging-while-drilling tool such as Impulse will experience start and stops as well as pressure pulses. Consequently, there is a strong need for a model to help understand the operations of face seals. The starting point for the present work is the model developed by R.F. Salant in 2002-2003. The present work consisted in validating the di erent elements of the model, generalizing the applicability and translating the code from Fortran to Octave/Matlab. The aim of the porting to Octave/Matlab was twofold. Firstly to allow easier model interpretation and development in graphical environment and secondly to provide thecode to software developer in a friendly way.

The application of many existing numerical models of river channel morphology is limited by their inability to account for bank erosion and changing channel width through time. In this research, a physically-based numerical model which simulates the evolution of channel morphology, including channel width, through time has been developed and tested. Predictions of channel evolution are obtained by solving deterministically the governing equations of flow resistance, flow, sediment transport, bank stability and conservation of sediment mass. The model is applicable to relatively straight, sand-bed streams with cohesive bank materials. In the channel evolution model, a method is used to solve the shallow water flow equations, and to account for lateral shear stresses which significantly influence the flow in the near bank zone. The predicted distribution of flow is then used to predict the sediment transport over the full width of straight river channels. Deformation of the bed is calculated from solution of the sediment continuity equation. Predictions obtained in the near bank zone allow the variation in bank geometry to be simulated through time. Since bank stability is determined by the constraints of the geometry of the bank and the geotechnical properties of the bank material, channel widening can, therefore, be simulated by combining a suitable bank stability algorithm with flow and sediment transport algorithms. In combining bank stability algorithms with flow and sediment transport algorithms, there are two paramount considerations. First, the longitudinal extent of mass failures within modelled reaches must be accounted for. Second, it is necessary to maintain the continuity of both the bed and the bank material mixture in the time steps following mass failure, when the bed material consists of mixtures of bed and bank materials with widely varying physical properties. In this model, a probabilistic approach to prediction of factor of safety is used to estimate the fraction of the banks in the modelled reaches that fail in any time step. Mixed layer theory is then used to model the transport of the resulting bed and bank material mixture away from the near bank zone. Comparisons of model predictions with observations of channel geometry over a 24 year period indicate that the new model is capable of simulating temporal trends of channel morphology with a high degree of accuracy. The model has been used successfully to replicate the form of empirically-derived hydraulic geometry equations, indicating that the model is also able to predict stable channel geometries accurately. The numerical model has also been used to investigate the influence of varying the independent variables and boundary conditions on channel adjustment dynamics.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Apresenta-se uma metodologia de análise numérica para dutos enterrados usados no transporte de petróleo e gás, considerando não-linearidades geométricas e não linearidades de material baseada na formulação Lagrangeana Total. Emprega-se uma modelagem com base em uma discretização com elementos especiais de viga. As equações de equilíbrio são formuladas a partir do principio dos trabalhos virtuais, segundo as componentes de tensão e deformação no elemento viga-duto, com emprego da técnica do Módulo Reduzido de Integração Direta (RMDI), na qual incorpora-se o comportamento plástico do material. Esta técnica exclui da análise os efeitos da flambagem local nas paredes do duto. As matrizes para resolução por elementos finitos destas equações são derivadas. Incorporam- se, nesta metodologia os efeitos de pressão interna constante no duto assim como a interação solo-duto através da modelagem do solo por meio de molas elasto-plásticas verticais e horizontais. Na modelagem desenvolvida as cargas distribuídas são consideradas como constantes no sistema global de eixos. Desenvolve-se um programa para computador segundo a metodologia apresentada. São estudados alguns exemplos com o objetivo de avaliar numericamente os resultados de análise obtidos e formular algumas conclusões sobre o comportamento de dutos enterrados.
This work presents a numerical methodology for the analysis of buried pipes employed by the transport of oil and gas. Both geometric and material nonlinearities are considered in a total Lagrangean formulation. A special type of beam element is employed in the finite element discretization. The equilibrium equations are formulated based on the virtual work principle considering the stress and deformation components of the beam-pipe element. The Reduced Modulus Direct Integration (RMDI) technique is employed through which the plastic material behavior is incorporated. This technique excludes from the analysis the local buckling effects of the pipe walls. The corresponding finite element matrices for this element are obtained. In this methodology the effects of the constant internal pressure as well as the soil-pipe interaction by means of elastic-plastic uplift, bearing and longitudinal springs are included. Distributed loads are considered constant with respect to the global axis. A computer code is developed according to the methodology presented. Some examples are studied with the objective to evaluate numerically the analysis results and to formulate some conclusions to the behavior of buried pipes.

Thesis: S.B., Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences, 2008.
Cataloged from PDF version of thesis.
Includes bibliographical references (page 24).
In this thesis, spontaneous tropical cyclogenesis occurring in a cloud-resolving numerical model is studied. The model environment is one of radiative convective-equilibrium on an f-plane with doubly periodic boundary conditions and constant sea surface temperature. While a variety of initial conditions may exhibit spontaneous tropical cyclogenesis, this study focuses on one. Using assumptions of axisymmetry for the growing disturbance and focusing on the large scale processes, fields were created for a number of thermodynamic variables along constant height surfaces and as azimuthal means plotted against height. The tropical cyclone is hypothesized to develop in three steps. First, convective aggregation creates regions of high moist static energy, and regions of cold dry air. Importantly, a deep moist column is created which provides a perfect environment the developing storm. In the second step, mid-level cyclone intensification, a mid-level cold core cyclone develops in the deep moist region, and benefits from moist static energy and potential vorticity fluxes from the upper troposphere. Exhibiting anticyclonic convergent flow, the upper troposphere is an unlikely source for the mid-level disturbance, while convective downdrafts and divergent surface flow hinder energy transport from the ocean to the growing system. In fact, a cold surface anticyclone exists near the center for much of the second step. It is not until potential vorticity anomalies advect down to the surface that the final step, low-level cyclone intensification, creates a classical hurricane structure. Potential vorticity advection stimulates cyclonic flow at the surface, extinguishing the surface anticyclone, and thereby linking the mid-level disturbance to the oceanic energy source. While like some cold core cyclones previously studied, the anticyclone as an energy source is unique to this spontaneous case.
by Paul M. Hoffman.
S.B.

This paper is concerned with numerical studies on the theoretical results obtained in Strasser [1] and [2]. These papers provide asymptotic expansions for conditional expectations of non i.i.d. Bernoulli trials and their application to the covariance structure of conditional maximum likelihood estimates for the Rasch model. In the present paper systematic numerical studies of the accuracy of the approximations given in Strasser [1] and [2] are presented. It is shown that the order of approximation claimed by the theoretical results can be established numerically. (author's abstract)
Series: Research Report Series / Department of Statistics and Mathematics

This dissertation contains work that addresses both theoretical and numerical aspects of reduced order models (ROMs). In an under-resolved regime, the classical Galerkin reduced order model (G-ROM) fails to yield accurate approximations. Thus, we propose a new ROM, the data-driven variational multiscale ROM (DD-VMS-ROM) built by adding a closure term to the G-ROM, aiming to increase the numerical accuracy of the ROM approximation without decreasing the computational efficiency. The closure term is constructed based on the variational multiscale framework. To model the closure term, we use data-driven modeling. In other words, by using the available data, we find ROM operators that approximate the closure term. To present the closure term's effect on the ROMs, we numerically compare the DD-VMS-ROM with other standard ROMs. In numerical experiments, we show that the DD-VMS-ROM is significantly more accurate than the standard ROMs. Furthermore, to understand the closure term's physical role, we present a theoretical and numerical investigation of the closure term's role in long-time integration. We theoretically prove and numerically show that there is energy exchange from the most energetic modes to the least energetic modes in closure terms in a long time averaging. One of the promising contributions of this dissertation is providing the numerical analysis of the data-driven closure model, which has not been studied before. At both the theoretical and the numerical levels, we investigate what conditions guarantee that the small difference between the data-driven closure model and the full order model (FOM) closure term implies that the approximated solution is close to the FOM solution. In other words, we perform theoretical and numerical investigations to show that the data-driven model is verifiable. Apart from studying the ROM closure problem, we also investigate the setting in which the G-ROM converges optimality. We explore the ROM error bounds' optimality by considering the difference quotients (DQs). We theoretically prove and numerically illustrate that both the ROM projection error and the ROM error are suboptimal without the DQs, and optimal if the DQs are used.
Doctor of Philosophy
In many realistic applications, obtaining an accurate approximation to a given problem can require a tremendous number of degrees of freedom. Solving these large systems of equations can take days or even weeks on standard computational platforms. Thus, lower-dimensional models, i.e., reduced order models (ROMs), are often used instead. The ROMs are computationally efficient and accurate when the underlying system has dominant and recurrent spatial structures. Our contribution to reduced order modeling is adding a data-driven correction term, which carries important information and yields better ROM approximations. This dissertation's theoretical and numerical results show that the new ROM equipped with a closure term yields more accurate approximations than the standard ROM.