Dissertations / Theses on the topic 'Collapse models'

2008/2009
We introduce the measurement problem in quantum mechanics and we briefly discuss the solutions proposed in literature. We then focus our attention on models of spontaneous wavefunction collapse. We describe the two most popular models (GRW, CSL) and list other proposals. We analyze in detail a third collapse model (QMUPL), which is particularly simple (but physically meaningful) to be studied in great mathematical detail. We discuss its main properties. We also describe a "finite temperature" version of this model, which includes dissipative terms. These models are Markovian, i.e. the collapse mechanism is driven by a white noise. Since the ultimate goal is to identify the noise responsible for the collapse with a random field in Nature, it becomes important to study non-Markovian generalizations of collapse models, where the collapsing field has a generic correlation function, likely with a cut off at high frequencies. Models of this kind have already been studied, as a generalization of the CSL model. In this thesis we describe in mathematical detail the generalization of the QMUPL model to non-Markovian noises. After having proved, under suitable conditions, the separation of the center-of-mass and relative motions for a generic ensemble of particles, we focus our analysis on the time evolution of the center of mass of an isolated system (free particle case). We compute the explicit expression of the Green's function via the path integral formalism, for a generic Gaussian noise. We analyze in detail the case of an exponential correlation function, providing the exact analytical solution. We next study the time evolution of average quantities, such as the mean position, momentum (which satisfy Ehrefest's theorem) and energy (which is not conserved like in the other collapse models). We also compute the non-Markovian master equation for an harmonic oscillator, according to this model, and compare its structure to the well-known Lindblad structure of Markovian open quantum systems. We eventually specialize to the case of Gaussian wave functions, and prove that all basic facts about collapse models (reduction process, amplification mechanism, etc.), which are known to be true in the white noise case, hold also in the more general case of non-Markovian dynamics. We further analyze the evolution of Gaussian wave function according to the three different realizations of the QMUPL model so far developed (Markovian, non-Markovian and "finite temperature"), comparing their fundamental features. Finally, by analyzing different localization criteria, we set new lower bounds on the parameters of these models, and we compare them with the upper bounds coming from known experimental data.
Nel primo capitolo si introduce il problema della misura in Meccanica Quantistica e si discutono brevemente le soluzioni proposte nella letteratura. Nel capitolo 2 si discutono i modelli di collasso spontaneo della funzione d'onda, con particolare attenzione per i modelli GRW e CSL; si elencano altri modelli. Si analizza in dettaglio anche il modello di riduzione QMUPL, il quale è particolarmente semplice (ma fisicamente significativo) da poter essere studiato dettagliatamente dal punto di vista matematico. Si discutono le sue proprietà principali. Si descrive inoltre una versione "a temperatura finita" di questo modello, che include termini dissipativi. Questi modelli sono Markoviani, ovvero il meccanismo di collasso è guidato da un rumore bianco. Poichè parte significativa della ricerca consiste nell'identificare il rumore responsabile del collasso con un campo stocastico esistente in Natura, diventa importante studiare le generalizzazioni non-Markoviane dei modelli di riduzione, in cui il campo di collasso ha una funzione di correlazione generale, probabilmente con un cutoff ad alte frequenze. Modelli di questo tipo, come la generalizzazione del modello CSL, sono già stati studiati. In questa tesi si descrive in dettaglio la generalizzazione a rumori non-Markoviani del modello QMUPL. Dopo aver provato, sotto particolari condizioni, la separazione del moto del centro di massa da quello relativo per un generico ensemble di particelle, si pone attenzione all'evoluzione temporale del centro di massa di un sistema isolato (particella libera). Si dà l'espressione esplicita per la funzione di Green attraverso il formalismo del path-integral, per un generico rumore Gaussiano. Si analizza in particolare il caso della funzione di correlazione esponenziale, fornendo la soluzione analitica esatta delle equazioni. Successivamente si studia l'evoluzione dei valori medi, in particolare della posizione, del momento (che soddsfa il teorema di Ehrenfest) e dell'energia (che non è conservata come negli altri modelli di riduzione). Si scrive inoltre la master equation non-Markoviana per un oscillatore armonico per questo modello, e si confronta la sua struttura con le ben nota struttura di Lindblad dei sistemi quantistici aperti Markoviani. Ci si specializza al caso di funzioni d'onda Gaussiane, e si prova che tutte le nozioni di base sui modelli di riduzione (processo di collasso, meccanismo di amplificazione, ecc.), che sono note essere vere nel caso Markoviano, valgono anche nel caso più generale di dinamiche non-Markoviane. Infine, si analizza l'evoluzione di funzioni d'onda Gaussiane secondo le tre differenti realizzazioni del modello QMUPL finora analizzate (Markoviana, non-Markoviana e "a temperatura finita"), confrontando le loro caratteristiche fondamentali. Inoltre, analizzando differenti criteri di localizzazione, si individano nuovi limiti inferiori per i parametri di questi modelli, e si confrontano con i limiti superiori che vengono da dati sperimentali noti.
XXII Ciclo
1982

2012/2013
In order to solve the measurement problem, collapse models modify the Schroedinger dynamics by adding non linear and stochastic terms. Collapse models provide different predictions compare to Quantum mechanics. In this thesis we focus on two phenomena where the predictions of quantum mechanics and collapse models are different: the electromagnetic radiation emission from charged systems and the flavour oscillations. We analysed both of them and obtained the quantitative deviations from standard quantum behaviour.
Al fine di risolvere il problema della misura, i modelli di collasso spontaneo della funzione d'onda modificano la dinamica data dall'equazione di Schroedinger aggiungendo termini non lineari e stocastici. I modelli di collasso forniscono previsioni differenti rispetto alla meccanica quantistica. In questa tesi studieremo due fenomeni dove le predizioni della meccanica quantistica e dei modelli di collasso sono diverse: l'emissione di radiazione elettromagnetica da sistemi elettricamente non neutri e le oscillazioni dei sapori. Analizzeremo entrambi i fenomeni al fine di ottenere deviazioni quantitative dal comportamento quantistico standard.
XXVI Ciclo
1985

We conduct an investigation into the role that turbulence plays in the formation of stars. In small clouds, with masses of ~ 30 Mʘ and where the turbulence is only injected at the start, we find that the turbulence does not trigger star formation. Instead, the dissipation of the kinetic energy allows the mean Jeans mass of the cloud to control the formation of stars. The equipartition of the kinetic and thermal energies in the final stages before star formation, allows the pre-protostellar clumps to fragment. Binary and multiple systems are thus a natural product of star formation in a turbulent environment. We find that globally unbound clouds can be the sites of star formation. Furthermore the star formation efficiency is naturally less than 100%, thus in part providing an explanation for the low efficiency in star forming regions. Globally unbound GMCs not only form stars, and naturally disperse, within a few crossing times, but also provide a mechanism for the formation of OB associations.

We study the collapse transition of a lattice based protein model including an explicit coarse-grained model of a solvent. This model accounts for explicit hydrophobic interactions, and it is studied by Monte Carlo simulation. The protein is modelled as self-avoiding random walk with nearest neighbor interactions on a two dimensional lattice. Without the solvent, universal quantities of the chain around the collapse transition temperature are well known. Hydrophobicity is then modelled through a lattice of solvent molecules in which each molecule can have Q states depending of an orientation variable. Only one state is energetically favored, when two neighboring solvent molecules are both in the same state of orientation. The monomers are placed in interstitial position of the solvent lattice, and are only allowed to occupy sites surrounded by solvent cells of the same orientation. The potential of mean force between two interstitial solute molecules is calculated, showing a solvent mediated attraction typical of hydrophobic interactions. We then show that this potential increases with the energy of hydrogen bond formation as it appears in the model, while its characteristic range decreases. More importantly, we show that the chain embedded in the solvent undergoes a collapse transition, with the temperature of the transition being shifted relative to that of the chain in isolation. We calculate several critical exponents near the collapse transition, and we observe that their values are not conserved in presence of the explicit solvent.

Studying the uncertainty in computationally expensive models has required the development of specialized methods, including alternative sampling techniques and response surface approaches. However, existing techniques for response surface development break down when the model being studied exhibits discontinuities or bifurcations. One uncertain variable that exhibits this behavior is the thermohaline circulation (THC) as modeled in three-dimensional general circulation models. This is a critical uncertainty for climate change policy studies. We investigate the development of a response surface for studying uncertainty in THC using the Deterministic Equivalent Modeling Method, a stochastic technique using expansions in orthogonal polynomials. We show that this approach is unable to reasonably approximate the model response. We demonstrate an alternative representation that accurately simulates the model’s response, using a basis function with properties similar to the model’s response over the uncertain parameter space. This indicates useful directions for future methodological improvements.
Abstract in HTML and technical report in PDF available on the Massachusetts Institute of Technology Joint Program on the Science and Policy of Global Change website (http://mit.edu/globalchange/www/).
This research was supported in part by the Methods and Models for Integrated Assessments Program of the National Science Foundation, Grant ATM-9909139, by the Office of Science (BER), U.S. Department of Energy, Grant Nos. DE-FG02-02ER63468 and DE-FG02-93ER61677, and by the MIT Joint Program on the Science and Policy of Global Change (JPSPGC).

A structure subjected to extreme load due to explosion or human error may lead to progressive collapse. One of the direct methods specified by design guidelines for assessing progressive collapse is the Alternate Load Path method which involves removal of a structural member and analysing the structure to assess its potential of bridging over the removed member without collapse. The use of this method in assessing progressive collapse therefore requires that the vertical load resistance function of the bridging beam assembly, which for a typical laterally restrained reinforced concrete (RC) beams include flexural, compressive arching action and catenary action, be accurately predicted. In this thesis, a comprehensive study on a reliable prediction of the resistance function for the bridging RC beam assemblies is conducted, with a particular focus on a) the arching effect, and b) the catenary effect considering strength degradations. A critical analysis of the effect of axial restraint, flexural reinforcement ratio and span-depth ratio on compressive arching action are evaluated in quantitative terms. A more detailed theoretical model for the prediction of load-displacement behaviour of RC beam assemblies within the compressive arching response regime is presented. The proposed model takes into account the compounding effect of bending and arching from both the deformation and force points of view. Comparisons with experimental results show good agreement. Following the compressive arching action, catenary action can develop at a much larger displacement regime, and this action could help address collapse. A complete resistance function should adequately account for the catenary action as well as the arching effect. To this end, a generic catenary model which takes into consideration the strength degradation due to local failure events (e.g. rupture of bottom rebar or fracture of a steel weld) and the eventual failure limit is proposed. The application of the model in predicting the resistance function in beam assemblies with strength degradations is discussed. The validity of the proposed model is checked against predictions from finite element model and experimental tests. The result indicate that strength degradation can be accurately captured by the model. Finally, the above developed model framework is employed in investigative studies to demonstrate the application of the resistance functions in a dynamic analysis procedure, as well as the significance of the compressive arching effect and the catenary action in the progressive collapse resistance in different designs. The importance of an accurate prediction of the arching effect and the limiting displacement for the catenary action is highlighted.

Collapse calderas are defined as the volcanic depression that result from the disruption of the geometry of the magma chamber roof due to down faulting during the course of an eruption. These structures have received considerable attention due to their link to Earth's ore deposits and geothermal energy resources, but also because large pyroclastic eruptions and associated caldera collapse structures represent one of the most catastrophic geologic events that have occurred on the Earth's surface in the Phanerozoic time and in the historical time.
After several pioneering works, collapse calderas have been the subject of studies of diverse disciplines. However, some important aspects on caldera dynamics and structure remain poorly understood yet.

First, we have revised important works concerning field data about collapse calderas and summarized the most relevant aspects and results. We have created a database to record existing information about collapse calderas: Collapse Caldera DataBase (CCDB). After an exhaustive analysis of the included information we have observed two types of collapse caldera: type-A and type-B.

Experiments on caldera collapse modelling allow a qualitative study of the structural evolution of a caldera collapse process and suggest which of factors play a more relevant role. Analogue models have verified that caldera collapse formation is influenced by multiple aspects (e.g. regional tectonics). We have performed three types of semi-quantitative analyses of particular interest for volcanic hazard: the measurement of the erupted magma chamber volume fraction required to achieve each step of the collapse process, the estimation of the subsidence pattern and the study of the influence of the roof aspect ratio in the dimensions of the collapse parts at surface.

This work includes also a summary of the most important aspects concerning mathematical models of collapse calderas. In base of a mathematical analysis of the pressure evolution inside the chamber during volcanic cycles, we have defined two collapse caldera end-members: under- and overpressure calderas. We have (1) reproduced numerically some of the analogue experiments set out in this work; (2) studied the influence of the selected geometrical setting (e.g. axial symmetric or three-dimensional) in the obtained results and subsequent interpretations and (3) demonstrated that results obtained with mathematical models not strictly related to collapse caldera processes are also applicable to the study of collapse mechanisms and controlling factors.

Finally, we compare the different results obtained by the three distinct disciplines, in order to propose a genetic classification for collapse calderas and to describe the dynamic and structural evolution of the defined end-members. We distinguish between "Cordilleran type" and "Composite volcano type" calderas. Calderas related to the first group correspond to commonly rhyolitic or dacitic, large plate/piston or trap-door calderas formed from a sill-like overpressurized magma chamber in the presence of a regional extensive stress field and a large scale doming or underplating. These calderas tend to occur in areas of thick or thin continental crust and in evolved transitional thick crust. They are associated with C-type subduction zones and areas of continental rifting. "Composite volcano type" calderas occur at the culmination of a long eruptive cycle in composite volcanoes. They take place at the summit of a long-lived volcanic edifice, which has undergone various periods of magma chamber inflation and deflation and different eruptions. The caldera-forming eruption begins with overpressure inside the chamber that triggers, once overcome the tensile strength of the host rock, magma injection into the host rock and finally, an eruption. Calderas included in this group tend to be smaller and not too voluminous.

Concluding, the combination of field studies with experimental and theoretical/mathematical and modelling allows us to identify and quantify the main factors controlling collapse calderas.

The use of check valves in the nuclear industry is of great importance from a safety precaution point ofview (McElhaney, 1995). Choosing check valves for these high-pressurized systems comes with agreat challenge. The valves causes what is called check valve slams when closing, leading to a hugepressure wave traveling through the system. To prevent this from happening calculations have to bedone to see what kind of forces are generated during a check valve slam. When the forces are known itis easier designing systems that will endure these slams. A commonly used software in the nuclearindustry is RELAP5 (Reactor Excursion and Leak Analysis Program), its main purpose is to calculatetransients in piping systems. This program can also be used when calculating a check valve slam. Buthow precise is the code compared to the real event? By doing an experiment measuring pressures created by swing check valves during slams, the codewas compared to real data and analyzed to decide what was of importance when modeling for thesetypes of simulations. The RELAP5 code was not initially designed to calculate transients during a check valve slam. This isclearly shown when the code overestimates the pressure waves in the system when using themanufacturer data for the check valve model. Matching the data from the simulations in RELAP5 withthe data recorded from the experiment is not easy. The parameters used for this have no connection tothe specifications for the check valve, which means that transients are hard to estimate withoutexperimental data.

In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates are i.i.d. random variables. We derive a diffusion approximation using a novel method. The diffusion has a random drift, and hence depending on the realisations of service rates, the system can be in Quality Driven (QD), Efficiency Driven (ED) or Quality-Efficiency-Driven (QED) regime. When the system is under QD or QED regime, the abandonments are negligible in the fluid limit, but when it is under ED regime, the probability of abandonment will converge to a non-zero value. We then analyse the optimal staffing levels to balance holding costs with staffing costs combining these three regimes. We also analyse how the variance of service rates influence abandonment rate. Next, we focus on the state space collapse (SSC) phenomenon. We prove that under some assumptions, the system process will collapse to a lower dimensional process without losing essential information. We first formulate a general method to prove SSC results inside pools for heavy traffic systems using the hydrodynamic limit idea. Then we work on the SSC in multi-class queueing networks under the Halfin-Whitt heavy traffic when service rates are i.i.d. random variables within pools. For such systems, exact analysis provides limited insight on the general properties. Alternatively, asymptotic analysis by diffusion approximation proves to be effective. Further, limit theorems, which state the diffusively scaled system process weakly converges to a diffusion process, are usually the central part in such asymptotic analysis. The SSC result is key to proving such a limit. We conclude by giving examples on how SSC is applied to the analysis of systems.

The thesis is focused on two different issues relative to reinforced flexible pipelines for the unbonded cases: tensile force and external pressure. Mainly, the work is carried out comparing theoretical and numerical models for what concerns reinforced flexible pipes, then the analytical models were used for parametric studies and comparison with composite - based pipelines. For the numerical simulation, the FEM software used was ABAQUS. The elevation point for the tensile load case was involving the pressure armor layer in the design of the cross-section and exploiting the plastic properties of the materials, obtaining a valid estimation for the pipe's tensile strength. While for the hydrostatic load case, the elevation point was to carry out a formulation valid for the minimum requirement for the initial ovality in terms of both radial displacements and collapse pressure.

unto L’anguilla europea, Anguilla anguilla L., è una specie catadroma e semelpara che vive quasi tutta la sua vita negli ambienti di acqua dolce, di transizione o di mare costieri (stadio di anguilla gialla). E’ presente, sebbene per poco tempo, anche in ambienti oceanici, infatti quando raggiunge la maturità sessuale allo stadio di anguilla argentina, gli individui iniziano a migrare dai sistemi di acqua dolce o marini costieri e di transizione, raggiungono il Mar dei Sargassi (Oceano Atlantico) per compiervi l’accoppiamento e la deposizione delle uova da parte delle femmine e successivamente gli animali muoiono. Le larve, allo stadio di “leptocefalo”, utilizzando le correnti oceaniche del Oceano Atlantico, compiono il percorso inverso raggiungendo le coste europee dove con una ulteriore metamorfosi si trasformano in “cieche” che si portano negli ambienti di transizione o di acqua dolce. I dati sugli stock giovanili indicano in modo inequivocabile un marcato declino durante gli ultimi quarant’anni, questo è vero non soltanto per A. anguilla, ma anche per A. rostrata L. (l’anguilla americana) e l’A. japonica T. & S. (l’anguilla giapponese). La pesca dell’anguilla nelle Valli di Comacchio (Italia, Nord Adriatico), dove è presente una delle più antiche tradizioni di pesca organizzata dell’anguilla al mondo, dimostra largamente questo declino. Prendendo in esame e mettendo a confronto i dati di A. anguilla a Comacchio, da periodi passati di analisi e dati di raccolte effettuate nel 2011-2012, oltre che dati di letteratura, sono state svolte le ricerche inerenti la tesi di dottorato con i seguenti obbiettivi: a) Sviluppare una nuova relazione lunghezza-peso (LWR) e una nuova relazione lunghezza –età (LAR) per Anguilla anguilla della Valle di Comacchio sulla base dei dati raccolti nel 2011, e confrontarle con le relazioni descritte in precedenza in bibliografia . b) Sviluppare un modello dimensione-età con metodi Bootstrap e Bayesiano per la comprensione della dinamica di popolazione dell’anguilla in una laguna semichiusa, ed applicare il modello medesimo alla popolazione di Comacchio. c) Analizzare una serie di lungo termine sulla produzione di A. anguilla a Comacchio, ed analisi della bibliografia per identificare il ruolo sia al livello locale sia al livello globale, delle varie tipologie di stress sul collasso della popolazione. d) La maggior parte della tesi utilizza modelli matematici relativi alla dinamica della popolazione di anguilla e alle caratteristiche morfometriche. Tali modelli consistono di molte funzioni bivariate che descrivono attributi isolati delle popolazioni. Per questo motivo è stato aggiunto nella tesi un ulteriore capitolo teorico che riporta una review della letteratura e una sintesi di vari tipi di molte funzioni che possono essere usate per risolvere problemi ecologici, ambientali o più genericamente biologici. I risultati della tesi evidenziano che lo stock di Anguilla di Comacchio presenta circa il 99% di femminilizzazione, questo probabilmente legato alla riduzione del numero degli individui della popolazione. L’analisi della relazione LWR mostra che questa non viene influenzata dalla riduzione del numero degli individui della popolazione e si avvicina a quanto stimato alla fine degli anni Settanta prima del crollo della popolazione. Invece LAR viene influenzata dalla riduzione numerica sì da ridurre le classi di età e di conseguenza i tassi di maturazione risultano più veloci (anguille argentine più giovani, più lunghe e più pesanti prima della loro migrazione). Il modello dimensione-età è stato calibrato con i dati 2011 ed ha restituito una curva di sopravvivenza, un valore di stock, di tasso di reclutamento e un tasso di metamorfosi (da gialla ad argentina) per la popolazione di Comacchio. Il modello è stato validato con successo usando i dati 2012. L’approccio modellistico includeva un metodo di correzione degli errori dovuti alla dimensione delle maglie delle reti, mentre una nuova funzione bivariata per la stima della curva di sopravvivenza è stata inserita nel modello. Il procedimento di bootstrap era utilizzato per valutare il livello di incertezza per ogni parametro inserito nel modello utilizzando gli intervalli 95% della distribuzione “highest posterior density” (approccio Bayesiano). Lo stock stimato e il reclutamento del modello erano almeno dieci volte più bassi delle stime rispettive ottenute in precedenti studi usando dati della fine degli anni ’80 mettendo in evidenza lo stato cruciale della popolazione. I dati di produzione di anguille argentine dalle Valli di Comacchio, che equivale alla totalità degli individui migranti, copre il periodo dal 1781 al 2013, e costituisce la più lunga raccolta di dati annuale al mondo per la pesca di uno specifico tipo di pesce. I dati includono anche informazioni sulla perdita di habitat e di altri fattori di stress per la popolazione (i.e. temperature molto basse, ipersalinità, inondazioni, inquinamento, ecc.). Il ruolo dei fattori di stress locali sono stati analizzati come causa del declino della popolazione, mentre informazioni addizionali, provenienti dalla letteratura, venivano anche usate e discusse per verificare effetti di stress di tipo globale (i.e. raccolta di cieche a scopi acquacolturali, cambiamenti climatici oceanici, perdita di habitat, inquinamento e parassitismo) su tre differenti specie di anguilla, A. anguilla, A. rostrata e A. japonica. Il collasso della popolazione nelle Valli di Comacchio, che ha avuto inizio negli anni ’70, non mostra segni di possibile recupero, e non può essere spiegato dagli stress di tipo locale. La letteratura relativa agli stress di tipo globale, suggerisce che le tre specie di anguille, subiscono l’effetto combinato di più fattori negativi. L'acquacoltura, che dipende interamente dalle cieche catturate in natura, svolge un ruolo chiave nel declino degli stock naturali. La relazione fra produzione da acquacoltura europea rispetto alle rese delle Valli di Comacchio ed altri dati pubblicati dimostrano, nella riduzione delle popolazioni, il ruolo chiave delle catture di cieche a scopi acquacolturali. Stime conservative fatte usando dati FAO, mostrano che la quantità corrente di cieche necessarie a sostenere la produzione acquacolturale in Europa e in Asia è di circa 2x109 individui. Questa domanda, largamente soddisfatta da cieche di specie Anguilla anguilla, può giustificare il marcato declino della specie, in quanto il mercato delle cieche si è espanso a livello internazionale. Un ultimo studio teorico ha prodotto un totale di 20 modelli che possono descrivere curve a campana simmetriche e non, curve convesse o semplici sigmoidi (tipo curva di crescita con saturazione), curve doppio sigmoidi (tipo curva di crescita con saturazione), curve bilineari e periodiche. I modelli possono anche essere modificati per descrivere la relativa variazione di una variabile dipendente (range della variabile dipendente fra 0 e 1). Sono state anche prodotte linee guida aggiuntive su come creare una curva specchio basata su ognuno dei 20 modelli.
The European eel (Anguilla anguilla L.) is a catadromous and semelparous species that spends most of its life in fresh water, brackish and coastal habitats (yellow eel stage). When reaching maturity passes to the silver eel stage and migrates to the Sargasso Sea (Atlantic Ocean) in order to spawn and die. The larvae (leptocephalus) drift back using oceanic currents and metamorphose into transparent glass eels when they reach the European coastlines. Records of juvenile stocks indicate a tremendous decline during the last four decades not only for A.anguilla but also for other important eel species like the American eel (Anguilla rostrata L.) and the Japanese eel (Anguilla japonica T. & S.). The eel fishery in the Comacchio Lagoon (Italy), which is one of the oldest organized eel fisheries in the world, also faces large stock decline. Taking into account data about A.anguilla in Comacchio from older surveys and surveys performed during 2011-2012 and other information from the international literature, the following objectives were set in the context of the thesis: a) Development of new length-weight (LWR) and length-age (LAR) relationships of A.anguilla from the Comacchio Lagoon using data of 2011 and comparison with previous surveys. b) A size-age model development based on bootstrapping and Bayesian approaches for the assessment of eel population dynamics in semi-closed lagoons and application of the model for the Comacchio population. c) Analysis of the long-term series of A.anguilla production in the Comacchio and conducting a literature review and analysis about the contribution of local and global stressors on the population collapse. d) The major part of the thesis deals with mathematical models related to eel population dynamics and morphometric characteristics. Such models consist of many bi-variate functions which describe isolated attributes of the populations. For this reason, a supplementary theoretical chapter was included in the thesis and concerns the literature review and synthesis of various types of such functions which can be used in ecological, biological and environmental problems. The results of the thesis showed that the eel stock of Comacchio has undergone 99% feminization, probably due to the population density reduction. The analysis of LWR showed that it was not affected by the reduction of population density and approximates the estimated ones of the late seventies before population collapse. On the other hand, LAR was affected leading to age classes reduction and consequently faster maturation rates (younger, longer and heavier silver eels before their migration). The size-age model was calibrated using the data of 2011 and assessed the survival curve, stock, recruitment and metamorphosis rates (from yellow to silver) of Comacchio population. The model was successfully validated using data from 2012. The modeling approach included a method for correcting errors inserted by net selectivity while a new bi-variate function for estimating survival curve was also incorporated. A bootstrap procedure was used to assess the level of uncertainty for each model parameter using the 95% intervals of the highest posterior density distribution (Bayesian approach). The estimated stocks and recruitment by the model were at least ten times lower from the respective estimations of previous studies using data from the late 80s highlighting the crucial state of the population. The data for the silver eel production from Comacchio Lagoon (equivalent to the total migrating population) cover the period 1781-2013 and constitute the longest annual records in the world about the fishery of the specific fish species. The data include information related to habitat loss and other local stressors of the population (e.g. frost, hypersalinity, floods, pollution events etc). The role of the local stressors on the decline of the local stock was investigated while additional information from the literature was also used to discuss the effects of global stressors (e.g. glass eel harvest for aquaculture, climate-oceanographic changes, habitat loss, pollution and parasitism) on the three eel species A.anguilla, A.japonica, A.rostrata. The population collapse in Comacchio, which started in the ‘70s with no signs of recovery, could not be explained by local stressors. The literature about the global stressors suggested that the three eel species are under a combined threat from various directions. Aquaculture, which depends entirely on wild-caught glass eels, was found to play a key role in the decline of natural stocks. The correlations between European aquaculture production versus the Comacchio yields and other published data from other European eel and glass eel fisheries were found significantly high exposing the crucial role of aquaculture. Conservative estimations using FAO data showed that the current amount of glass eels needed to support aquaculture production in Europe and Asia exceeds the 2×109 specimens. This demand, largely covered by A. anguilla glass eel, can justify eel populations decline since glass eel trade has been expanded at international level. The supplementary theoretical study provided a total of 20 models which can describe symmetric and non symmetric bell-shaped curves, convex and simple sigmoid curves (saturation-growth type), double sigmoid curves (saturation-growth type), bilinear and periodical curves. The models were also modified in order to describe the relative variation of a dependent variable (range of dependent variable between 0-1). Additional guidelines were also provided on how to create a mirror curve based on each one of the aforementioned 20 models.

Muitas são as pesquisas que avaliam as variáveis intervenientes no colapso dos solos: contudo, pouco tem sido publicado a respeito da influência da trajetória de ciclos de umedecimento e secagem, no comportamento colapsível do solo, e do colapso em condições de carregamento triaxial. O presente trabalho tem como objetivo estudar o colapso de um solo arenoso, típico da região centro-oeste do Estado de São Paulo, frente a tais variáveis através de ensaios edométricos convencionais, edométricos com controle de sucção e triaxiais. Dos ensaios edométricos convencionais caracterizou-se o colapso sob vários níveis de tensão, determinando assim a sobrecarga de inundação que causa máximo colapso. Nos ensaios de compressão triaxial, cada amostra foi inundada sob um determinado estado de tensão, caracterizado pela relação ▟/□. Nestes ensaios foi observado que as deformações volumétricas são dependentes da tensão confinante e da relação ▟/□, e que as deformações axiais por colapso são menores que as medidas nos ensaios edométricos convencionais. Nos ensaios edométricos com sucção controlada verificou-se que o valor inicial da sucção apresenta influência no valor do colapso total. Quanto aos ciclos de umedecimento e secagem, o solo sofreu colapso insignificante quando a sucção foi reduzida a um mesmo valor pela segunda vez. Os resultados experimentais dos ensaios edométricos com sucção controlada foram então modelados de acordo com o modelo de ALONSO et. al, (1990), e as adaptações a esse modelo propostas por FUTAI (1997) e MACHADO (1998), verificando-se a capacidade de cada formulação em representar matematicamente o comportamento colapsível do solo estudado.
There are many researches that evaluate and discuss the factors which interfere in the collapse of soils. However, not many have been published regarding the influence of the cycles of wetting in the collapsible behavior of the soil, and neither have collapse strains under triaxial load. The present work deals with the collapse behavior of a sandy soil, typical from the center-west of the State of São Paulo, considering the aforesaid aspects and using conventional oedometer, suction controlled oedometer and triaxial compression tests. In conventional oedometer tests, the influence of overburden stress on the induced wetting on collapse strains was characterized. Collapse strains were also measured in triaxial compression tests, varying the ratio of principal stress (▟/□) when the samples are inundated. It was observed that collapse volumetric strains are dependent on confining stress and on ▟/□, and that, axial and radial strains are related to the ratio of ▟/□. The axial collapse strains observed in triaxial compression tests were shown to be lower than the ones measured in conventional oedometer tests. In controlled suction tests, the amount of collapse strains under gradual suction reduction was studied including the influence of suction reversals. It was noted that the initial suction influences the amount of collapse strains, and that, in the cycles of wetting and drying, the strains after the second cycle tended to be negligible. Experimental results from suction controlled oedometer tests were modeled through the model by ALONSO et. al. (1990) and by the adaptations to this model proposed by FUTAI (1997) and MACHADO (1998).

Thesis: S.M. in Building Technology, Massachusetts Institute of Technology, Department of Architecture, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 27-31).
The Roman Pantheon is among the largest unreinforced masonry dome ever built and is an unparalleled example of the construction capabilities of the ancient Romans. As one of the most well-known buildings in the world, its preservation remains important because of its cultural and societal significance, and the methods used to assess the safety of historic masonry structures continue to be developed, particularly for three-dimensional vaulted forms. Through a study of the Roman Pantheon, this thesis compares analytical and experimental results on a 1:100 scale model of the variable thickness, hemispherical dome. The model is created using additive manufacturing for accuracy. This thesis, using a physical scale model, quantifies the safety of the Roman Pantheon against the two most probable causes of collapse (i) deformation of the building geometry and (2) seismic activity. The structural behavior of the model is compared to analytical predictions of (1) spreading supports, simulating leaning walls that result from the dome thrust or settling of the foundations, and (2) tilting, a first-order approximation of horizontal ground acceleration. The experimental tests lead to the formation of a mechanism and collapse due to instability. High-speed imagery captures the observed collapse mechanisms and failure limits. Experimental results are compared to analytical predictions for hemispherical masonry domes. The results of the physical experiment demonstrate the potential for digitally fabricated scale models in approximating the behavior of three-dimensional structures with complex geometries. The low cost and rapid approach provides a useful method for validating analytical predictions of the limit states and collapse mechanisms of unreinforced masonry structures.
by J. William Plunkett.
S.M. in Building Technology

Des méthodes micromécaniques spécifiques ont été développées pour la détermination du comportement effectif de matériaux cellulaires dotés d’une architecture discrète à l’échelle microscopique. La méthode d’homogénéisation discrète a été appliquée à des structures tissées monocouches ainsi qu’à l’os trabéculaire. La topologie discrète initiale de ces milieux est remplacée à l’échelle mésoscopique par un milieu effectif anisotrope micropolaire, qui rend compte des effets d’échelles observés. Ces méthodes d’homogénéisation permettent d’accéder à des propriétés classiques et non classiques dont la mesure expérimentale est souvent difficile. Des modèles 3D ont été développé afin de décrire la rupture fragile et ductile de l’os trabéculaire, incorporant des effets de taille des surfaces d’écoulement plastique. Nous avons construit par des analyses éléments finis de la microstructure de l’os trabéculaire un milieu de substitution 3D homogène, orthotrope de type couple de contraintes, sur la base d’une équivalence en énergie. Les tissus osseux ont la capacité d’adapter leur densité locale et leur taille et forme aux stimuli mécaniques. Nous avons développé des modèles de remodelage interne et externe dans le cadre de la thermodynamique des processus irréversibles, aux échelles cellulaire et macroscopique. Finalement, le remodelage interne anisotrope a été couplé à l’endommagement de fatigue, dans le cadre de la théorie continue de l’endommagement
A methodology based on micromechanics has been developed to determine the effective behavior of network materials endowed with a discrete architecture at the microscopic level. It relies on the discrete homogenization method, which has been applied to textile monolayers and trabecular bones. The initially discrete topology of the considered network materials results after homogenization at the mesoscopic level in anisotropic micropolar effective continuum, which proves able to capture the observed internal scale effects. Such micromechanical methods are useful to remedy the difficulty to measure the effective mechanical properties at the intermediate mesoscopic level scale. The bending and torsion responses of vertebral trabecular bone beam specimens are formulated in both static and dynamic situations, based on the Cosserat theory. 3D models have been developed for describing the multiaxial yield and brittle fracture behavior of trabecular bone, including the analysis of size-dependent non-classical plastic yield. We have constructed by FE analyses a homogeneous, orthotropic couple-stress continuum model as a substitute of the 3D periodic heterogeneous cellular solid model of vertebral trabecular bone, based on the equivalent strain energy approach. Bone tissues are able to adapt their local density and load bearing capacities as well as their size and shape to mechanical stimuli. We have developed models for combined internal and external bone remodeling in the framework of the thermodynamics of irreversible processes, at both the cellular and macroscopic levels. We lastly combined anisotropic internal remodeling with fatigue continuum damage

Voltage Impasse Region (VIR) is a phenomenon in power systemswhose dynamics are describe by a set of Differential AlgebraicEquations (DAE). VIR denotes a state-space area where voltagecausality is lost, i.e. the Jacobian of the algebraic part of DAEis singular. In a Time Domain Simulation (TDS) once system trajectoriesenter VIR, TDS experiences non-convergence of the solution.Then, there is no reason to continue with the simulation. Thisis why it is important to understand the mechanisms that introduceVIR. It is known that VIR appears in relation to static, non-linearload models. However, it remained unknown what the cumulativeeffect of several static, non-linear loads would be.This master thesis has further expanded the concept of VIRby carrying out a structured study on how the load modelling affectsVIR. For this purpose, this thesis proposes a quasi-dynamicmethodology to map VIR in the relative rotor angle space. Themethodology introduces a new discrete index called Voltage ImpasseRegion Flag (VIRflag), which allows to determine if the algebraicequations of DAE are solvable or not and, thus, to locate VIR.A test system is used to test the proposed quasi-dynamic approach.The VIRflag was first used to map VIR for various load combinations.Then, the relationship between TDS non-convergence issuesand the intersection of a trajectory with VIR is examined toverify the proposed methodology.The proposed method has been proved to be efficient in the determinationof VIR regardless of the number of non-linear loads inthe power system. Among the static exponential load models, theConstant Power (CP) load component has been identified as theone with the largest influence on VIR appearance and shape. TheConstant Current (CC) loads induce ”smaller" VIR areas and theConstant Impedance (CI) load can only alter the shape of VIR inthe presence of non-linear load models.
VIR (Voltage Impasse Regions) är ett fenomen i kraftsystem varsdynamiska förlöp beskrivs av differential-algebraiska ekvationer(DAE). VIR betecknar ett område i tillståndsrummet där går förlorad,dvs Jakobianen av den algebraiska delen av DAE är singulärI tidsdomän-simuleringar (TDS) när en trajektoria träffar VIR,konvergerar TDS inte till en lösning. Då finns ingen anledning attfortsätta med simuleringen. Därför är det viktigt att förstå mekanismernasom introducerar VIR. Det är känt att VIR är relateradetill statiska, icke-linjära lastmodeller. Det var dock okänt vadden kumulativa effekten av flera statiska, icke-linjära belastningarskulle vara.Denna uppsats har vidareutvecklat begreppet VIR genom attgenomföra en strukturerad studie om hur lastmodellering påverkarVIR. För detta ändamål föreslår denna avhandling en kvasidynamiskmetod för att kartlägga VIR i det relativa rotorvinkelrummet.Metoden introducerar ett nytt diskret index som heterVoltage Impasse Region Flag (VIRflag), vilket gör det möjligt attbestämma om den algebraiska delen av DAE är lösbar eller inteoch därmed lokalisera VIR. Ett används för att testa det föreslagnakvasi-dynamiska tillvägagångssättet. VIRflag användes först för attkartlägga VIR för olika belastningskombinationer. Därefter granskasförhållandet mellan konvergensproblem i TDS och korsningenmellan en trajektoria och VIR för att verifiera den föreslagna metoden.Den föreslagna metoden har visat sig vara effektiv vid bestämningav VIR, oberoende av antalet icke-linjära belastningar. Bland destatiska exponentiella belastningsmodellerna har konstanteffektlast(CP) haridentifierats som den som har störst inflytande påVIR;s form. Den konstantströmlasten (CC) inducerar mindre"VIRområdenoch konstantimpedanslasten (CI) kan endast ändra formenav VIR i närvaro av icke-linjära belastningsmodeller.

Les comportements critiques des systèmes de mécanique statistique en 2 dimensions ou de mécanique quantique en 1+1 dimensions, ainsi que certains aspects des systèmes sans interactions en 2+1 dimensions, sont efficacement décrits par les méthodes de la théorie des champs conforme et de l'intégrabilité, dont le développement a été spectaculaire au cours des 40 dernières années. Plusieurs problèmes résistent cependant toujours à une compréhension exacte, parmi lesquels celui de la transition entre plateaux dans l'Effet Hall Quantique Entier. La raison principale en est que de tels problèmes sont généralement associés à des théories non unitaires, ou théories conformes logarithmiques, dont la classification se révèle être d'une grande difficulté mathématique. Se tournant vers la recherche de modèles discrets (chaînes de spins, modèles sur réseau), dans l'espoir en particulier d'en trouver des représentations en termes de modèles exactement solubles (intégrables), on se heurte à la deuxième difficulté représentée par le fait que les théories associées sont la plupart du temps non compactes, ou en d'autres termes qu'elles donnent lieu à un continuum d'exposants critiques. En effet, le lien entre modèles discrets et théories des champs non compactes est à ce jour loin d'être compris, en particulier il a longtemps été cru que de telles théories ne pouvaient pas émerger comme limites continues de modèles discrets construits à partir d'un ensemble compact de degrés de libertés, par ailleurs les seuls qui donnent a accès à une construction systématique de solutions exactes.Dans cette thèse, on montre que le monde des modèles discrets compacts ayant une limite continue non compacte est en fait beaucoup plus grand que ce que les quelques exemples connus jusqu'ici auraient pu laisser suspecter. Plus précisément, on y présente une solution exacte par ansatz de Bethe d'une famille infinie de modèles(les modèles $a_n^{(2)}$, ainsi que quelques résultats sur les modèles $b_n^{(1)}$, où il est observé que tous ces modèles sont décrits dans un certain régime par des théories conformes non compactes. Parmi ces modèles, certains jouent un rôle important dans la description de phénomènes physiques, parmi lesquels la description de polymères en deux dimensions avec des interactions attractives et des modèles de boucles impliqués dans l'étude de modèles de Potts couplés ou dans une tentative de description de la transition entre plateaux dans l'Effet Hall par un modèle géométrique compact.On montre que l'existence insoupçonnéede limite continues non compacts pour de tels modèles peut avoir d'importantes conséquences pratiques, par exemple dans l'estimation numérique d'exposants critiques ou dans le résultats de simulations de Monte Carlo. Nos résultats sont appliqués à une meilleure compréhension de la transition theta décrivant l'effondrement des polymères en deux dimensions, et des perspectives pour une potentielle compréhension de la transition entre plateaux en termes de modèles sur réseaux sont présentées
The critical points of statistical mechanical systems in 2 dimensions or quantum mechanical systems in 1+1 dimensions (this also includes non interacting systems in 2+1 dimensions) are effciently tackled by the exact methods of conformal fieldtheory (CFT) and integrability, which have witnessed a spectacular progress during the past 40 years. Several problems have however escaped an exact understanding so far, among which the plateau transition in the Integer Quantum Hall Effect,the main reason for this being that such problems are usually associated with non unitary, logarithmic conformal field theories, the tentative classification of which leading to formidable mathematical dificulties. Turning to a lattice approach, andin particular to the quest for integrable, exactly sovable representatives of these problems, one hits the second dificulty that the associated CFTs are usually of the non compact type, or in other terms that they involve a continuum of criticalexponents. The connection between non compact field theories and lattice models or spin chains is indeed not very clear, and in particular it has long been believed that the former could not arise as the continuum limit of discrete models built out of acompact set of degrees of freedom, which are the only ones allowing for a systematic construction of exact solutions.In this thesis, we show that the world of compact lattice models/spin chains with a non compact continuum limit is much bigger than what could be expected from the few particular examples known up to this date. More precisely we propose an exact Bethe ansatz solution of an infinite family of models (the so-called $a_n^{(2)}$ models, as well as some results on the $b_n^{(1)}$ models), and show that all of these models allow for a regime described by a non compact CFT. Such models include cases ofgreat physical relevance, among which a model for two-dimensional polymers with attractive interactions and loop models involved in the description of coupled Potts models or in a tentative description of the quantum Hall plateau transition by somecompact geometrical truncation. We show that the existence of an unsuspected non compact continuum limit for such models can have dramatic practical effects, for instance on the output of numerical determination of the critical exponents or ofMonte-Carlo simulations. We put our results to use for a better understanding of the controversial theta transition describing the collapse of polymers in two dimensions, and draw perspectives on a possible understanding of the quantum Hall plateautransition by the lattice approach

This thesis investigates the WCSPH model by considering fluid entry and exit, and integrates the WCSPH method into a new, novel, particle-based Bluff Morphology Model (BMM). Using the BMM, this thesis investigates the stability, collapse and equilibrium position of soft coastal bluffs (cliffs). Fluid and floating object interaction using a novel adaptation of the WCSPH method is investigated by incorporating a floating object model. In particular, this thesis examines the water impact, hydrodynamic forces, fluid motions, and movement of objects in the conventional case studies of object entry and exit from still water. A two-dimensional wedge drop analysis was examined, and the hydrodynamic forces show acceptable agreement with published experimental and numerical results. Simulations for water entry and exit of a buoyant and neutral density cylinder compares well with the previous experimental, numerical and empirical studies. These results provide a good foundation to evaluate the accuracy and stability of WCSPH for modelling complex flows, and therefore offers a platform for the use of WCSPH in a Bluff Morphology Model. The BMM combines a multiple wedge displacement method with an adapted Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method. At first the wedge method is applied to compute the stability of the bluff. Once the critical failure mechanism of the bluff slope has been identified, if the Factor of Safety for the mechanism is less than 1, the adapted WCSPH method is used to predict the failure movement and residual shape of the slope. The model is validated against benchmark test cases of bluff stability for purely frictional, purely cohesive, and mixed strength bluff materials including 2D static water tables. The model predictions give a good correlation with the expected values, with medium resolution models producing errors of typically less than 2.0%. In addition, the prediction of lateral movement of a surveyed cliff and the dynamic collapse of a vertical bluff are computed, and compare well with published literature. This model is further extended to then investigate the effect of two dimensional seepage on the stability and collapse of soil slopes and levees. To incorporate the seepage in the model, Darcy’s Law is applied to the interactions among neighbouring soil particles and ghost particles are introduced along the enclosed soil boundary to ensure that no fluid crosses the boundary. The contribution of partially saturated soils and matric suction, as well as the change in hydraulic conductivity due to seepage, are predicted well by this model. The predicted time evolution of slope stability and seepage induced collapse are in reasonable agreement with the experimental results for homogeneous frictional sand and multiple layered cohesive soils. Rapid drawdown over a sand soil is also investigated, and the location and time of the levee collapse occurrence are captured well. A toe erosion model is incorporated within the numerical model, and the location and quantity of erosion caused by lateral seepage is well predicted. The interplay of erosion, seepage and slope instability is examined.

Thesis (Civ. E.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 137-138).
This thesis re-analyzes the well-documented failure of a 30m deep braced excavation underconsolidated marine clay. Prior analyses of the collapse of the Nicoll Highway have relied on simplified soil models with undrained strength parameters based on empirical correlations and piezocone penetration data. In contrast, the current research simulates the engineering properties of the key Upper and Lower Marine Clay units using a generalized effective stress soil model, MIT-E3, with input parameters calibrated using laboratory test data obtained as part of the post-failure site investigation. The model predictions are evaluated through comparisons with monitoring data and through comparisons with results of prior analyses using the Mohr-Coulomb (MC) model. The MIT-E3 analyses provide a modest improvement in predictions of the measured wall deflections compared to prior MC calculations and give a consistent explanation of the bending failure in the south diaphragm wall and the overloading of the strut-waler connection at the 9th level of strutting. The current analyses do not resolve uncertainties associated with performance of the JGP rafts, movements at the toe of the north-side diaphragm wall or discrepancies with the measured strut loads at level 9. However, they represent a significant advance in predicting excavation performance based directly on results of laboratory tests compared to prior analyses that used generic (i.e., non site-specific) design isotropic strength profiles.
by Gonzalo Andrés Corral Jofré.
Civ.E.

In the standard cosmological model the formation of cosmic structures is described by the collapse of density perturbations. These perturbations have grown by the action of gravity from small Gaussian initial fluctuations. In a ΛCDM Universe cosmic structures formation is driven by the collapse of dark matter,leading to the creation of virialized systems,called dark matter halos. Baryonic matter follows the dark matter potential wells, where it cools transforming its kinetic energy into thermic energy, eventually forming visible systems, stars and galaxies (White and Rees 1978; Blumenthal et al. 1984). Structures then grow hierarchically, from smaller to larger ones. Therefore, halos containing large galaxies are formed through repeated merger of smaller halos. The collapse and subsequent formation of dark matter halos is due only to gravity, so it is simpler to explain compared to the formation of stars and galaxies themselves. However, the problem involves a high number offluid-like particles, and does not admit an analytical solution. Therefore it is better studied through use of N-body numerical simulations. This technique allows to evolve a large number of particles subject only to their mutual gravitational interaction. In this way we can simulate a region of Universe, analyse the motion of particles and the formation of bound structures. The present thesis has the following structure: • Chapter1:We present the standard cosmological model for the formation of cosmic structures, and briefly describe the statistical properties of linear perturbation fields and the growth of linear perturbation in the light of Jeans’ theory. • Chapter 2: We describe the analytical approaches to the study of perturbations in the non linear regime. First of all we present the Zel’dovich approximation in case of a quasi-linear regime, and two main dynamical models: spherical and ellipsoidal collapse. Later we describe two analytic approaches to determine halo statistics starting from the initial fluctuation field: the excursion sets approach and the peaks formalism. We also briefly describe some attempts to merge the two approaches together. • Chapter 3: We describe the main approach to the study of non linear and bound structures: N-body simulations. We also describe the main features of simulations employed in this work. Finally we describe the main properties of dark matter halos, focussing on the contributions of N-body simulation to the study of halo properties. • Chapter 4: Firstly we describe different halo identification methods and relaxation criteria and we explain the choice adopted in this work. Later we describe how we calculate the parameters of the ellipsoidal collapse model starting from the eigenvalues of the deformation tensor smoothed on different scales. At a later stage we present a method to describe the distribution of halo formation time separating the contribution of relaxed and non relaxed halos. • Chapter 5: We explain our peaks identification algorithm and present a statistic of peaks identified in our simulations. We study the correlation functions between protohalo centres of mass, and peaks of different quantities. At a later stage we present an alternative to the peaks model for halo formation. In fact, spherical and ellipsoidal collapse model are missing a dipole term which is present in perturbation theory. We study the points where initial dipole vanishes and we correlate them to the protohalo mass centres. • Chapter 6: In the first part we present a statistic of Lagrangian parameters, and compare it with results obtained by other authors. Afterwards we investigate the correlation between the Lagrangian parameters δL and qL and the halo formation redshift z50 as a function of rescaled mass ν and identification redshift zid. • Chapter 7: Whereas in the previous chapter we described Lagrangian parameters, here we present profiles. Firstly we build Lagrangian profiles around the protohalo mass centres, and show how they correlate with Lagrangian shear and halo formation times. Later we study the relation between Lagrangian and (Eulerian) profile, and show how Lagrangian shear and formation times affect the final halo profiles. Finally we study the evolution of halo particle profiles with time.
Nel quadro del modello cosmologico standard, la formazione delle strutture è descritta attraverso il collasso di perturbazioni di densità con una distribuzione iniziale generalmente assunta come gaussiana. Queste fluttuazioni erano inizialmente piccole e sono cresciute successivamente per effetto della gravità. In un universo ΛCDM la formazione delle strutture cosmiche è guidata dal collasso della materia oscura che porta alla formazione di aloni virializzati. La materia barionica cade dentro alle buche di potenziale create da questi aloni, si raffredda e conduce alla formazione di stelle e galassie, trasformando la sua energia cinetica in energia termica (White and Rees 1978; Blumenthal et al. 1984). Successivamente, le strutture crescono in modo gerarchico, dalle più piccole alle più grandi. Quindi, aloni contenenti galassie massicce si formano tramite l’accrescimento di aloni più piccoli da parte dell’alone principale. Il collasso e la successiva formazione di aloni di materia oscura è dovuto unicamente alla gravità; per questo motivo la sua descrizione è semplice in linea di principio e coinvolge un alto numero di particelle. Un modo efficace di analizzare la formazione di questi aloni passa per l’utilizzo di simulazioni a N corpi. Con questo approccio non si ricerca una soluzione analitica, bensì viene fatto evolvere un gran numero di particelle soggette alla sola interazione gravitazionale. È così possibile simulare una regione di universo e analizzare il moto delle particelle e la formazione di strutture collassate. La struttura di questo lavoro è la seguente: • Capitolo 1: Presentiamo il modello cosmologico standard per la formazione delle strutture cosmiche e descriviamo brevemente le proprietà statistiche dei campi di fluttuazionelinearielacrescitadiperturbazionilineariallalucedellateoriadiJeans. • Capitolo 2: Descriviamo i principali approcci analitici allo studio delle perturbazioni in regime non lineare. Prima di tutto presentiamo l’approssimazione di Zel’dovich applicabile al caso di un regime quasi lineare. e descriviamo i due principali modelli dinamici per lo studio del collasso delle strutture: il modello di collasso sferico e il modello di collasso ellissoidale. Più avanti descriviamo due approcci analitici per la determinazione la statistica degli aloni a partire dal campo di fluttuazioni iniziale: il modello degli excursion sets e il formalismo dei picchi. Descriviamo anche brevemente alcuni tentativi di fondere assieme questi due approcci. • Capitolo 3: Descriviamo il metodo principale utilizzato per lo studio di strutture fortemente non lineari: le simulazioni a N corpi. Descriviamo inoltre le caratteristiche principali delle simulazioni numeriche utilizzate in questo lavoro. Infine, descriviamo le proprietà principali degli aloni di materia oscura, concentrandoci sul contributo dato a questo campo dalle simulazioni numeriche. • Capitolo 4: Inizialmente descriviamo i diversi metodi per l’identificazione di aloni e i criteri di rilassamento usati in questo lavoro. Successivamente descriviamo come sono stati calcolati i parametri del collasso ellissoidale a partire dagli autovalori del tensore di deformazione smussati su diverse scale. L'ultima sezione del capitolo è infine dedicata allo studio di una descrizione della distribuzione dei tempi di formazione dei soli aloni rilassati. • Capitolo 5: Descriviamo il metodo usato per l’identificazione dei picchi nei campi iniziali e presentiamo una descrizione statistica dei picchi suddetti. Successivamente analizziamo la funzione di correlazione tra i centri di massa dei protoaloni e i picchi e le valli nella distribuzione dei parametri di interesse. L'ultima parte del capitolo è dedicata all'analisi di un’alternativa al formalismo dei picchi per l’identificazione della formazione degli aloni. Infatti, il collasso sferico e quello ellissoidale mancano di un termine di dipolo presente invece nella teoria delle perturbazioni. Studiamo dunque i punti dove il dipolo iniziale svanisce e li relazioniamo ai centri di massa dei protoaloni. • Capitolo 6: Nella prima parte presentiamo una descrizione statistica dei parametri Lagrangiani, svolgendo un opportuno confronto coi risultati di altri autori. Successivamente indaghiamo la correlazione tra i parametri lagrangiani δL e qL e i redshift di formazione degli aloni z50 in funzione della massa universale ν e del redshift di identificazione. • Capitolo 7:Mentre nel precedente capitolo abbiamo descritto parametri smussati su una sola scala, la scala lagrangiana degli aloni, passiamo ora all’analisi dei profili. Primariamente costruiamo i profili lagrangiani attorno al centro di massa dei protoaloni e mostriamo come correlano con il parametro di shear e il redshift di formazione. Successivamente studiamo la relazione tra i profili lagrangiani e i profili euleriani e mostriamo che l’effetto dello shear lagrangiano e del tempo di formazione ancora presente nei profili finali. Infine studiamo l’evoluzione dei profili delle particelle dell’alone a diversi tempi cosmici.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Introdução: A luxação do quadril em uma criança pode interferir com a função dessa articulação, causando dor, limitação de movimento, entre outras consequências. Na redução aberta da articulação, diversas estruturas anatômicas são abordadas como o ligamento redondo (LR) que, tradicionalmente, é ressecado. Porém, existe controvérsia a respeito de sua importância funcional. Objetivo: Comparar através de análise biomecânica, bioquímica e histológica o LR de quadris instáveis (luxados e subluxados) com o ligamento de quadris normais. Métodos: Estudo experimental com coelhos esqueleticamente imaturos, utilizando um modelo para luxação do quadril. Oitenta e oito coelhos foram submetidos à fixação do joelho de uma das patas traseiras em extensão, o que leva à instabilidade do quadril ipsilateral, devido ao desequilíbrio muscular e à alteração em posicionamento no membro. Dezenove coelhos morreram, 28 foram excluídos por não evoluírem com a luxação e 5 foram excluídos pela impossibilidade de identificação do LR. Dos 36 coelhos que compuseram a amostra, estratificamos as análises em quantitativas: biomecânica (12 coelhos), zimografia (8 coelhos), histologia (14 coelhos) e qualitativa: imuno-histoquímica (2 coelhos). Realizamos análise estatística para comparação entre o lado luxado e o controle de cada coelho quanto às análises quantitativas. Resultados: No ensaio biomecânico, a média da força máxima do ligamento redondo no lado luxado foi de 43,25 ± 16,25N e 46,62 ± 15,56N para o lado normal (p=0,594) e a média da deformação máxima foi de 3,94 ± 1,88mm para o lado luxado e 4,55 ± 1,19mm para o normal (p = 0,328). Histologicamente foi quantificada a celularidade, mostrando em média, para o ligamento do lado luxado, 6,83 ± 3,47 células por campo e 3,87 ± 2,13 para o lado normal (p<0,001), além de 74,3 ± 10,5% de ocupação por colágeno no lado luxado e 84,5 ± 9,5% no lado normal (p<0,001). Na zimografia, a quantidade de metaloproteinase 2 (MMP2) em forma ativa foi 481,8 ± 228UA, em média, para o lado luxado e de 294,4 ± 78UA para o lado normal (p=0,068). Conclusão: Embora tenham ocorrido alterações significativas no LR dos quadris instáveis do ponto de vista histológico e com diferença importante na zimografia, esta sem significância estatística, isso não foi observado no ensaio biomecânico, no qual não houve diferença estatística entre os lados.
In the open reduction, used in the treatment of the hip dislocation in children, several structures are approached, such as the round ligament (RL) that has traditionally been resected. However, there is controversy regarding its possible maintenance as well as its functional importance. The aim of this study was to compare the RL properties of stable and unstable hips. Methods: Experimental study with young rabbits using a model for congenital hip dislocation. Eighty-eight rabbits underwent fixation of the knee of one hind leg in extension, which leads to ipsilateral hip instability. Nineteen rabbits died and 28 were excluded because they did not develop dislocation. Five additional rabbits also excluded because they did not present the RL. Thirty-six rabbits composed the sample that was stratified for quantitative analysis: biomechanical (12 rabbits), zymography (8 rabbits), histology (14 rabbits) and qualitative: immunohistochemistry (2 rabbits). We performed statistical analysis for comparison between the unstable side and the control of each rabbit. Results: Biomechanical assay showed the mean maximal strength of the RL on the unstable side was 43.25 ± 16,25N and 46.62 ± 15,56N for the control side (p = 0.594) and the mean maximum deformation was 3.94 ± 1,88mm for the unstable side and 4.55 ± 1,19mm for the control (p = 0.328). Histologically, there was an increase in cellularity on the unstable side showing, on average, 6.83 ± 3,47 cells per field and 3.87 ± 2,13 for the control side (p <0.001), in addition to 74.3 ± 10,5% of collagen occupancy on the unstable side and 84, 5 ± 9,5% on the control side (p <0.001). In zymography, the amount of metalloproteinase 2 (MMP-2) was 481.8 ± 228UA, on average, for the unstable side and 294.4 ± 78UA for the control side (p = 0.068). Conclusions: Although there were significant changes in the RL of the unstable hips from the histological analysis and there were an important diference in zymography without statistical significance, that was not observed in the biomechanical test.

VYSOKÉ UČENÍ TECHNICKÉ V BRNĚ The purpose of this work is to design and implement a computer system, which should be used for simplification of a polygonal models in 3D space. The system should be allowed to reduce a given number of geometrical primitives from source object. User should have impact to the reducing process by selecting a method, size of target object etc. System uses 3DS file format for model loading and saving. Reader should understand principles of the polygon reduction and used algorithms.

Present graphic requires a lot of optimizations of rendering techniques and mathematical calculations. It is caused by increased requirements of scene's visualization. One of scene's optimizing techniques is the Level of detail. This thesis is focused on methods used by LOD in OpenSceneGraph and OpenGL library. Next it will be described how to choose the right level of detail in a scene. Later it will be explained how to simplify 3D models. These techniques will be implemented in converting tool and demonstrating application. Methods for simplify 3D models will be tested for their speed and quality.

Background & Purpose: The current standard dosimetry in brachytherapy treatment planning, the TG-43 formalism, ignore the presence of non-water media and finite patient dimensions. This can cause clinically relevant errors in dose estimates. To over- come the limitations of the TG-43 formalism, Model-Based Dose Calculation Algorithms (MBDCAs) have evolved. One of the commercial available MBDCAs is the Advanced Collapsed cone Engine (ACE) by Elekta. In ACE, the total dose is divided into three components, the primary, the first-scattered and the multiple-scattered dose, where the two last mentioned are calculated by the means of the Collapsed Cone Algorithm. In this study the performance of ACE has been investigated. The study has been di- vided into 2 parts, where the aim of part 1 was to analyze the relationship between the so called discretization artifacts, caused by the collapsed cone approximation, and the number of dwell positions. The severeness of the artifact is thought to decrease as the number of dwell positions are increased. The second part focus on ACE’s behavior in cortical bone, with the aim to form a hypothesis (explanation and solution) to the previously observed dose underestimation of the dose to bone made by ACE. Materials and Methods: The generic 192Ir source, the Oncentra Brachy (OcB) treatment planning system (TPS) and the Monte Carlo (MC) platform ALGEBRA have been utilized. In the first part of the study, six source configurations, all with a different number of dwell positions, were created and placed in the center of large water phantoms, i.e. under TG-43 conditions in which the TG-43 formalism can be assumed to yield a high accuracy of the estimated dose. The accuracy of ACE has been judged by its’ deviation from TG-43. In the second part of the study, a cubic source configuration, of 27 dwell positions, was positioned at the center of a cubic water phantom. Three cases where constructed, with a small cortical bone heterogeneity positioned at different distances from the source configu- ration. The ACE calculated dose distribution has been divided into its’ three constituents. The accuracy of ACE and TG-43 has been judged by its’ deviation from MC. Results: Part 1 showed that increasing the number of dwell positions does not guar- antee an improved accuracy of ACE. Local dose difference ratios of > 2%, caused by the artifacts, were mainly located outside the 5% isodose line. A general dose underestima- tion was observed in ACE, with an increased magnitude as the dose level decreased. The majority of local dose difference ratios below -4% were found where the multi-resolution voxelization grid of ACE has a voxel size of ≥23 mm3, that is at a distance of ≥8 cm from the closest dwell position when using the ACE standard accuracy level. In part 2, ACE underestimated the dose to cortical bone, with an increased magnitude as the bone was positioned farther away from the source configuration. The TG-43 formalism gave slightly better estimates of the mean dose to bone than ACE, especially at higher dose levels. For a mean dose to the cortical bone heterogeneity equal to 45% of the prescribed dose, TG-43 and ACE underestimated the mean dose with 1% and 4%, respectively. The estimated mean dose to a volume located directly behind the heterogeneity agreed within 1% between ACE and MC. However, an increased amount of positive local dose difference ratios were observed in this volume. Conclusions: Increasing the number of dwell positions cause a ”blurring” effect of the artifact, but may also increase the fluence gradient. In such situations the severeness of the artifact may not be improved. In patient cases the dwell positions are usually added in a more random manner which may favor the ”blurring effect”. The underestimations observed in ACE are thought to be caused by both the multiple- resolution voxelization grid of ACE and the relationship between the dimensions of the phantom in which the multiple-scattered kernel has been generated and the current calcu- lation volume. ACE was unsuccessful to predict the dose to cortical bone, and should hence be used with caution when cortical bone is an organ at risk, as long as the problem remains. The results indicates that the error in ACE is located in the scatter dose calculations and that the heterogeneity cause ACE to displace the dose. The error is thought to be located in the multiple-scattered dose component, which was also shown by Terribilni et al.. A hypothesis is that the problem is caused by the neglected effect of media dependent absorption coefficients in the multiple-scattered dose calculation. A suggested solution, left to be proven, is to use effective attenuation scaling factors.

La investigación que sigue aborda el problema del modelo y su lugar en la producción artística moderna. Se localiza, particularmente, en el momento en que la pintura se hace partícipe de la crítica de la representación y su relación con el mundo visible se vuelve marcadamente problemática. Esto es, fines del siglo XIX y principios del XX. Esta tesis toma por motivo un momento crucial en ese contexto histórico como es la obra de Cézanne y la lectura interpretativa de la misma a la luz del problema del modelo. En este sentido lo que pone a operar es la noción de modelo y su rol, tanto en la producción pictórica de Cézanne, como en las interpretaciones que la toman como referente para producir a su vez un modelo de comprensión de la pintura moderna, que se habría desarrollado a partir de las fórmulas cezanneanas.

The collapse of Redcliffs’ cliff in the 22 February 2011 and 13 June 2011 earthquakes were the first times ever a major failure incident occurred at Redcliffs in approximately 6000 years. This master’s thesis is a multidisciplinary engineering geological investigation sought to study these particular failure incidents, focusing on collecting the data necessary to explain the cause and effect of the cliff collapsing in the event of two major earthquakes. This study provides quantitative and qualitative data about the geotechnical attributes and engineering geological nature of the sea-cut cliff located at Redcliffs. Results from surveying the geology of Redcliffs show that the exposed lithology of the cliff face is a variably jointed rock body of welded and (relatively intact) unwelded ignimbrite, a predominantly massive unit of brecciated tuff, and a covering of wind-blown loess and soil deposit (commonly found throughout Canterbury) on top of the cliff. Moreover, detailing the external component of the slope profile shows that Redcliffs’ cliff is a 40 – 80 m cliff with two intersecting (NE and SE facing) slope aspects. The (remotely) measured geometry of the cliff face comprises of multiple outstanding gradients, averaging a slope angle of ~67 degrees (post-13 June 2011), where the steepest components are ~80 degrees, whereas the gentle sloping sections are ~44 degrees. The physical structure of Redcliffs’ cliff drastically changed after each collapse, whereby seismically induced alterations to the slope geometry resulted in material deposited on the talus at the base of the cliff. Prior to the first collapse, the variance of the gradient down the slope was minimal, with the SE Face being the most variable with up to three major gradients on one cross section. However, after each major collapse, the variability increased with more parts of the cliff face having more than one major gradient that is steeper or gentler than the remainder of the slope. The estimated volume of material lost as a result of the gradient changes was 28,267 m³ in February and 11,360 m³ in June 2011. In addition, surveys of the cliff top after the failure incidents revealed the development of fissures along the cliff edge. Monitoring 10 fissures over three months indicated that fissured by the cliff edge respond to intense seismicity (generally ≥ Mw 4) by widening. Redcliffs’ cliff collapsed on two separate occasions as a result of an accumulated amount of damage of the rock masses in the cliff (caused by weathering and erosion over time), and two Mw 6.2 trigger earthquakes which shook the Redcliffs and the surrounding area at a Peak Ground Acceleration (PGA) estimated to be around 2 g. The results of the theoretical study suggests that PGA levels felt on-site during both instances of failure are the result of three major factors: source of the quake and the site affected; topographic amplification of the ground movement; the short distance between the source and the cliff for both fault ruptures; the focus of seismic energy in the direction of thrust faulting along a path that intercepts Redcliffs (and the Port Hills). Ultimately, failure on the NE and SE Faces of Redcliffs’ cliff was concluded to be global as every part of the exposed cliff face deposited a significant volume of material on the talus at the base of the cliff, with the exception of one section on the NE Face. The cliff collapses was a concurrent process that is a single (non-monotonic) event that operated as a complex series of (primarily) toppling rock falls, some sliding of blocks, and slumping of the soil mantle on top of the cliff. The first collapse had a mixture of equivalent continua slope movement of the heavily weathered / damaged surface of the cliff face, and discontinuous slope movement of the jointed inner slope (behind the heavily weathered surface); whereas the second collapse resulted in only discontinuous slope movement on account of the freshly exposed cliff face that had damage to the rock masses, in the form of old and (relatively) new discontinuous fractures, induced by earthquakes and aftershocks leading up to the point of failure.

This project is focused on understanding the processes of failure evolution (from triggering to propagation) and deformation mechanisms of Deep Seated Gravitational Movement (DSGSD) and Rock Avalanches (RA) in massive brittle rock slopes. In particular, the focus of this work is directed to the failure mechanism of these phenomena, the influence of failure mechanisms on the slope stability and dynamics of the collapse. This research aims to improve the understanding and modeling of brittle fracture and progressive failure in massive metamorphic rock slopes though a combination of structural geology, geomechanics, geomorphology, numerical and experimental modeling. Triggering factors and failure mechanisms were study on one mass wasting phenomena in the Easten Alps (Ridnaun Valley Rock Avalanche). The left slope of the Ridnaun Valley (Sterzing/Vipiteno, South Tyrol, Italy), set on the crystalline units of the Austoalpine Nappe of the alpine orogenic wedge, shows evidence of quaternary gravitational evolution which highly depends on the brittle/ductile structural setting of the slope. Detailed field work and LiDAR-derived digital elevation model analysis clearly revealed different gravitational movements. A fully evolved gravitational collapse, having the typical features of a Rock Avalanche (RA), characterizes the central part of the slope; whereas to the east and west of the RA, deep - seated gravitational slope deformations, pointed out for the first time with this research, still involve the slope. Making use of different approaches, such as geomorphology, structural geology and geomechanical analysis, and numerical modeling, the present work shows how the brittle/ductile tectonic setting acts on one hand as primary controlling factors of the detected large mass movements; on the other hand, can control the evolutionary type of failure (i.e.: rock avalanche). It is expected that the findings obtained through this investigation will enhance our fundamental knowledge on DSGSD evolutionary type on poly - deformed metamorphic masses, particularly with regard to understanding the key stages of the progressive evolution of rock slope failures from a secondary creep stage to the sudden collapse.
Questo progetto di ricerca ha come focus la comprensione dei meccanismi di deformazione e di collasso (dall'innesco alla prpagazione della rottura) che governano Deformazioni Gravitative Profonde di Versante (DGPV) e valanghe di roccia (rock avalanches) in versanti rocciosi. In particolare, l'attenzione primaria di questo lavoro è indirizzata ai meccanismi di propagazione della rottura, alla loro influenza sulla stabilità dei versanti ed alle dinamiche del collasso. Lo scopo principale è migliorare le conoscenze ed i modelli relativi ai meccanismi di fratturazione e di rottura progressiva in ammassi rocciosi foliati, attraverso un approccio multidisciplinare che prevede l'analisi delversante con tecniche geologico - strutturali, geomorfologhiche, geomeccaniche e di modellazione numerica. Cause innascanti e meccanismi di rottura progressiva sono stati analizzati prendendo come caso studio un collasso gravitativo di grandi dimensioni nelle Alpi orientali (la rock avalanche della Val Ridanna). Il versante sinistro della Val Ridanna (Sterzing/Vipiten, Alto Adige, Italia), collocato geologicamente nelle unità cristalline della falda Austroalpina del prisma orogenetico delle Alpi, mostra evidenze un'evoluzione gravitativa quaternaria di tipo differenziale, la quale è fortemente controllata dall'assetto geologico duttile/fragile delle unità metamorfiche costituenti il versante. Indagini di terreno, unita ad una dettagliata analisi del modello digitale del terreno ottenuti da acquisizioni LiDAR, ha permesso di riconoscere differenti deformazioni gravitative all'interno del versante studio. La parte centarle della valle è caratterizzata da un evidente accumulo derivante da un collasso gravitativo di tipo rock avalanche; lungo il verante, ad ovest ed ad est dell'area sorgente della rock avalanche, due DGPV, riconosciute per la prima volta grazie a questo lavoro, coinvolgono il versante. Il presente lavoro mostra come l'assetto duttile/fragile agisca da un lato come fattore predisponente alle deformazioni gravitative riconosciute; dall'altro controlla direttamente le modalità evolutive delle deformazioni stesse. Si ritiene che i risultati ottenuti da questa tesi di dottorato possano contribuire al miglioramento delle conoscenze sull'evoluzione di DGPV in rocce metamorfiche polideformate, in particolare per quanto concerne i meccanicsmi che governano l'evoluzione parossistica di un ammasso roccioso in deformazione lenta.

Nowadays, the numerical models are important allies for the study of physical and natural phenomena. They become progressively more complicated because various differential equations are included to consider the different processes involved in a singular phenomenon. The number of parameters used to adapt the numerical results to the real measurements increase consequently. Among the huge quantity of natural phenomena studied, the landslides are definitely important and, among them, the flow-slides are a type, which actually have an increasing occurrence frequency because of the climate change. When the velocity of the flowing material is high, this type of natural hazard becomes even more worrying. The risk and the damage, which may result, are significant, especially when the landslide is located in close proximity to residential areas. The catastrophic effects range from the destruction of buildings and infrastructures, to the most tragic loss of human lives. Three processes of a flow-slide could be individuated: the trigger mechanism, the propagation and the final deposit. Topic of this thesis is the study of the last two phases that occur after the mass collapse has already happened. The propagation and the deposit phases will be here analyzed using a model which integrates the Saint Venant‘s equations developed for the flow of an equivalent homogeneous material according to the shallow water hypothesis. The model is applied before to the simulation of several laboratory experiments and, then, for reproducing a debris flow really occurred in 2010 in Italy. The calibration phase is the basic operation for using a numerical model. The parameters considered have to be smartly defined to reproduce the phenomenon with a satisfactory likelihood. When the parameters have a physical meaning, it is necessary to check if they allow the model to produce reliable results, even when the model necessarily introduces strong approximations. Sometimes, anyway, the parameters to include in the calculation have just a mathematical significance. In this case, it is even more important to calibrate the model paying attention to all the complexities of the phenomenon, because if the calibration strategy does not take into account the various aspects of the case study, the parameters obtained by the back-analysis may be senseless. This thesis wants to show the complexity that may characterize the calibration procedure. Once the numerical model has been adopted and its possibilities and limitations have been evaluated, the analysis of different cases will help to evidence the difficulties that the back-analysis can present. To this aim, in this work, three main case studies are presented: the spreading of a column of cohesive material on a horizontal plane, numerous flume tests performed using three-phases mixtures and, finally, a real debris flow occurred in 2010 along the Rotolon stream, in North-Western sector of Veneto region (Italy). It is important to underline that all the laboratory tests are performed on purpose to apply the back-analysis, paying therefore particular attention to the data acquisition conditions. For all the case studies, many calibration procedures are applied in order to individuate the most suitable to reduce the uncertainty in the determination of the fitting parameters.
Oggigiorno, i modelli numerici ricoprono un ruolo di fondamentale importanza per lo studio di fenomeni fisici e naturali. Essi diventano via via sempre più complessi grazie all’aumento del numero di equazioni differenziali implementate in ciascun modello al fine di tener conto dei differenti aspetti che caratterizzano il fenomeno oggetto studio. Conseguentemente cresce anche il numero dei parametri da valutare per adattare i risultati ottenuti dal modello numerico alle misure reali. Tra tutti i fenomeni naturali che si possono considerare, i frane sono indiscutibilmente molto importanti. Tra i diversi tipi di frane, le colate sono una tipologia che si presenta sempre con maggior frequenza a causa dei cambiamenti climatici in atto e con effetti molto dannosi. Quando, poi, la velocità raggiunta in questi fenomeni diventa elevata, aumenta il loro potere distruttivo. I rischi e i danni che ne possono nascere non sono trascurabili, in modo particolare quando le colate avviene in prossimità di aree residenziali. Gli effetti catastrofici che ne possono scaturire spaziano dalla distruzione di edifici e infrastrutture, fino ad arrivare alla ancor più tragica perdita di vite umane. Quando si studia un movimento di colata, tre processi devono essere presi in considerazione: il meccanismo di innesco, la fase di propagazione ed infine il deposito. Questa tesi riguarda principalmente lo studio degli ultimi due processi che si verificano, cioè, quando il materiale ha già iniziato il suo movimento. Le fasi di propagazione e di arresto sono qui analizzate utilizzando un modello numerico sviluppato integrando le equazioni di Saint Venant per il flusso di un materiale monofase omogeneo in acque basse. Il modello è stato applicato sia per la simulazione di esperimenti di laboratorio sia per riprodurre un debris flow avvenuto nel nord Italia nel 2010. Quando si utilizza un modello numerico, la fase di calibrazione rappresenta un’operazione essenziale affinché si possano ottenere buoni risultati. I parametri utilizzati dal codice devono essere attentamente definiti in modo che il modello possa riprodurre il fenomeno fisico con elevata accuratezza. Quando i parametri hanno un significato fisico, risulta necessario controllare se il loro utilizzo, considerando le approssimazioni che il modello inevitabilmente comporta, permette di produrre risultati affidabili. A volte, tuttavia, i parametri che devono essere inseriti nel modello prescindono dalla natura fisica del caso in esame, ed hanno solamente un significato in termini matematici. Quando questo avviene, risulta ancor più importante calibrare il modello, cercando di cogliere l’intera complessità del fenomeno. Se la strategia di calibrazione non tiene conto dei vari aspetti che caratterizzano il caso di studio, infatti, i parametri ottenuti tramite back-analysis potrebbe non aver alcun senso. Questa tesi si pone l’obiettivo di sottolineare la complessità che può contraddistinguere il processo di calibrazione. Dopo aver deciso quale modello numerico utilizzare ed averne comprese possibilità e limitazioni, lo studio di casi di studio differenti permette di evidenziare le criticità e le problematiche che la back-analysis può presentare. A tale scopo, in questo lavoro vengono considerati principalmente tre casi di studio. Il primo riguarda il collasso di una colonna di materiale coesivo su di un piano orizzontale. Successivamente la procedura è applicata ad un gruppo di prove in canaletta condotte con diverse miscele di argilla e sabbia. Infine, viene analizzata la colata detritica avvenuta nel 2010 lungo il torrente Rotolon, situato in nella parte nord-occidentale del Veneto. È importante sottolineare che tutti i test di laboratorio sono stati eseguiti appositamente per la successiva applicazione della back-analysis, prestando quindi particolare attenzione alle modalità di acquisizione dei dati. Per tutti e tre i casi, è stata ricercata ed applicata una strategia di calibrazione per ridurre l’incertezza nell’identificazione dei parametri ottimali.

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In this study, the methodological procedures involved in digital imaging of collapsed paleocaves in tufa using GPR are presented. These carbonate deposits occur in the Quixer? region, Cear? State (NE Brazil), on the western border of the Potiguar Basin. Collapsed paleocaves are exposed along a state road, which were selected to this study. We chose a portion of the called Quixer? outcrop for making a photomosaic and caring out a GPR test section to compare and parameterize the karst geometries on the geophysical line. The results were satisfactory and led to the adoption of criteria for the interpretation of others GPR sections acquired in the region of the Quixer? outcrop. Two grids of GPR lines were acquired; the first one was wider and more spaced and guided the location of the second grid, denser and located in the southern part of the outcrop. The radargrams of the second grid reveal satisfactorily the collapsed paleocaves geometries. For each grid has been developed a digital solid model of the Quixer? outcrop. The first model allows the recognition of the general distribution and location of collapsed paleocaves in tufa deposits, while the second more detailed digital model provides not only the 3D individualization of the major paleocaves, but also the estimation of their respective volumes. The digital solid models are presented here as a new frontier in the study of analog outcrops to reservoirs (for groundwater and hydrocarbon), in which the volumetric parameterization and characterization of geological bodies become essential for composing the databases, which together with petrophysical properties information, are used in more realistic computer simulations for sedimentary reservoirs.
Nesse trabalho s?o apresentados os procedimentos metodol?gicos envolvidos no imageamento digital de paleocavernas colapsadas em tufas carbon?ticas que ocorrem na borda oeste da Bacia Potiguar com GPR. Foi mapeada uma ?rea em Quixer? (CE) e selecionado um afloramento em um corte de estrada, denominado de Afloramento Quixer?. Foi escolhida uma por??o deste afloramento para confec??o de um fotomosaico e levantamento de uma se??o-teste com o GPR para a compara??o e parametriza??o das geometrias c?rsticas aflorantes e imageadas na linha geof?sica. Os resultados foram satisfat?rios e permitiram a ado??o de crit?rios para a interpreta??o das paleocavernas colapsadas em outras se??es GPR, levantadas na regi?o do afloramento. Foram adquiridas duas malhas de linhas GPR, a primeira mais ampla e espa?ada norteou a loca??o da segunda, mais adensada, na por??o sul do Afloramento Quixer?. Nos radargramas foram interpretadas e parametrizadas as geometrias das principais paleocavernas colapsadas. Para cada malha foi elaborado um modelo de s?lido digital do Afloramento Quixer?, sendo que o primeiro modelo permitiu o reconhecimento da distribui??o geral das tufas e a localiza??o das paleocavernas colapsadas, enquanto o segundo modelo digital, por ser mais detalhado, possibilitou n?o apenas a individualiza??o 3D das principais paleocavernas, mas tamb?m o c?lculo dos seus respectivos volumes. Os modelos de s?lidos digitais s?o aqui apresentados como uma nova fronteira no estudo de afloramentos an?logos a reservat?rios (h?dricos ou petrol?feros), na qual a parametriza??o e a caracteriza??o volum?trica dos corpos geol?gicos passam a ser fundamental para compor bancos de dados, que conjuntamente com informa??es de propriedades petrof?sicas s?o utilizados em simula??es computacionais mais real?sticas de reservat?rios.

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Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico
The ferromagnetic and antiferromagnetic Ising model on a two dimensional inhomogeneous lattice characterized by two exchange constants (J1 and J2) is investigated. The lattice allows, in a continuous manner, the interpolation between the uniforme square (J2 = 0) and triangular (J2 = J1) lattices. By performing Monte Carlo simulation using the sequential Metropolis algorithm, we calculate the magnetization and the magnetic susceptibility on lattices of differents sizes. Applying the finite size scaling method through a data colappse, we obtained the critical temperatures as well as the critical exponents of the model for several values of the parameter α = J2 J1 in the [0, 1] range. The ferromagnetic case shows a linear increasing behavior of the critical temperature Tc for increasing values of α. Inwhich concerns the antiferromagnetic system, we observe a linear (decreasing) behavior of Tc, only for small values of α; in the range [0.6, 1], where frustrations effects are more pronunciated, the critical temperature Tc decays more quickly, possibly in a non-linear way, to the limiting value Tc = 0, cor-responding to the homogeneous fully frustrated antiferromagnetic triangular case.
Investigamos o diagrama de fases do modelo de Ising, com intera??es feromagn?ticas e antiferromagn?ticas, emuma rede bidimensional inomog?nea caracterizada por duas constantes de troca (J1 e J2), a qual permite interpolar cont?nuamente as redes quadrada (J2 = 0) e triangular (J2 = J1) uniformes. Utilizando o m?todo de simula??o de Monte Carlo, atrav?s da din?mica deMetropolis aplicada de forma seq?encial, calculamos a magnetiza??o e a susceptibilidade para redes de diversos tamanhos e aplicando t?cnicas de escalonamento para tamanhos finitos obtemos, atrav?s de um colapso de dados, valores para a temperatura cr?tica e expoentes cr?ticos em fun??o do par?metro α = J2 J1, contido no intervalo [0, 1]. No caso ferromagn?tico observamos que a temperatura cr?tica Tc cresce linearmente com α em todo o intervalo de varia??o deste par?metro, enquanto no caso antiferromagn?tico, o comportamento linear (decrescente) de Tc ? observado somente para pequenos valores de α; no intervalo [0.6, 1], onde os efeitos de frustra??o s?o mais pronunciados, a temperatura cr?tica sofre uma redu??o mais significativa, possivelmente n?o linear, para seu valor limite Tc = 0, que corresponde ? rede triangular homog?nea, antiferromagn?tica, completamente frustrada.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work a basic immigration process was investigated which starts with a single colony with a single individual at the origin of a homogeneous tree with the other empty vertices. The process colonies are established at the vertices of the graph and each one grows during a random time, according to a process of general counting until a disaster that annihilates part of the population occurs. After the collapse a random amount of individuals survives and attempts to establish, in a independent manner, new colonies in a neighboring vertices. After a time these formed colonies also suffer catastrophes and the process is repeated. It is important to emphasize that the time until the disaster of each colony is independent of the others. Here this general process was studied under two methods, Poisson growth with geometric catastrophe and Yule growth with binomial catastrophe. That is, in each colony the population grows following a Poisson (or Yule), process during a random time, considered here exponential, and soon after that time its size is reduced according to the geometric (or binomial) law. Conditions were analyzed in the set of parameters so that these processes survived and limits were established that were relevant for the probability of survival, the number of colonies generated during the process and the range of the colonies in relation to the initial point.
Neste trabalho foi investigado um processo básico de imigração o qual é iniciado com uma única colônia com um único indivíduo na origem de uma árvore homogênea com os demais vértices vazios. As colônias do processo se estabelecem nos vértices do grafo e cada uma cresce durante um tempo aleatório, de acordo com um processo de contagem geral até ocorrer um desastre que aniquila parte da população. Após o colapso uma quantidade aleatória de indivíduos sobrevive e tenta estabelecer, de forma independente, novas colônias em vértices vizinhos. Depois de um tempo essas colônias formadas também sofrem catástrofes e o processo se repete. É importante enfatizar que o tempo até o desastre de cada colônia independe do das demais. Aqui esse processo geral foi estudado sujeito a dois métodos, crescimento de Poisson com catástrofe geométrica e crescimento de Yule com catástrofe binomial. Ou seja, em cada colônia a população cresce seguindo um processo de Poisson (ou Yule), durante um tempo aleatório, considerado aqui exponencial, e logo após esse tempo seu tamanho é reduzido de acordo com a lei geométrica (ou binomial). Foram analisadas condições no conjunto de parâmetros para que esses processos sobrevivam e foram estabelecidos limites relevantes para a probabilidade de sobrevivência, o número de colônias geradas durante o processo e o alcance das colônias em relação ao ponto inicial.