Dissertations / Theses on the topic 'Collapse'

Through large sculptural works that are often caricatures of representational objects, my work explores the complicated moments and tangled histories of childhood Jewish schooling in Winnipeg and travels to Israel and Palestine as an adult. My thesis exhibition Collapse, as well as most of my graduate work, examines my investigation through manmade constructions that control and restrict or unite and connect the movement of others. Sculptures about a destroyed bridge’s imagined longing for exotic places, a giant onion serving as a resuscitation mechanism against tear gas or a construction crane to Armageddon are some examples of work that explore the poetry I find in dichotomies, and serve as a series of recollections that negotiate experiences beyond full understanding.

This project is an active exploration of subjectivities through the medium of weaving. In a narrative illustrated with woven works, the emotional trajectory of this person of mixed cultural background through Swedish society is described. First, the work is contextualized in terms of the larger politico-cultural-discursive context, entitled the outside. It is then positioned in terms of the individual context, the inside, largely dramatized as the developments in the art of western tapestry in the past century. This culminates in the final works, three of which are presented in the final exhibition. They are entitled monads, the etymology of which, in Greek, relates to the words one, alone, or singularity. Each is a conceptual microcosm proposing a different light distribution scheme. They are imprints of alternative actualizing tendencies. There could only be one; at the end of the experiment, Schrodinger’s cat is either dead or alive. The collapse involves the very structure of the ground, and is therefore embedded directly into the weave structure. But remember, each act of observation is an irreversible disturbance to the system. In the interpretation of the primary emanation arises difference, but in which direction will the pendulum swing, and on what forces does its motion hinge? Do subjectivities follow the locality assumption? Do you produce subjectivities or do they produce you?

This dissertation examines the collapse of masonry structures in response to large support displacements and horizontal ground accelerations. There are two main classes of masonry structure: arches that thrust, and supporting elements, such as walls and buttresses, which resist the thrust. This dissertation analyses the safety of arches and buttresses and identifies the resulting collapse mechanisms due to support displacements or horizontal accelerations. In particular, this research investigates the stability of a masonry arch supported on buttresses and the conditions necessary for collapse to occur. Engineers are frequently asked to determine the safety of masonry structures that have been severely distorted over the years, often due to subsidence or other long-term movements in the foundations, and this dissertation provides guidance in the assessment of such structures. The resistance of masonry buttresses to high-level horizontal loads is examined. In the case of failure due to overturning, a fracture will develop in the masonry, significantly reducing the resistance of the buttress. The capacity is further reduced by outward leaning of the buttresses, a common source of distress for masonry structures due to movements in the supporting foundations. Based on these considerations, new measures of safety are proposed for buttresses under horizontal loading. Outward leaning of the buttresses increases the span of the arch or vault. Spreading supports will cause large deformations in the arch, which increase the horizontal thrust of the arch and may lead to collapse. In addition, lateral ground accelerations can cause the collapse of arches. The influence of seismic action can be approximated to first order by equivalent static analysis to determine the initial collapse mechanism. These problems are analysed for circular masonry arches, and the collapse conditions are identified for various geometries. The findings are combined to investigate the stability of the masonry arch supported on buttresses. The safety of the system is examined by studying the influence of imposed displacements. As the buttresses lean, the thrust of the vault increases and the resistance of the buttress decreases. The collapse mechanisms are identified for both the static case of leaning buttresses and the dynamic case of horizontal acceleration. This analysis illustrates that the arch will collapse and the buttresses will remain standing in most cases. Based on these considerations, new methods are proposed for assessing the safety of masonry structures and determining the influence of future movements on the stability of existing masonry structures.

The thesis is concerned with the modelling of urinary motion during bladder collapse and is mathematically based. The bladder model as a collapsing vessel is developed as a step towards complementing use of nomograms. Urine motion inside is taken as unsteady flow of incompressible fluid, while the dimensions and collapse rate of the vessel are prescribed using data which is close to realistic biological values. Evolutions of velocities, volume ow rates and effects of the collapse rate are examined. An introduction is made which includes lower urinary tract urodynamics as well as the unique feature that the bladder changes shape and size substantially compared with other vessels. An investigation of simple two-dimensional shapes takes place in chapter two, along with limiting cases for thin vessels. Chapter three analyses simple axisymmetric shapes especially the sphere because of its relevance in addition to its fundamental nature. Development of a numerical scheme is addressed in the next chapter to tackle more complex shapes through the boundary element method and an iterative finite difference scheme with emphasis on flexibility of approach. An extension to more advanced structures of the vessel is constructed in chapter five by means of a concise boundary condition and shape definition. Chapter six takes the work a step further as the approach is applied to axisymmetric configurations. While in an appendix, an extension to implement full viscous effects is then inspected. Finally, further work is discussed in the conclusion.

A numerical approach to including electromagnetism with general relativity is developed using GRAXI as a starting point. We develop a mathematical model describing electromagnetism coupled to a scalar field in an evolving axisymmetric spacetime. As there are numerous formulations of electromagnetism, we evalute different formulations in a limited flat space case. The full curved space system is then developed, using the flat case as a guide to implementing electromagnetism. This model is then implemented using GRAXI as a code base.

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

This Thesis is focused on a photometric and spectroscopic study of four Type IIn supernovae (i.e. SN 20 06gy, 2007bt, 2007bw and 2008fz), which are among the brightest supernovae (SNe) ever detected. They belong to the sample of overluminous or Very Luminous SuperNovae (VLSNe) which currently includes other 3-4 well studied events. Their absolute luminosity at maximum, MV < -20 is much higher than any other previous supernovae, either core-collapse and or thermonuclear. Their huge brightness (> 10^(51)erg) are emitted in the first »200 days) link these events to massive or supermassive progenitors, which experi- enced extreme mass-losses during their last stages of evolution. However, other explosion mechanisms or sources of energy are being investigated; the debate on their nature is still open. The first object discussed in this Thesis is SN 2006gy, which is one the most debated supernovae ever. Contrary to typical IIn SNe, this event did dot show any strong x-rays or radio emission near the epoch of maximum. This has lead to consider other feasible non-standard sources of energy beyond interaction. In this thesis, the evolution of multiband light curves, the pseudo-bolometric (BVRI) light curve and an extended spectral sequence are presented and used to derive constraints on the origin and evolution of the nature of the SN. Its light curve is characterized by a broad, bright (MR = -21.7 at about 70 days) peak, followed by a rapid luminosity fading which turns into a slower decline by day 180. At late phases (> 237 days), because of the large lu- minosity drop (> 3 mag), only upper visibility limits are obtained in the B, R and I bands. In the near-infrared, two K-band detections on days 411 and 510 possibly indicate dust formation or IR echoes scenarios. At all epochs the spectra are characterized a multicomponent Halpha profile, without any P-Cygni. By means of a semi-analytical code, the light curve in the first 170 days is found to be consistent with the explosion of a compact progenitor (R (6 -8 x 10^(12) cm, Mej =5 -14Msol), whose ejecta collided with massive (6 - 10Msol¯), opaque clumps of previously ejected material. These clumps do not completely obscure the SN photosphere, so that at its peak the luminosity is due both to the decay of 56Ni and to interaction with the circumstellar medium (CSM). After 170 days spectroscopic and photometric similarities are found between SN 2006gy and bright, interaction-dominated SNe (e.g. SN 1997cy, SN 1999E and SN 2002ic). This suggests that ejecta-CSM interaction plays a key role in SN 2006gy about 6 to 8 months after maximum, sustaining the late-time-light curve. Alternatively, the late luminosity may be related to the radioactive decay of 3Msol of 56Ni. In this scenario, a supermassive star is not required to explain the observational data, nor is an extra-ordinarily large explosion energy. For the SNe 2007bt, 2007bw and 2008fz UBVRI light curves and an extended spectral sequence are also presented. Analogies and differences are highlighted, both among each other and with respect to the sample of VLSNe from the literature. Photometrically, it is shown that the light curves of SNe 2007bt and 2007bw are substantially dfferent from that of SN 2008fz, evolving more slowly, being redder at the earlier phases and decaying with a rate consistent with that pre- dicted by the radioactive decay of 56Co. On the contrary, the photometric evolution of SN 2008fz is reminiscent to the light curves of IIL SNe, showing a short peak followed by a steep decline. Spectroscopically the three events are characterized by high-velocity (up to 12000km/s), slowly-decelerating emission lines. The spectra of the SNe 2007bt and 2007bw are dominated by Balmer lines, overimposed on a relatively °at continuum (TBB = 6000 ¡ 7000 K); an asymmetry in the early profile of Halpha is observed, slowly disappearing with time. Measurements of the narrow components of Halpha in SN 2007bt indicate CSM speed of 320 km/s , which are only consistent with the winds surrounding luminous blue variable (LBV) stars. The early spectra of SN 2008fz are found to be similar to SN 2006gy; however, they show higher temperatures (TBB=14000 K) and a more rapid evolution. For the three events, the energetic, luminosity, initial radius (> 10^(15)cm) and the kinematic derived from the analysis of the light curves and spectra could be reproduced by the conversion of kinetic energy into radiation by a clumpy CSM which is hit by the energetic SN ejecta, similarly to what was proposed for SN 2006gy. For SNe 2007bt and 2007bw the asymmetry in the Halpha line can be explained if a massive (>10 Msol) clumpy CSM lies face-on in the direction of the observer. The asymmetry in the CSM distribution around the star could be due by a binarity fefect in the progenitor system, or asymmetric mass ejection of a single star. For SN 2008fz the rapid expansion of the black-body radius favor a less massive CSM ( 1Msol), which is efficiently warmed up and accelerated by the high-velocity SN ejecta. Because of the relatively small mass in the CSM/shell, the photon diffusion time is smaller than that calculated for SN 2006gy, and the radiated energy plummets rapidly as the light curve. As for the case of SN 2006gy, these scenarios have the advantage that they do not involve any exotic explosion mechanism for these VLSNe. However, other scenarios could be consistent with their photometric evolution. Among these, the possibility of a pair-instability explosion cannot be excluded. This and other likely hypothesis proposed by other authors are discussed.
Questa Tesi si incentra sullo studio fotometrico e spettroscopico di quattro su pernovae (SNe) di tipo IIn (cioµe SN 2006gy, 2007bt, 2007bw e 2008fz), che sono tra le supernovae più brillanti mai scoperte. Infatti appartengono alla classe delle SNe iperluminose o Very Luminous SuperNovae (VLSNe, supernovae molto brillanti), che al momento include altri 3-4 oggetti ben studiati. La loro luminosità assoluta all'epoca del massimo, MV < -20, è superiore rispetto a qualsiasi altro evento, sia di natura termonucleare che di collasso del core. L'enorme luminosità emessa (> 10^(51)erg nei primi 200 giorni) associa questi eventi a progenitori massicci o supermassicci, che hanno subito fenomeni di perdita di massa estremi durante le loro fasi evolutive finali. Comunque, al momento si stanno studiando anche altri meccanismi o possibili fonti di energia, e il dibattito sulla natura di questi eventi è tuttora aperto. Il primo oggetto discusso è la SN 2006gy, che è una delle supernovae più dibattute in assoluto. Contrariamente alle tipiche IIn, essa non mostrava alcuna emissione X o radio all'epoca del massimo di luminosità. Questo ha portato a considerare altre possibili sorgenti di energia oltre all'interazione. In questa Tesi, l'evoluzione delle curve di luce multibanda, la curva di luce pseudo-bolometrica e una sequenza di spettri vengono studiati per ricavare delle infor- mazioni sull'evoluzione e sulla natura della supernova e del progenitore. La curva di luce µe caratterizzata da un picco ampio e luminoso (MR = -21.7 a circa 70 giorni), seguito da un declino di luminosità veloce, il quale si assesta su un declino piµu lento, a circa 180 giorni. A fasi avanzate (>237 giorni), a causa del forte indebolimento della luminosità (>3 mag) vengono ricavati solo dei limiti ottici nelle bande B, R ed I. Nel vicino infrarosso, due detection nella banda K' indicano una possibile presenza di regioni di formazione di polvere, o eventualmente di echi infrarossi. A tutte le epoche gli spettri sono caratterizzati dalla presenza di pro¯li di righe a multi-componente, senza però alcun pro¯lo P-Cygni. Tramite un codice semi-analitico si trova che la curva di luce nei primi 170 giorni è consistente con l'esplosione di un progenitore compatto (R = 6-8 x 10^(12)cm, Mej = 5-14Msol), le cui ejecta collidono con dei clumps massicci (6-10 Msol) e opachi di materiale espulso precedentemente. Tali clumps non oscurano completamente la fotosfera della supernova, cosicché all'epoca del picco la luminosità è dovuta sia al decadimento radioattivo del 56Ni che all'interazione con il mezzo circumstellare. Vengono inoltre evidenziate, a partire da circa 170 giorni, delle analogie fotometriche e spettroscopiche tra la SN 2006gy e un gruppo di supernovae interagenti (cioè SN 1997cy, 1999E e 2002ic). Ciò suggerisce che l'interazione tra ejecta e CSM gioca un ruolo importante anche nella SN 2006gy a circa 6-8 mesi dal massimo, sostenendo la curva di luce a fasi avanzate. In alternativa, la luminositµa a queste fasi potrebbe essere dovuta al decadimento radioattivo di 3Msol di 56Ni. Questo scenario non richiede la presenza di una stella supermassiccia o di un'energia straordinariamente grande per spiegare i dati osservativi. Anche per le supernovae 2007bt, 2007bw e 2008fz vengono presentate delle curve di luce UBVRI e una sequenza di spettri estesa. Vengono messe in luce analogie e differenze tra tali supernovae e tra le VLSNe in letteratura. Dal punto di vista fotometrico si mostra che le curve di luce delle SNe 2007bt e 2007bw differiscono sostanzialmente da quella della SN 2008fz, poiché evolvono più lentamente, sono piµu rosse a fasi iniziali e decadono ad un tasso consistente con quello predetto dal decadimento del 56Co. Spettroscopicamente i tre eventi sono caratterizzati da righe di emissione ad alte velocità, ¯fino a 12000 km/s . Gli spettri delle supernovae 2007bt e 2007bw sono dominati dalle righe di Balmer su un continuo relativamente piatto (TBB = 6000-¡ 7000 K). Inoltre viene osservata un'asimmetria nel profilo iniziale di Halpha, che però si indebolisce col tempo. Dalla misura della componente strette di Halpha nella SN 2007bt si ricavano velocità di 320 km/s , le quali sono consistenti solo con i venti di stelle LBV (luminose, blu, variabili). Si trova inoltre che i primi spettri della SN 2008fz sono consistenti con quelli della SN 2006gy; tuttavia, essi indicano temperature maggiori (TBB = 14000 K) ed un'espansione piµu rapida. Per i tre eventi, l'energia in gioco, la luminositµa, il raggio iniziale (> 10^(15)cm) e la cinematica derivati dall'analisi delle curve di luce e degli spettri potrebbe essere riprodotta dalla conversione di energia cinetica in radiazione da parte di un mezzo circumstellare ricco di clumps, il quale viene raggiunto dalle ejecta energetiche della supernova, similmente a quanto supposto per SN 2006gy. Per le SNe 2007bt e 2007bw l'asimmetria del pro¯lo di Halpha può essere spie- gata se un mezzo massiccio (>10 Msol ) ricco di clumps si trova esattamente davanti all'osservatore, perpendicolarmente alla linea di vista. L'asimmetria nella distribuzione del mezzo circumstellare potrebbe essere dovuta ad effetti di binarietà del sistema del progenitore, o ad espulsioni di materiale asimmetriche in una stella singola. Per la SN 2008fz la rapida espansione del raggio iniziale di corpo nero tende a favorire un mezzo meno massiccio (> 10Msol), il quale viene riscaldato ed accelerato efficientemente dalle ejecta ad alta velocità. A causa della massa relativamente piccola del mezzo, il tempo di diffusione dei fotoni inferiore di quanto calcolato per la SN 2006gy, cosicché l'energia radiativa diminuisce rapidamente, come la curva di luce. Come nel caso della SN 2006gy, il vantaggio di questi scenari è che non involvono alcun meccanismo di esplosione esotico. Tuttavia, la loro evoluzione fotometrica può essere consistente anche con altri scenari. Tra questi, anche l'esplosione di una supernova di instabilità di coppia non può essere esclusa. Questi ed altri scenari vengono discussi nel capitolo conclusivo.

This thesis is organized as follows: In chapter 1 the theory of a massless scalar field in curved spacetime is introduced. Furthermore the Bogolubov transformation are discussed. In chapter 2 the Hawking effect is derived with the necessary approximations. Then it is briefly mentioned the problem of the information loss paradox In chapter 3 the contribution of the Hawking radiation to the bi-dimensional stress energy tensor is analyzed. In chapter 4 a generic model of gravitational collapse is analyzed with emphasis on the quantum effects. Then we restrict to the case of the collapse of a thin shell, and the accuracy of the Unruh state approximation is examined. In chapter 5 the proposals that the emission of pre-Hawking radiation could prevent the formation of an event horizon for a collapsing object are analyzed. In chapter 6 the arguments which aim to disprove the possibility that pre-Hawking radiation could prevent the formation of a black hole are discussed. Then is questioned the existence of pre-Hawking radiation.

This thesis constitutes a numerical study concerning the dynamics of an inviscid fluid subject to Newtonian gravity. Type-II critical phenomena has been previously measured in gravitational collapse simulations of isothermal-gas-spheres in Newtonian gravity. Our first objective was to extend this work by applying the more general polytropic-gas equation-of-state to the spherically symmetric fluid. We showed that under generic conditions of critical collapse, the polytropic gas allows for scale-invariant solutions. These solutions display self-similarity of the first kind with non-linear scaling between the space and time variables. One of these solutions was identified as the critical solution in critical collapse simulations. Such solution was found to have a single unstable mode with a Lyapunov exponent whose value depends on the polytropic index (Γ) from the equation of state. We argued that this behavior constitutes evidence of type-II critical phenomena with a transition from type-II to type-I behavior occurring at Γ ≥ 6/5. Thus, the polytropic gas exhibits both types of critical behavior. These phenomena was investigated dynamically and also from perturbation analysis. In the second phase of the project we extended the hydrodynamic model to treat axi-symmetric gravitational collapse. This allowed us to study the effect of angular momentum on the critical solution. As previously predicted, infinitesimal initial rotation introduces a non-spherical, unstable axial mode into the dynamics. The measured scaling behavior of the specific angular momentum of the collapsed core agrees with the predicted growth rate (Lyapunov exponent) of the axial perturbation. This two-mode linear regime modifies the scaling laws via the introduction of universal functions that depend on the two-parameter family of initial data. The predicted universality of these functions was confirmed through careful measurements of the collapsed mass and its angular momentum near the collapse threshold. A two-parameter space survey reveals a universal behavior of the order-parameters, with no mass-gap even in the presence of finite initial rotation. The behavior changes slightly beyond some initial rotation threshold. The results then, can be interpreted as an intermediate convergence to a non-spherical self-similar critical solution with a single unstable mode.
Science, Faculty of
Physics and Astronomy, Department of
Graduate

In the first part of this thesis, we solve the coupled Einstein-Vlasov system in spherical symmetry using direct numerical integration of the Vlasov equation in phase space. Focusing on the case of massless particles we study critical phenomena in the model, finding strong evidence for generic type I behaviour at the black hole threshold that parallels what has previously been observed in the massive sector. For differing families of initial data we find distinct critical solutions, so there is no universality of the critical configuration itself. However we find indications of at least a weak universality in the lifetime scaling exponent, which is yet to be understood. Additionally, we clarify the role that angular momentum plays in the critical behaviour in the massless case. The second part focuses on type II critical collapse. Using the critical collapse of a massless scalar field in spherical symmetry as a test case, we study a generalization of the BSSN formulation due to Brown that is suited for use with curvilinear coordinates. We adopt standard dynamical gauge choices, including 1+log slicing and a shift that is either zero or evolved by a Gamma-driver condition. With both choices of shift we are able to evolve sufficiently close to the black hole threshold to 1) unambiguously identify the discrete self-similarity of the critical solution, 2) determine an echoing exponent consistent with previous calculations, and 3) measure a mass scaling exponent, also in accord with prior computations. Our results can be viewed as an encouraging first step towards the use of hyperbolic formulations in more generic type II scenarios, including the as yet unresolved problem of critical collapse of axisymmetric gravitational waves. In the last part, we present simulations of nonlinear evolutions of pure gravity waves. We describe a new G-BSSN code in axial symmetry that is capable of evolving a pure vacuum content in a strong gravity regime for both Teukolsky and Brill initial data. We provide strong evidence for the accuracy of the numerical solver. Our results suggest that the G-BSSN is promising for type II critical phenomena studies.
Science, Faculty of
Physics and Astronomy, Department of
Graduate

The first stars, galaxies and black holes in the universe produced large quantities of ionising UV radiation; forming H II regions in the neutral gas before the Epoch of Reionisation (EoR). These ionisation fronts will have come into contact with overdensities in the surrounding Intergalactic Medium (IGM), including haloes which were in the process of collapse. Previous studies have shown that the feedback processes on these secondary haloes can either disrupt the gas, or induce further cooling from the formation of molecular hydrogen. The ionising source will eventually die and create a defunct H II region, which expands into the surrounding neutral IGM. Minihaloes at the edge of these defunct H II regions are particularly susceptible to positive feedback due to not having been photoevaporated like their counterparts further inside the ionised volume. In this thesis, numerical simulations of minihaloes at the edges of H II regions formed by the first luminous objects before the EoR are presented. A methodology of including secondary ionisations from high energy photons is also implemented into the radiation hydrodynamical code ZEUS-RT. The interaction of differing spectral index sources with minihaloes including secondary ionisation is discussed. The secondary ionisations show the greatest effect for hard spectral sources with a large fraction of high energy photons; where a decrease in photoheating and an increase in ionisation rate is found at the outer reaches of the ionisation front (I-front). The increased ionisation rate lowers the optical depth of the gas for subsequent photons, and thus reduces the trapping of I-fronts in high densities found in the minihalo cores. The ratio of the free electron fraction to the temperature in the core of the minihaloes is found to constrain the resulting evolution. A high ratio is correlated with the creation of molecular hydrogen, which can then induce further cooling and the collapse of the system.A large parameter suite of 3780 two-dimensional minihalo models utilising radiative hydrodynamical simulations with 12 species and a coupled reaction network, including H2 cooling, HD cooling, Lyman-Werner radiation and secondary ionisation is performed. The parameter space includes: the spectral index representing different sources such as quasars or galaxies, the mass of the minihaloes from 105 - 106 Mʘ, the redshift of ionisation from z ~ 10 - 30, and other factors which denote the position of the minihalo relative to the boundary of the H II region. Minihaloes with average core densities of n0 = 2 - 10 cm-3 show almost unanimous positive feedback, while the majority of minihaloes under this average density are disrupted. Minihaloes with core densities above this value generally would have collapsed in isolation anyway, but are found to not be delayed by the I-front. The H2 fraction in the minihalo gas is also increased in models with no blowout by factors between 2 - 100 times that of an isolated minihalo. This is especially significant for lower redshift, z ≤ 15, minihaloes. Finally, a parameter suite of larger 106 - 107 Mʘ minihaloes results in the creation of self-gravitating clumps of gas moving out of the dark matter potential. The gas core is compressed by the I-front, enriched with molecular hydrogen, and ejected by the pressure front after the source dies. These "baryon bullets" could be progenitors of primordial globular clusters found in the haloes of galaxies today. Properties such as old stellar populations and the lack of dark matter haloes can be explained by this radiative ejection method. The dynamical nature of these interacting systems and diversity of subsequent evolution suggest that minihaloes less than 108 Mʘ are important in the early formation history of the universe, and in determining the constraining parameters of the EoR. The feedback mechanisms investigated, and secondary ionisation physics, should be included in astrophysical simulations and analytical calculations determining the evolution of the universe at this critical epoch.

The progenitors of core-collapse supernovae are stars with an initial mass greater than about 8M⊙. Understanding the evolution of these stars is necessary to comprehend the evolution and differences between supernovae. We have constructed new and unique opacity tables to increase model accuracy during the latest stages of stellar evolution. We have investigated how initial mass, initial composition and mass loss affects the progenitors and their populations. There are many prescriptions for mass loss. Different research groups use their preferred rates. We have compared 12 different prescriptions and determined which provides the best fit to observations. We use our preferred mass-loss scheme to make suggestions as to the source of the differences between supernova types from our progenitor models. Binary evolution is considered in order to search for low luminosity SN progenitors and progenitor types not possible from single stars. Removal of the hydrogen envelope is more common and we find quite different hydrogen deficient SN progenitors. We discuss the implications of our binary models for ultra-luminous X-ray sources and gamma-ray bursts. We present an estimation of the mass distribution for black holes at various metallicities showing that massive black holes are not formed until very low metallicities. Finally we combine the single star and binary results to determine their relative populations and compare to observations. However it is not possible to draw many firm conclusions because of the uncertainty in observations to date.

Soil collapse is amongst one of the most significant ground related hazards. A collapsible soil, in particular loess, typically has an open-structure and collapse occurs when as a consequence of the addition of water and/or load the particles rearrange to form a more dense fabric. Collapse leads to a suite of problems for buildings and infrastructures built on or in collapsing soil. Treatment to mitigate collapse often involves in densification. However, such approaches have been reported not always effective enough to combat the problem. This stems from a lack of understanding of soils’ geochemistry and structure, the result of which is an oversimplification of complex geotechnical and geological interactions. An important example of such limited knowledge is the increasing evidence of restoration of the collapsing structure upon wetting-drying cycles, which is widely ignored in the current compaction practice. This research aims to first identifying collapse micro-mechanisms in fine-grained soils, examining the contribution of a handful of soil constituents in collapsibility, and finally developing a practical tool for ground engineers to evaluate the efficiency of the current compaction practice for systematically classified fine-grained soils, and to take modified/novel earthwork approaches where the current practice fails to fully remove the collapse risk.

The collapse of buildings over the last century as a result of abnormal loads has renewed interest in the field of structural engineering. Key events such as the disproportionate collapse of the Ronan Point building in London, the collapse of the Alfred Murray Building and the World Trade Centre are structural failures that have triggered more research into progressive collapse. Consequently, new design guidelines around the globe with a prescriptive recommendation for improving structural integrity based on tying force provision have been developed. However, in existing design guidelines and codes throughout the world, there is a lack of a codified modelling technique for progressive collapse. As a result of this limitation, researchers adopt different methods. Generally, during the progressive collapse, structural members experiencing significant displacements and rotations, while the beam-column connections are subjected to large tensile forces not envisaged at the conventional design phase. Hence, this study presents an assessment of the effect of column removal time, the modelling techniques and the susceptibility of simple connections designed to Eurocode 3 Part: 1-8 to progressive collapse. A computationally efficient approach and column removal time for progressive collapse assessment are proposed. The findings show that a braced framed system is likely to exhibit at least 35% progressive collapse when compared with a moment resisting frame system using the joint displacement and rotation criteria. Furthermore, the research shows that the UK tie provision in EN1991-1-7 underestimates the magnitude of the catenary force developed under the progressive collapse scenario. Consequently, the connection is disposed to progressive collapse with the shear force in the column and catenary action in the beam as the critical internal forces. Based on this assessment, five times the tensile force specified in EC3 for tensile force connection design checks is recommended. Shear force in the column and catenary force action in the beam are the internal governing forces that determine the maximum dynamic amplification factor of a simple connection. The work provides evidence that the tie beam-column web connection at the corner column is more critical under progressive collapse scenario as compared with the primary beam. Column web failure in yielding is attributed to the large catenary force developed in the tie beam connected to the web of the column.

The Microelectronics industry has continuously pushed the limit of critical dimensions to sub-20 nm. One of the challenges is pattern collapse, caused by unbalanced capillary forces during the final rinse and drying process. The use of surfactants offers a convenient method to reduce capillary forces but causes another deformation issue. This thesis work focuses on alternative approaches that are compatible with lithographic processes to mitigate pattern collapse. First, an e-beam lithography pattern with a series of varying line and space widths has been specifically designed in order to quantitatively study pattern collapse behavior. This pattern generates increasing stress in the pairs of resist lines as one moves across the pattern array and eventually a sufficiently small space value (critical space, S1c) is reached in each array such that the stress applied to the resist exceeds the critical stress (σc) required for pattern bending and subsequently feature deformation and collapse occurrs. The patterns we designed allow us to qualitatively and quantitatively study pattern collapse and obtain consistent, reproducible results. In the first part of the thesis work, a quick surface crosslink (called a reactive rinse) that involves the strengthening of the resist using crosslinking via carbodiimide chemistry while the resist structures are still in their wet state, has been developed and demonstrated. This technique provides efficient and significant improvement on the pattern collapse issue. In the second part of the thesis work, a triethoxysilane compound, vinyl ether silane (VE), has been successfully synthesized. It can be used to modify the silicon or silicon nitride substrates and form a covalent bond with the resist film instead of manipulating the surface energies using common HMDS. Compared to traditional Hexamethyldisilazane (HMDS) vapor primed surfaces, the implementation of the VE adhesion promoter resulted in a significant improvement in the adhesion and resistance to adhesion based pattern collapse failure in small sub-60 nm resist features. In the third part of the thesis work, the effect of drying rates and drying methods has been systematically studied. SEM analysis and critical stress results showed that fast drying appear to reduce the resist collapse. The line pair orientations in each pattern array with respect to the wafer radius reveal an apparent effect of fluid flow and centrifugal forces on collapse. Finally, a comprehensive pattern collapse model that incorporates adhesion based pattern failure and elastoplastic deformation-based failure, and dimensionally dependent resist modulus properties has been developed. This model provides such an excellent prediction of the experimental data and supports the idea that this level of combined adhesion-failure and elastoplastic-failure based pattern collapse modeling, where one explicitly considers the dimensionally dependent mechanical properties of the resist can be quantitatively predictive and useful for understanding the pattern collapse behavior of polymeric nanostructures.

During the course of development, expression of attractive and inhibitory guidance cues play a pivotal role in the pathfinding decisions of a growing neuron. In addition, injury-induced recapitulation of their expression, particularly inhibitory cues, likely influences the course of axonal regeneration, thus providing a rationale for the intense focus in this area of research. Though significant progress has been made, it remains poorly described what signaling cascades, and in what combination, are involved during inhibitory-cue induced growth cone collapse. Therefore, to further understand why neurons are repelled or inhibited by certain cues, the aim of this thesis is to identify the underlying intracellular mechanisms regulating growth cone collapse induced by inhibitory cues. Using a novel anti-invasive compound called Motuporamine C(MotC), I have characterized in chapter 2 its effects as a regulator of neuronal outgrowth. I found that MotC was a robust stimulator of growth cone collapse leading to a cessation of neurite growth. This was partially mediated through Rho-ROCK signaling, a pathway involved in regulating actin dynamics. Based on this partial response, I hypothesized that other signal transduction pathways were involved. I addressed this in chapter 3 by identifying calcium-activated calpain, a protease well-characterized in playing a role in adhesion regulation, was also activated during MotC-induced growth cone collapse. Furthermore, I show that concurrent inhibition of both Rho-ROCK and calpain pathways are necessary for maximum attenuation of the MotC-mediated collapse response. Since these results were identified using an organic molecule not endogenously expressed in vertebrate organisms, I hypothesized in chapter 4 that similar pathways would be activated in response to a physiological in vivo guidance cue. Using the inhibitory cue Semaphorin 5B (Sema5B), I found in addition to the activation of calpain, the phosphatase calcineurin was also involved in mediating Sema5B-induced growth cone collapse. Moreover, it is the combination of calpain- and calcineurin-mediated pathways that is required for evoking maximal growth cone collapse and that cross-talk between these two effector molecules occurs. These results are of particular interest since previously it was proposed by Gomez and Zheng (2006) that calpain and calcineurin signaling cascades were parallel pathways. Taken together, my findings show that different inhibitory cues activate multiple intracellular pathways that appear to impinge on different aspects of the intracellular machinery regulating motility. The combinatorial activation of these pathways is necessary for mediating maximal growth cone collapsing effects. Moreover, the elucidation of common signaling cascades between inhibitory cues to induce growth cone collapse may eventually provide novel targets for the development of new therapeutic strategies to promote functional recovery following neuronal injury.
Medicine, Faculty of
Graduate

This thesis presents a study of the ultimate strength capacity of two offshore platforms located in the Gulf of Mexico. The objective of the study was to validate existing non-linear finite element models for estimating the loads and strength of offshore platforms.
From August 24 to 26 1992, hurricane Andrew moved through the Gulf of Mexico with sustained winds of 140 miles per hour. Thirty-six major platforms suffered significant damage, of these, ten were completely toppled and twenty-six were leaning significantly or had significant topside damage.
Structures "H" and "K" were bridge-connected platforms, located in the ST151 field of the South Timbalier area of the Gulf of Mexico, platform "H" collapsed during Andrew, while "K" survived undamaged. They were both designed, fabricated, and installed in the early 1960's.
A push-over analysis, using the program USFOS was used to estimate the ultimate strength of the two structures in three direction: end-on, diagonal and broadside.
In the first series of analyses, all the primary members such as legs, vertical and horizontal braces, piles, soil, conductors and deck structure were precisely defined with appropriate finite elements as well as secondary members such as conductors guides barge bumpers. In the second series of analyses it was assumed that there was no horizontal or vertical movements at the level of the mudmat. In the third series of analysis the model used in the first series of analysis was modified by increasing stiffness and resistance of the piles 10 times. Finally a fourth model was investigated in which the soil resistance of the mud-level horizontal members is modelled. (Abstract shortened by UMI.)

This research was designed to investigate possible mechanisms that fires could initiate that might lead to collapse of a tall building of similar design to the WTC Towers. It was not designed to be a forensic study and no initial damage was applied to the structure. The effects of fire on long span, truss based floor systems was investigated both locally and globally using finite element models.

In this thesis, we are concerned with models of explicit wavefunction collapse as a possible solution to the measurement problem of quantum mechanics. We examine the models where collapse is to near-position eigenstates, originally introduced by Ghirardi, Rimini and Weber in 1986, where the wavefunction is spontaneously localized at random times. Subsequent models where some of the problems of the GRW model are solved, are discussed, for both sudden localization and continuous localization processes. We comment briefly on the possible origins of collapse. The consequences of possible wavefunction collapse on the operation of quantum computers are described. Finally, we look at an attempt to describe the collapse process in a Lorentz-invariant manner.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references.
Theory predicts that the approach of catastrophic thresholds in natural systems may result in an increasingly slow recovery from small perturbations, a phenomenon called critical slowing down. In this thesis, we used replicate laboratory populations of the budding yeast Saccharomyces cerevisiae for direct observation of critical slowing down in spatio-temporal dynamics before population collapse. In the first project, we mapped the bifurcation diagram experimentally and found that the populations became more vulnerable to disturbance closer to the tipping point. Fluctuations of population density increased in size and timescale near the tipping point, in agreement with the theory. In the second project, we used spatially extended yeast populations to evaluate early warning signals based on spatio-temporal fluctuations. We found that indicators based on fluctuations increased before collapse of connected populations; however, the magnitude of increase was smaller than that observed in isolated populations, as local variation is reduced by dispersal. Furthermore, we propose a generic indicator based on deterministic spatial patterns, recovery length. In our experiments, recovery length increased substantially before population collapse, suggesting that the spatial scale of recovery can provide a warning signal before tipping points in spatially extended systems. In the third project, we characterized how different environmental drivers influence the dynamics of yeast populations. We compared the performance of early warning signals across multiple deteriorating environments. We found that the varying performance is determined by how a system responds to changes in a specific driver, which can be captured by a relation between stability and resilience. Furthermore, we demonstrated that the positive correlation between stability and resilience, as the essential assumption of indicators based on critical slowing down, can break down when multiple environmental drivers are changed simultaneously.
by Lei Dai.
Ph. D.

In this dissertation, I explore the time-variable rate of star formation, using both numerical and analytic techniques. I discuss the dynamics of collapsing regions, the effect of protostellar jets, and development of software for use in the hydrodynamic code RAMSES. I perform high-resolution adaptive mesh refinement simulations of star formation in self-gravitating turbulently driven gas. I have run simulations including hydrodynamics (HD), and HD with protostellar jet feedback. Accretion begins when the turbulent fluctuations on largescales, near the driving scale, produce a converging flow. I find that the character of the collapse changes at two radii, the disk radius r_d, and the radius r_* where the enclosed gas mass exceeds the stellar mass. This is the first numerical work to show that the density evolves to a fixed attractor, ρ(r, t) → ρ( r), for r_d < r < r_*; mass flows through this structure onto a sporadically gravitationally unstable disk, and from thence onto the star. The total stellar mass M_*(t) ~ (t – t_*)², where (t – t _*)² is the time elapsed since the formation of the first star. This is in agreement with previous numerical and analytic work that suggests a linear rate of star formation. I show that protostellar jets change the normalization of the stellar mass accretion rate, but do not strongly affect the dynamics of star formation in hydrodynamics runs. In particular, M_*(t) ∞ (1 – f _jet)²(t – t_*) ² is the fraction of mass accreted onto the protostar, where f_jet is the fraction ejected by the jet. For typical values of f_jet ~ 0.1 – 0.3 the accretion rate onto the star can be reduced by a factor of two or three. However, I find that jets have only a small effect (of order 25%) on the accretion rate onto the protostellar disk (the "raw" accretion rate). In other words, jets do not affect the dynamics of the infall, but rather simply eject mass before it reaches the star. Finally, I show that the small scale structure—the radial density, velocity, and mass accretion profiles—are very similar in the jet and no-jet cases.

Lateral collapse is a failure mode of wood pallets which most frequently occurs during transportation and handling. The study objective was to develop a simplified procedure for making relative comparisons in the lateral collapse potential of competing pallet designs. A theoretical model was developed to predict the maximum horizontal force a pallet can sustain. A simple equilibrium of forces approach including joint rigidity was used. A lateral load test machine was built which induces and measures the amount of horizontal force required to collapse a pallet. After testing, the model was shown to be accurate when no upper deckboard bending occurred and inaccurate when bending occurred. To account for bending, two multiple regression equations were developed to predict modification factors using a matrix structural analysis program. predicts K-factors for two stringer A closed form solution designs. These K-factors are used to modify the resisting moments generated by the fastened joints. The modified model was shown to slightly overpredict maximum collapse load but did accurately discern differences in relative lateral collapse potential. The ratio of the maximum horizontal load to the vertical load on the pallet provides a means of ranking the potential for lateral collapse. Those designs whose ratios fall between 0.0 and 0.6 are at high risk, from 0.6 but less then 1.0 are at medium risk, and from 1.0 to infinity are at low risk of lateral collapse. These ratios have been calibrated against documented cases of lateral collapse. The factors that influence the lateral collapse potential of a design are stringer aspect ratio, joint characteristics, unit load, and upper deck flexural rigidity.
M.S.

The events of 11 September 2001 have instigated a comprehensive debate among the structural engineering community regarding the performance of tall buildings under extreme loading conditions such as blast, impact or fire. The main issues that have been identified include the dynamic robustness of such buildings, the parameters that could possibly initiate progressive collapse following the extreme event, and the design guidance that needs to be introduced in order for buildings to survive such events and assure life safety of their occupants. Since the structural components of buildings subject to extreme loading events are likely to undergo large inelastic deformations, which can induce excessive ductility demands in the joint regions of the members involved, the behaviour and modelling of joints is discussed in detail. With respect to design recommendations, this thesis proposes a multi-level framework for progressive collapse assessment of building structures subject to sudden column loss, which is the design scenario adopted by most recent guidelines to assess the potential of multi-storey buildings for progressive collapse. The proposed framework offers a rational and practical means for assessing structural robustness at various levels of structural idealisation, it accommodates both simplified and detailed models of the nonlinear structural response, and importantly it moves the debate on structural robustness towards the quantifiable. Application of the new approach is demonstrated with reference to steel-framed composite buildings with partial-strength joints. Furthermore, a methodology is developed, based on the proposed assessment framework for sudden column loss, to consider the impact of floor failure on a lower floor, in order to establish whether this would in fact trigger progressive collapse. Application of this methodology is also illustrated by means of a case study, where consideration is given to a floor grillage system subject to impact of the floor above, and the ability of the impacted floor members to sustain the dynamically induced loads associated with various impact scenarios is thoroughly examined. From the presented application studies, important conclusions are drawn relating to the inherent robustness of steel-framed structures, the factors influencing this robustness, and the adequacy of current regulations for the avoidance of progressive collapse.

A core-collapse supernova (CCSN) is an astronomical explosion that indicates the death of a massive star. The iron core of the star collapses into either a neutron star or a black hole while the rest of the material is expelled at high velocities. Supernovae (SNe) are important for the chemical evolution of the Universe because a large fraction of the heavier elements such as oxygen, silicon, and iron are liberated by CCSN explosions. Another important role of SNe is that the ejected material seed the next generation of stars and planets. From observations, it is clear that a large fraction of all massive stars undergoes SN explosions, but describing how SNe explode has remained a challenge for many decades. The attached papers focus on comparing theoretical predictions with observations, primarily observations of SN 1987A. The compact remnant in SN 1987A has not yet been detected and we have investigated how a compact object can remain hidden in the ejecta (Paper I and II). Because of the high opacity of the metal-rich ejecta, the direct X-ray observations are not very constraining even for potentially favorable viewing angles. However, the combined observations still strongly constrain fallback accretion and put a limit on possible pulsar wind activity. The thermal surface emission from a neutron star is consistent with the observations if our line of sight is dust-obscured, and only marginally consistent otherwise. Future observations provide promising opportunities for detecting the compact object. We have also compared the most recent three-dimensional neutrino-driven SN models that are based on explosion simulations with early X-ray and gamma-ray observations of SN 1987A (Paper III). The models that are designed to match SN 1987A fit the data well, but not all tensions can be explained by choosing a suitable viewing angle. More generally, the asymmetries do not affect the early emission qualitatively and different progenitors of the same class result in similar early emission. We also find that the progenitor metallicity is important for the low-energy X-ray cuto↵. Current instruments should be able to detect this emission from SNe at distances of 3–10 Mpc, which correspond to distances slightly beyond the Local Group.
En kärnkollapssupernova (CCSN) är en astronomisk explosion som indikerar slutet av en massiv stjärnas liv. Stjärnans järnkärna kollapsar antingen till en neutronstjärna eller ett svart hål medan resten av materialet slungas iväg med höga hastigheter. Supernovor (SNe) är viktiga för Universums kemiska utveckling eftersom en stor andel av alla tyngre element såsom syre, kisel, och järn frigörs i CCSN-explosioner. Ytterligare en viktig roll för SNe är att nästa generations stjärnor och planeter bildas av det utkastade materialet. Från observationer är det tydligt att en stor andel av alla massiva stjärnor genomgår SN-explosioner, men att förklara hur SNe exploderar har kvarstått som en utmaning under flera decennier. De bifogade artiklarna fokuserar på att jämföra teoretiska förutsägelser med observationer, primärt observationer av SN 1987A. Det kompakta objektet i SN 1987A har ännu inte blivit detekterat och vi har undersökt hur ett kompakt objekt kan förbli dolt i ejektat (Paper I och II). De direkta röntgenobservationerna är inte så begränsande även längs potentiellt gynsamma siktlinjer på grund av det metallrika ejektats höga opacitet. Däremot begränsar kombinationen av alla observationer starkt ackretion och sätter en gräns för möjlig pulsarvindsaktivitet. Den termiska ytstrålningen från en neutronstjärna är konsistent med observationerna om vår siktlinje är skymd av stoft, och bara marginellt konsistent annars. Framtida observationer utgör lovande möjligheter för att detektera det kompakta objektet. Vi har också jämfört de senaste tredimensionella neutrinodrivna SN-modellerna, som är baserade på explosionssimuleringar, med tidiga röntgen- och gamma-observationer av SN 1987A (Paper III). SN 1987A-modellerna passar datan väl, men alla diskrepanser kan inte förklaras av ett lämpligt val av observationsvinkel. Generellt så påverkar inte asymmetrierna den tidiga emissionen kvalitativt och olika föregångarstjärnor av samma kategori resulterar i likartad strålning. Vi finner också att föregångarstjärnans metallisitet är viktig för egenskaperna av lågenergiröntgenstrålningen. Befintliga instrument borde kunna detektera denna emission på 3--10 Mpc, vilket motsvarar avstånd lite bortom den Lokala galaxhopen.

Examintor: Professor Mark PearceQC 20190121

The work of this PhD investigates spontaneous collapse models, which are a proposed modification of quantum mechanics and their consistency with special relativity. Since soon after they were first proposed there have been many attempts to construct a relativistic collapse model, but currently there is not a satisfactory model. This thesis considers what it means for an irreversible dynamics to be consistent with special relativity and reviews the existing proposals and their issues. The key results are a demonstration of why a relativistic point-like collapse model is not possible and that a relativistic generalisation of one of the most studied collapse models, Continuous Spontaneous Localisation is not possible.

In general relativity, critical collapse is a phenomenon for which in dependence of the choice of some parameter of initial data, the resulting spacetimes can be regular or singular and so the evolution could finish in dispersal or in a formation of a black hole/naked singularity, respectively. Moreover, in the second case, it was found the power-law scale for the black hole masses. These phenomena in gravitational collapse were first found by Choptuik in numerical simulation of spherically symmetric massless scalar field. In the present thesis the study of these example have been extended to a wider class of models. The collapsing time and the bouncing time, in order to understand if the collapse or the bouncing happens in a finite time, have been analysed and we have proved that it is so. Moreover we have observed that also at the end of supercritical evolution the singularity is naked and so the singularity is not covered.

Turbulence, magnetic fields and gravity driven flows are important for the formation of new stars. Although magnetic fields have been proven to be important in the formation of stars, only a few works have been done combining magnetic field and kinematic information. Such studies are important to analyze both gravity and gas dynamics and be able to compare them with the magnetic field. In this thesis we will combine dust polarization studies with kinematic analysis towards different star-forming regions. We aim to study the physical properties at core scales (<0.1 pc) from molecular line and dust emission, and study the role of the magnetic field in their dynamic evolution. For this, we will use millimeter and submillimeter observational data taken towards low- and high- mass star-forming regions in different environments and evolutionary states. The first project is the study of the physical, chemical and magnetic properties of the pre-stellar core FeSt1-457 in the Pipe nebula. We studied the emission of the molecular line N2H+(1-0) which is a good tracer of dense gas and therefore describes well the structure of the core. In addition, we detected more than 15 molecular lines and found a clear chemical spatial differentiation for molecules with nitrogen, oxygen and sulfur. Using the ARTIST radiative transfer code (Brinch & Hogerheijde 2010, Padovani et al., 2011, 2012, Jørgensen et al., 2014), we simulated the emission of the different molecules detected and estimated their abundance. In addition, we estimated the magnetic field properties of the core (using the Chandrasekhar-Fermi approximation) from polarization data previously obtained by Alves et al., (2014). Finally, we found interesting correlations between the polarization properties and the chemistry in the region. The second project is the study of a high-mass star-forming region called NGC6334V. NGC6334V is in a more advanced evolutionary state and in an environment surrounded by other massive star-forming regions. During the project we studied the magnetic field from the polarized emission of the dust and also the kinematics of the gas from the molecular line emission of the different tracers of dense gas. From the molecular emission of the gas tracing the envelope of the dense core, we see two different velocity structures separated by 2 km/s and converging towards the potential well in the region. In addition, the magnetic field also presents a bimodal pattern following the distribution of the two velocity structures. Finally, we compared the observational results with 3D magnetohydrodynamic simulations of star-forming regions dominated by gravity. The last project is the study of a lower-mass star-forming region, L1287. From the data obtained with the SMA, the dust continuum structure shows six main dense cores with masses between ~0.4 and 4 solar masses. The dense gas tracer DCN(3-2) shows two velocity structures separated by 2-3 km/s, converging towards the highest-density region, the young stellar object IRAS00338+6312, in a similar scenario to the one observed in the higher-mass case of NGC6334V. Finally, the studies of the pre-stellar core FeSt1-457 and the massive region NGC6334V, show how the magnetic field has been overcome by gravity and is not enough to avoid the gravitational collapse. In addition, NGC6334V and the lower- mass region L1287 present very similar scenarios with the material converging from large scales (~0.1 pc) to the potential wells of both regions at smaller scales (~0.02 pc) through two dense gas flows separated by 2-3 km/s. In a similar scenario, FeSt1-457 is located just in the region where two dense gas structures separated by 3 km/s appear to converge.
La turbulencia, el campo magnético y la gravedad juegan un papel importante en la formación estelar. Aunque se ha mostrado que el campo magnético es importante, sólo se han llevado a cabo un número limitado de trabajos combinando el estudio del campo magnético y la cinemática del gas. Este tipo de trabajos son esenciales para estudiar la gravedad y la dinámica del gas y poder compararlas con el campo magnético a las mismas escalas espaciales. En este trabajo combinamos estudios de polarización a partir de la emisión del polvo, con el análisis de la cinemática del gas en diferentes regiones de formación estelar. El objetivo es estudiar las propiedades físicas a escalas de núcleos densos (<0.1 pc) a partir de la emisión molecular y del polvo, y estudiar el papel del campo magnético en la evolución dinámica de las regiones. Para ello hemos utilizado datos observacionales milimétricos y submilimétricos. Los estudios se han realizado en 3 regiones de formación estelar. El núcleo pre- estelar FeSt 1-457 localizado en un entorno aislado y muy magnetizado en la nebulosa de la Pipa. NGC 6334 V, una región de mayor masa, en un estado evolutivo más avanzado y en un entorno rodeado de otras regiones de formación estelar masiva. Y L1287, una región menos masiva pero con características similares a NGC 6334 V, con presencia de gas de alta velocidad y fuentes centimétricas e infrarrojas. Los estudios del núcleo pre-estelar FeSt 1-457 y la región de formación estelar de alta masa NGC 6334 V, muestran como el campo magnético ha sido superado por la gravedad y no es suficiente para evitar el colapso gravitatorio. Además NGC 6334 V y la región de menor masa L1287 presentan escenarios muy similares, con el material convergiendo desde escalas grandes hacia los pozos de potencial de ambas regiones a escalas más pequeñas a través de flujos de gas denso separados por 2-3 km/s. En un escenario parecido, FeSt 1-457 se encuentra justo en la zona donde parecen converger dos flujos de gas denso separados por 3 km/s.