This thesis explores topics related to the formation and development of the large-scale structure in the Universe, with the focus being to compute properties of the evolved non-linear density field in an approximate way. The first three chapters form an introduction: Chapter 1 contains the theoretical basis of modern cosmology, Chapter 2 discusses the role of N-body simulations in the study of structure formation and Chapter 3 considers the phenomenological halo model. In Chapter 4 a novel method of computing the matter power spectrum is developed. This method uses the halo model directly to make accurate predictions for the matter spectrum. This is achieved by fitting parameters of the model to spectra from accurate simulations. The final predictions are good to 5% up to k = 10 hMpc-1 across a range of cosmological models at z = 0, however accuracy degrades at higher redshift and at quasi-linear scales. Chapter 5 is dedicated to a new method of rescaling a halo catalogue that has previously been generated from a simulation of a specific cosmological model to a different model; a gross rescaling of the simulation box size and redshift label takes place, then individual halo positions are modified in accord with the large scale displacement field and their internal structure is altered. The final power spectrum of haloes can be matched at the 5% level up to k = 1 hMpc-1, as can the spectrum of particles within haloes reconstituted directly from the rescaled catalogues. Chapter 6 applies the methods of the previous two chapters to modified gravity models. This is done in as general a way possible but tests are restricted to f(R) type models, which have a scale-dependent linear growth rate as well as having 'chameleon screening' - by which modifications to gravity are screened within some haloes. Taking these effects into account leads to predictions of the matter spectrum at the 5% level and rescaled halo distributions that are accurate to 5% in both real and redshift space. For the spectrum of halo particles it is demonstrated that accurate results may be obtained by taking the enhanced gravity in some haloes into account.

abstract: Fluctuations with a power spectral density depending on frequency as $1/f^\alpha$ ($0<\alpha<2$) are found in a wide class of systems. The number of systems exhibiting $1/f$ noise means it has far-reaching practical implications; it also suggests a possibly universal explanation, or at least a set of shared properties. Given this diversity, there are numerous models of $1/f$ noise. In this dissertation, I summarize my research into models based on linking the characteristic times of fluctuations of a quantity to its multiplicity of states. With this condition satisfied, I show that a quantity will undergo $1/f$ fluctuations and exhibit associated properties, such as slow dynamics, divergence of time scales, and ergodicity breaking. I propose that multiplicity-dependent characteristic times come about when a system shares a constant, maximized amount of entropy with a finite bath. This may be the case when systems are imperfectly coupled to their thermal environment and the exchange of conserved quantities is mediated through their local environment. To demonstrate the effects of multiplicity-dependent characteristic times, I present numerical simulations of two models. The first consists of non-interacting spins in $0$-field coupled to an explicit finite bath. This model has the advantage of being degenerate, so that its multiplicity alone determines the dynamics. Fluctuations of the alignment of this model will be compared to voltage fluctuations across a mesoscopic metal-insulator-metal junction. The second model consists of classical, interacting Heisenberg spins with a dynamic constraint that slows fluctuations according to the multiplicity of the system's alignment. Fluctuations in one component of the alignment will be compared to the flux noise in superconducting quantum interference devices (SQUIDs). Finally, I will compare both of these models to each other and some of the most popular models of $1/f$ noise, including those based on a superposition of exponential relaxation processes and those based on power law renewal processes. / Dissertation/Thesis / Doctoral Dissertation Physics 2018

Higher education professionals are always seeking new and better ways to prepare students for life after college—a goal that requires not only providing knowledge and experience in their chosen field, but also helping them stay engaged in the process. Recently, computer based simulations have magnified role playing and case study techniques that have been used in classrooms for many years. These simulations have found great success in many settings, including engineering, business, and medicine, but there have been very few computer simulations designed for writing classes. Given that some of the greatest challenges in such classes are teaching students to respond to a context, write to an audience, and stay engaged in the process, simulations have great potential to improve pedagogy in writing classes by providing a more authentic and engaging context. In this pilot study of a computer simulation designed for technical writing classes, we examined how the simulation affected these factors (authenticity and engagement). We combined qualitative and quantitative methods, doing surveys in three classes (the class using the simulation and two classes with other pedagogies) and focus groups with the simulation class. While the results of the survey were rather inconclusive, the surveys and focus groups combined taught us two main lessons: (1) the simulation needs to be believable to be effective—making it too much like a game can backfire with some students, and (2) students remain more interested when the simulation is complex and leaves them some autonomy concerning what happens. While not necessarily groundbreaking, knowing what worked and what didn’t in our simulation can provide valuable insights for future simulation designers.

In finance, various stochastic models have been used to describe the price movements of financial instruments. After Merton's [38] seminal work, several jump diffusion models for option pricing and risk management have been proposed. In this dissertation, we add alpha-stable Levy motion to the process related to dynamics of log-returns in the Black-Scholes model where the volatility is assumed to be constant. We use the sample characteristic function approach in order to study parameter estimation for discretely observed stochastic differential equations driven by Levy noises. We also discuss the consistency and asymptotic properties of the proposed estimators. Simulation results of the model are also presented to show the validity of the estimators. We then propose a new model where the volatility is not a constant. We consider generalized alpha-stable geometric Levy processes where the stochastic volatility follows the Cox-Ingersoll-Ross (CIR) model in Cox et al. [9]. A number of methods have been proposed for estimating parameters for stable laws. However, a complication arises in estimation of the parameters in our model because of the presence of the unobservable stochastic volatility. To combat this complication we use the sample characteristic function method proposed by Press [48] and the conditional least squares method as mentioned in Overbeck and Ryden [47] to estimate all the parameters. We then discuss the consistency and asymptotic properties of the proposed estimators and establish a Central Limit Theorem. We perform simulations to assess the validity of the estimators. We also present several tables to show the comparison of estimators using different choices of arguments ui's. We conclude that all the estimators converge as expected regardless of the choice of ui's. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

While simulators can be used in place of hands-on hardware, there was not a significant body of quantitative research supporting the use of simulators for college and career success at the secondary level in information technology (IT). The purpose of this quantitative, nonexperimental study was to determine if there was a significant difference in college and career readiness of New York state high school students in approved IT content cluster high school programs, between those who use simulations and those who use hands-on hardware. Kolb's theory of experiential learning was the theoretical foundation for this research. The research questions examined whether there was a significant difference in the written exam grades, the hands-on exam grades, and the certification pass rates of students, based on the percentage of simulation used in their coursework. A survey was used to collect data on 60 students. A one-way Welch ANOVA indicated no significant difference in written grades between groups. A Kruskal-Wallis ANOVA showed statistical significance between groups using all simulated labs and less than 50% simulated labs, as well as between all simulated labs and 50% or greater simulated labs for hands-on grades. Fisher's Exact Test indicated that the proportion of students in the less than 50% simulated labs group who earned industry-level certifications was statistically significantly higher than the 50% or greater simulated labs group or the all simulated labs group. Implications for social change are that workers with entry-level IT skills can fill jobs in the growing IT field that offers well-paying jobs with more promising futures.

Ce travail porte sur l'étude théorique et numérique des cristaux phononiques non linéaires. Les non linéarités étudiées sont celles dues aux constantes élastiques d'ordre deux (quadratiques) et trois (cubiques) des matériaux constituant les cristaux. Les effets non linéaires sont étudiés grâce à des méthodes d'éléments finis en simulant la propagation d'une onde élastique à travers les cristaux.Un premier projet de recherche a porté sur l'étude d'une structure osseuse, et plus spécifiquement sur la dispersion des ondes élastiques dans une structure constituée d'une alternance de couches de collagène et d'hydroxy apatite. Les simulations montrent qu'il existe un lien étroit entre l'hydratation des os et leur capacité à dissiper l'énergie.La seconde étude réalisée concerne un résonateur élastique. Une structure constituée d'inclusions d'acier dans de la silice présente un comportement de commutateur lorsque les non linéarités cubiques de l'acier sont prises en compte. Cet effet fortement non linéaire apparaît lorsque l'amplitude de l'onde incidente dépasse un certain seuil. Un modèle analytique complet est fourni.La dernière étude réalisée montre la conception de matériaux composites possédant de fortes non linéarités cubiques mais de faibles non linéarités quadratiques. La dérivation des lois de mélange des paramètres élastiques d'un matériau non linéaire dans un matériau linéaire est effectuée à l'ordre trois. Les équations montrent une forte amplification des paramètres non linéaires du matériau résultant pour certaines concentrations. Les simulations permettent de conclure que le résonateur mentionné ci-dessus peut effectivement être réalisé. / This work is dedicated to the theoretical and numerical study of nonlinear phononic crystals. The studied nonlinearities are those due to the second (quadratic) and third (cubic) order elastic constants of the materials that constitute the crystals. Nonlinear effects are studied by the means of finite element methods, used to simulate the propagation of an elastic wave through the crystals.A first research project concerns the study of a bone structure, namely the dispersion of elastic waves in a structure composed of collagen and hydroxy apatite alternate constituent layers. Simulations showed that it exists a strong link between bones hydration and their ability to dissipate the energy.The second study relates to an elastic resonator. A structure composed of steel inclusions in a silica matrix shows a switch behavior when the cubic nonlinearities of steel are taken into account. This strong nonlinear effect appears when the amplitude of the incident wave reaches a threshold. A full analytical model is provided.The last study demonstrates the design of composite materials with both strong cubic nonlinearities and weak quadratic nonlinearities. The derivation of the mixing laws of the elastic parameters of a nonlinear material inside a linear one is performed up to order three. Equations show a strong amplification of the nonlinear parameters of the material for some concentrations. Numerical simulations allow to conclude that the above mentioned resonator can be produced.

Doctor of Philosophy / First part of the thesis is focused on experimental preparation of new hard quaternary amorphous materials Si-B-C-N with high thermal stability. Materials were prepared in the form of thin films using reactive magnetron sputtering. The technique used proved to be suitable for reproducible synthesis of these materials. The Si-B-C-N films were generally found to be amorphous with low compressive stress and good adhesion to silicon or glass substrates. The process and film characteristics were controlled by varying the sputter target composition, the Ar fraction in the N2–Ar gas mixture, the negative rf-induced substrate bias, and the substrate temperature. Main conclusions describe the relationships between process parameters, discharge and deposition characteristics and film properties (elemental composition, chemical bonding structure, material hardness, compressive stress or electrical conductivity of materials prepared). Second part of the thesis is focused on ab-initio simulations of structures of experimentally prepared Si-B-C-N materials. In the performed liquid-quench simulations, the Kohn-Sham equations for the valence electrons are expanded in a basis of plane wave functions, while core electrons were represented using Goedecker-type pseudopotentials. We simplified the ion bombardment process by assuming that the primary impact creates a localized molten region of high temperature and sufficiently short cooling time, commonly referred to as a thermal spike. Main conclusions deal with N2 formation in studied materials, effect of implanted Ar on structure and properties of prepared materials, ability of Si to relieve that part of compressive stress which is caused by implanted Ar, and ability of B to improve thermal stability of Si-B-C-N materials. The calculated results are compared with experiment.

Scientific culture is not popular because the essential nature of science – the models and practises that make it up – cannot be communicated via conventional media in a manner that is interesting to the average person. These models and practises might be communicated in an interesting manner using the new medium of the digital game, yet very few digital games based upon scientific simulations have been created and thus the potential of such games to facilitate scientific knowledge construction cannot be studied directly. Scientific simulations have, however, been much used by scientists to facilitate their own knowledge construction, and equally, both simulations and games have been used by science educators to facilitate knowledge construction on the part of their students. The large academic literatures relating to these simulations and games collectively demonstrate that their ability to: re-create reality; model complex systems; be visual and interactive; engage the user in the practise of science; and to engage the user in construction and collaboration, makes them powerful tools for facilitating scientific knowledge construction. Moreover, the large non-academic literature discussing the nature of digital games (which are themselves both simulations and games) demonstrates that their ability to perform the above tasks (i.e. to re-create reality, model complex systems, and so forth) is what makes them enjoyable to play.¶Because the features of scientific and educational simulations and games that facilitate knowledge construction are the very same features that make digital games enjoyable to play, the player of a scientific-simulation-based digital game would be simultaneously gaining enjoyment and acquiring scientific knowledge. If science were widely communicated using digital games, therefore, then it would be possible for there to be a popular scientific culture.

Cette thèse s'inscrit dans le contexte général de l'étude des processus dynamiques intervenant dans les étoiles tels que la convection, la rotation ou le champ magnétique et de leurs interactions non-linéaires. Les résultats de simulations numériques obtenus avec le code 2D éléments finis STELEM et le code pseudo-spectral 3D ASH sont présentés. La première partie de cette thèse concerne la modélisation globale de la dynamo solaire, mécanisme de régénération du champ magnétique. Via des simulations numériques 2D utilisant la théorie des champs moyens, j'ai pu étudier l'influence d'une circulation méridienne au profil complexe dans les modèles de Babcock-Leighton. Même si ces modèles sont capables de reproduire une période de 22 ans, de nombreuses caractéristiques du cycle telles que la migration des taches solaires vers l'équateur sont perdues. Nous montrons que des doutes peuvent être formulés sur la capacité de ces modèles à rendre compte du fonctionnement réel de la dynamo solaire. Dans l'objectif de mieux contraindre les effets de la variabilité du cycle solaire sur le climat terrestre, nous présentons ensuite un premier effort d'application en physique solaire de techniques de prédiction sophistiquées utilisées en météorologie. J'ai également pu effectuer les premiers calculs MHD 3D en géométrie sphérique d'une des étapes clés de la dynamo : l'évolution non-linéaire de structures magnétiques de la base de la zone convective vers la surface où elles émergent sous forme de régions actives. Les effets globaux de la force de courbure magnétique et des écoulements moyens sont pris en compte. Des champs faibles sont susceptibles d'être modulés par les mouvements convectifs, favorisant ainsi l'émergence à des longitudes privilégiées. Nous montrons qu'il est nécessaire de prendre en compte l'effet de la convection dans l'angle de tilt et non d'expliquer la loi de Joy uniquement par la rotation et la force de Coriolis induite. L'introduction d'une atmosphère dans ces modèles est une étape vers une vision 3D globale du Soleil.

La dynamique des systèmes gravitationnels s'appuie traditionnellement sur la physique de Newton. Appliquée à l'échelle des galaxies, la gravitation newtonienne impose l'existence d'une certaine matière, actuellement invisible : la matière noire. Si ce modèle ($\Lambda$ Cold Dark Matter) rencontre des succès à grande échelle, des difficultés apparaissent à l'échelle des galaxies. Dans ma thèse, j'explore par des simulations numériques une alternative de la gravitation newtonienne : MOND (Modified Newtonian Dynamics), où la loi newtonienne de la gravité est modifiée selon une échelle d'accélération, sans l'intervention de la matière noire.<br />Cette expression de la gravitation est non-linéaire et impose une méthode différente de celle utilisée dans les systèmes avec matière noire. J'ai écrit un code permettant la résolution des deux modèles de gravité, ce qui a permis de les comparer. J'ai testé ainsi l'évolution de galaxies spirales isolées puis en interaction. Ces simulations modélisent aussi la dissipation du gaz froid et la formation d'étoiles. Celles-ci ont montré que les galaxies sont moins stables en gravitation modifiée qu'en gravitation newtonienne, elles forment des barres plus rapidement. Ces simulations ont aussi révélé des différences importantes sur les transferts de moment angulaire lors des formations des barres et sur les effets de friction dynamique qui ralentissent les barres. Ce travail a permis de réaliser, pour la première fois en gravité modifiée, des simulations de galaxies en interaction du type des Antennes. Là encore, les effets de friction dynamique ont un rôle majeur sur la durée du temps de fusion, plus long en gravitation modifiée. Ceci ouvre des horizons vers des simulations cosmologiques qui pourraient valoriser un modèle en analysant la formation hiérarchique des structures à partir des fluctuations de densité primordiales. Par ailleurs, la modélisation de la cinématique des galaxies (naines, spirales et elliptiques) est aussi approfondie. En particulier, l'analyse des courbes de rotation des galaxies spirales montre que celles-ci peuvent contenir un composant de gaz moléculaire froid deux fois plus massif que le composant atomique.