Kraft recovery boiler smelt is shattered into small droplets by an impinging steam jet to prevent smelt-water explosions in the dissolving tank. Inadequate shattering increases the likelihood of dissolving tank explosions. While industry has not dedicated much effort to smelt shattering, the safety implications require smelt shattering to be studied in detail. An experimental set-up was constructed to simulate the shattering operation using a water-glycerine solution and air instead of smelt and steam respectively. The objective was to examine how physical properties and flow characteristics affect shattering. It was found that increasing shatter jet velocity greatly reduced droplet mean diameter. Increasing the liquid flow rate greatly increased droplet size, as expected. Shattering was not significantly affected by viscosity, unless a weak shatter jet was used on a highly viscous fluid. Increasing the proximity of the shatter jet nozzle decreased droplet size.

Cette thèse comporte deux parties distinctes, toutes les deux liées à la théorie du transport optimal. Dans la première partie, nous considérons une variété riemannienne, deux mesures à densité régulière et un coût de transport, typiquement la distance géodésique quadratique et nous nous intéressons à la régularité de l’application de transport optimal. Le critère décisif à cette régularité s’avère être le signe du tenseur de Ma-Trudinger-Wang (MTW). Nous présentons tout d’abord une synthèse des travaux réalisés sur ce tenseur. Nous nous intéressons ensuite au lien entre la géométrie des lieux d’injectivité et le tenseur MTW. Nous montrons que dans de nombreux cas, la positivité du tenseur MTW implique la convexité des lieux d’injectivité. La deuxième partie de cette thèse est liée aux équations aux dérivées partielles. Certaines peuvent être considérées comme des flots gradients dans l’espace de Wasserstein W2. C’est le cas de l’équation de Keller-Segel en dimension 2. Pour cette équation nous nous intéressons au problème de quantification de la masse lors de l’explosion des solutions ; cette explosion apparaît lorsque la masse initiale est supérieure à un seuil critique Mc. Nous cherchons alors à montrer qu’elle consiste en la formation d’un Dirac de masse Mc. Nous considérons ici un modèle particulaire en dimension 1 ayant le même comportement que l’équation de Keller-Segel. Pour ce modèle nous exhibons des bassins d’attractions à l’intérieur desquels l’explosion se produit avec seulement le nombre critique de particules. Finalement nous nous intéressons au profil d’explosion : à l’aide d’un changement d’échelle parabolique nous montrons que la structure de l’explosion correspond aux points critiques d’une certaine fonctionnelle. / This thesis consists in two distinct parts both related to the optimal transport theory.The first part deals with the regularity of the optimal transport map. The key tool is the Ma-Trundinger-Wang tensor and especially its positivity. We first give a review of the known results about the MTW tensor. We then explore the geometrical consequences of the MTW tensor on the injectivity domain. We prove that in many cases the positivity of MTW implies the convexity of the injectivity domain. The second part is devoted to the behaviour of a Keller-Segel solution in the super critical case. In particular we are interested in the mass quantization problem: we wish to quantify the mass aggregated when the blow-up occurs. In order to study the behaviour of the solution we consider a particle approximation of a Keller-Segel type equation in dimension 1. We define this approximation using the gradient flow interpretation of the Keller-Segel equation and the particular structure of the Wasserstein space in dimension 1. We show two kinds of results; we first prove a stability theorem for the blow-up mechanism: we exhibit basins of attraction in which the solution blows up with only the critical number of particles. We then prove a rigidity theorem for the blow-up mechanism: thanks to a parabolic rescaling we prove that the structure of the blow-up is given by the critical points of a certain functional.

Dans cette thèse, nous étudions l’existence, non existence et multiplicité des ondes stationnairesavec les normes prescrites pour deux types d’équations aux dérivées partiellesnon linéaires elliptiques découlant de différents modèles physiques. La stabilité orbitale desondes stationnaires est également étudiée dans certains cas. Les principales méthodes denos preuves sont des arguments variationnels. Les solutions sont obtenues comme pointscritiques de fonctionnelle associée sur une contrainte.La thèse se compose de sept chapitres. Le Chapitre 1 est l’introduction de la thèse. Dansles Chapitres 2 à 4, nous étudions une classe d’équations de Schrödinger-Poisson-Slaternon linéaires. Nous établissons dans le Chapitre 2 des résultats optimaux non existencede solutions d’énergie minimale ayant une norme L2 prescrite. Dans le Chapitre 3, nousmontrons un résultat d’existence de solutions L2 normalisées, dans une cas où la fonctionnelleassociée n’est pas bornée inférieurement sur la contrainte. Nos solutions sonttrouvées comme des points de selle de la fonctionnelle, mais ils correspondent à des solutionsd’énergée minimale. Nous montrons également que les ondes stationnaires associéessont orbitalement instables. Ici, puisque nos points critiques présumés ne sont pas desminimiseurs globaux, il n’est pas possible d’utiliser de façon systématique les méthodesde compacité par concentration développées par P. L. Lions. Ensuite, dans le Chapitre4, nous montrons que sous les hypothèses du Chapitre 3, il existe une infinité de solutionsayant une norme L2 prescrite. Dans les deux chapitres suivants, nous étudions uneclasse d’équations de Schrödinger quasi-linéaires. Des résultats optimaux non existence desolutions d’énergie minimale sont donnés dans le Chapitre 5. Dans le Chapitre 6, nousprouvons l’existence de deux solutions positives ayant une norme donnée. L’une d’elles,relativement à la contrainte L2, est de type point selle. L’autre est un minimum, soit localou global. Le fait que la fonctionnelle naturelle associée à cette équation n’est pas biendéfinie nécessite l’utilisation d’une méthode de perturbation pour obtenir ces deux pointscritiques. Enfin, au Chapitre 7, nous mentionnons quelques questions que cette thèse asoulevées. / In this thesis, we study the existence, non-existence and multiplicity of standing waves withprescribed norms for two types of nonlinear elliptic partial differential equations arisingfrom various physical models. The orbital stability of the standing waves is also discussedin some cases. The main ingredients of our proofs are variational arguments. The solutionsare found as critical points of an associated functional on a constraint.The thesis consists of seven chapters. Chapter 1 is the Introduction of the thesis.In Chapters 2 to 4, we study a class of nonlinear Schrödinger-Poisson-Slater equations.We establish in Chapter 2 sharp non-existence results of least energy solutions having aprescribed L2-norm. In Chapter 3 we prove an existence result for L2-normalized solutions,in a situation where the associated functional is unbounded from below on the constraint.Our solutions are found as saddle points of the functional but they correspond to leastenergy solutions. We also prove that the associated standing waves are orbitally unstable.Here a key feature is that, since our suspected critical points are not global minimizers, itis not possible to use in a standard way the machinery of compactness by concentrationdeveloped by P. L. Lions. Then, in Chapter 4, we prove that under the assumptions ofChapter 3, there do exist infinitely many solutions having a prescribed L2-norm. In thefollowing two chapters, we investigate a class of quasi-linear Schrödinger equations. Sharpnon-existence results of least energy solutions are given in Chapter 5. In Chapter 6 weprove the existence of two positive solutions having a given norm. One of them, is relativeto the L2-norm constraint, of saddle point type. The other one is a minimum, either localor global. The fact that the natural functional associated with this equation is not welldefined requires the use of a perturbation approach to obtain these two critical points.Finally, in Chapter 7 we mention some questions that this thesis has raised.

This master's thesis deals with the issue of volcanic ash as a complex and its impact on aviation, including the volcanic activity itself (conditions for its existence, for existence of eruptions and their basic products). In addition, the thesis also deals with effect of volcanic ash on aircraft and airports, possibilities of its detection or monitoring as well as mechanism of its spreading in airspace. The emphasis is laid mainly on air incidents related to volcanic ash and on danger it poses to the airspace of the Czech Republic.

Cette thèse porte sur l’étude des propriétés qualitatives des solutions des équations des ondes et de la chaleur semi-linéaires. Les résultats qui y sont décrits sont les suivants. Les deux premiers concernent l’existence et la description de dynamiques explosives de concentration en temps fini de l’état stationnaire à symétrie radiale dans le régime dit énergie surcritique ; en outre, pour l’équation des ondes la stabilité de ces phénomènes est étudiée dans le cas radial, et pour l’équation de la chaleur le cas plus général d’un domaine borné avec conditions de Dirichlet au bord est considéré. Le troisième porte sur la classification des dynamiques possibles près de l’état stationnaire radial pour l’équation de la chaleur dans le régime dit énergie critique, trois scénarios ayant lieu : la stabilisation, l’instabilité par explosion auto-similaire à profil explosif constant en espace, et l’instabilité par dissipation vers la solution nulle. Enfin, le quatrième a pour objet l’existence et la stabilité de profils explosifs auto-similaires non constants en espace pour l’équation de la chaleur dans le cas énergie surcritique / This thesis is devoted to the study of qualitative properties for solutions to the semilinear heat and wave equations. The results that are described are the following. The first two concern the existence and description of blow-up dynamics in which the radially symmetric stationary state is concentrated in finite time in the so-called energy supercritical regime; in addition, for the wave equation the stability of these phenomena is studied in the radial case, and for the heat equation the more general case of a bounded domain with Dirichlet condition at the boundary is considered. The third one deals with the classification of the possible dynamics near the radial stationary state for the heat equation in the so-called energy critical regime, where three scenarii occur: stabilization, instability by blow-up with the constant in space blow-up profile, and instability by dissipation to the null solution. Eventually, in the forth result we investigate the existence and the stability of self-similar blow-up profiles that are not constant in space, for the heat equation in the energy supercritical case

Cette thèse est consacrée à l'étude des aspects linéaires et non-linéaires des équations de type Schrödinger [ i partial_t u + |nabla|^sigma u = F, quad |nabla| = sqrt {-Delta}, quad sigma in (0, infty).] Quand $sigma = 2$, il s'agit de l'équation de Schrödinger bien connue dans de nombreux contextes physiques tels que la mécanique quantique, l'optique non-linéaire, la théorie des champs quantiques et la théorie de Hartree-Fock. Quand $sigma in (0,2) backslash {1}$, c'est l'équation Schrödinger fractionnaire, qui a été découverte par Laskin (voir par exemple cite{Laskin2000} et cite{Laskin2002}) en lien avec l'extension de l'intégrale de Feynman, des chemins quantiques de type brownien à ceux de Lévy. Cette équation apparaît également dans des modèles de vagues (voir par exemple cite{IonescuPusateri} et cite{Nguyen}). Quand $sigma = 1$, c'est l'équation des demi-ondes qui apparaît dans des modèles de vagues (voir cite{IonescuPusateri}) et dans l'effondrement gravitationnel (voir cite{ElgartSchlein}, cite{FrohlichLenzmann}). Quand $sigma = 4$, c'est l'équation Schrödinger du quatrième ordre ou biharmonique introduite par Karpman cite{Karpman} et par Karpman-Shagalov cite{KarpmanShagalov} pour prendre en compte le rôle de la dispersion du quatrième ordre dans la propagation d'un faisceau laser intense dans un milieu massif avec non-linéarité de Kerr. Cette thèse est divisée en deux parties. La première partie étudie les estimations de Strichartz pour des équations de type Schrödinger sur des variétés comprenant l'espace plat euclidien, les variétés compactes sans bord et les variétés asymptotiquement euclidiennes. Ces estimations de Strichartz sont utiles pour l'étude de l'équations dispersives non-linéaire à régularité basse. La seconde partie concerne l'étude des aspects non-linéaires tels que les caractères localement puis globalement bien posés sous l'espace d'énergie, ainsi que l'explosion de solutions peu régulières pour des équations non-linéaires de type Schrödinger. [...] / This dissertation is devoted to the study of linear and nonlinear aspects of the Schrödinger-type equations [ i partial_t u + |nabla|^sigma u = F, quad |nabla| = sqrt {-Delta}, quad sigma in (0, infty).] When $sigma = 2$, it is the well-known Schrödinger equation arising in many physical contexts such as quantum mechanics, nonlinear optics, quantum field theory and Hartree-Fock theory. When $sigma in (0,2) backslash {1}$, it is the fractional Schrödinger equation, which was discovered by Laskin (see e.g. cite{Laskin2000} and cite{Laskin2002}) owing to the extension of the Feynman path integral, from the Brownian-like to Lévy-like quantum mechanical paths. This equation also appears in the water waves model (see e.g. cite{IonescuPusateri} and cite{Nguyen}). When $sigma = 1$, it is the half-wave equation which arises in water waves model (see cite{IonescuPusateri}) and in gravitational collapse (see cite{ElgartSchlein}, cite{FrohlichLenzmann}). When $sigma =4$, it is the fourth-order or biharmonic Schrödinger equation introduced by Karpman cite {Karpman} and by Karpman-Shagalov cite{KarpmanShagalov} taking into account the role of small fourth-order dispersion term in the propagation of intense laser beam in a bulk medium with Kerr nonlinearity. This thesis is divided into two parts. The first part studies Strichartz estimates for Schrödinger-type equations on manifolds including the flat Euclidean space, compact manifolds without boundary and asymptotically Euclidean manifolds. These Strichartz estimates are known to be useful in the study of nonlinear dispersive equation at low regularity. The second part concerns the study of nonlinear aspects such as local well-posedness, global well-posedness below the energy space and blowup of rough solutions for nonlinear Schrödinger-type equations.[...]

This thesis re-evaluates a positive reply given by the majority of existing secondary literature on the question of whether J. L. Fischer was a democrat and a theorist of democracy. On the other hand, some features of the author's work can cast doubts on his political orientation, and the existing secondary literature does not provide a clear disapproval of these doubts. The core of this thesis then lies in forging a newly designed interpretation of the author's compositional philosophy foregoing the Second World War. We are using the existential "bloody disjunction" of the author as our interpretational key with the hope that it can allow us to explain even the most difficult parts of J. L. Fischer's work constructively to the "uninformed reader". We are recognizing the specificity of this work as an author's-actor's creative expression. Therefore its internal expressional structure should not be reduced solely to the theoretical component without attention paid to the strong philosophical, artistic, and charismatic ambitions of the creator. This thesis interprets indicated components of Fischer's philosophy and his existential fight, which, even though manifested through breaches of argumentation, is at the same time giving to the compositional philosophy a whole new level of coherency. The...

To develop anaerobic digestion (AD), innovative solutions to increase methane yields in existing AD processes are needed. In particular, the adoption of low energy pre-treatments to enhance biomass biodegradability is needed to provide efficient digestion processes increasing profitability. To obtain these features, hydrodynamic cavitation has been evaluated as an innovative solutions for AD of waste activated sludge (WAS), food waste (FW), macro algae and grass, in comparison with steam explosion (high energy pre-treatment). The effect of these two pre-treatments on the substrates, e.g. particle size distribution, soluble chemical oxygen demand (sCOD), biochemical methane potential (BMP) and biodegradability rate, have been evaluated. After two minutes of hydrodynamic cavitation (8 bar), the mean fine particle size decreased from 489- 1344 nm to 277- 381 nm (≤77% reduction) depending of the biomasses. Similar impacts were observed after ten minutes of steam explosion (210 °C, 30 bar) with a reduction in particle size between 40% and 70% for all the substrates treated.  In terms of BMP value, hydrodynamic cavitation caused significant increment only within the A. nodosum showing a post treatment increment of 44% compared to the untreated value, while similar values were obtained before and after treatment within the other tested substrates. In contrast, steam explosion allowed an increment for all treated samples, A. nodosum (+86%), grass (14%) and S. latissima (4%). However, greater impacts where observed with hydrodynamic cavitation than steam explosion when comparing the kinetic constant K. Overall, hydrodynamic cavitation appeared an efficient pre-treatment for AD capable to compete with the traditional steam explosion in terms om kinetics and providing a more efficient energy balance (+14%) as well as methane yield for A. nodosum. / Det behövs innovativa lösningar för att utveckla anaerob rötning i syfte att öka metangasutbytet från biogassubstrat. Beroende på substratets egenskaper, kan förbehandling möjliggöra sönderdelning av bakterieflockar, uppbrytning av cellväggar, elimination av inhiberande ämnen och frigörelse av intracellulära organiska ämnen, som alla kan leda till en förbättring av den biologiska nedbrytningen i rötningen. För att uppnå detta har den lågenergikrävande förebehandlingsmetoden hydrodynamisk kavitation prövats på biologiskt slam, matavfall, makroalger respektive gräs, i jämförelse med ångexplosion. Effekten på substraten av dessa två förbehandlingar har uppmäts genom att undersöka distribution av partikelstorlek, löst organiskt kol (sCOD), biometan potential (BMP) och nedbrytningshastigheten. Efter 2 minuters hydrodynamisk kavitation (8 bar) minskade partikelstorleken från 489- 1344 nm till 277- 281 nm (≤77 % reduktion) för de olika biomassorna. Liknande påverkan observerades efter tio minuters ångexplosion (210 °C, 30 bar) med en partikelstorlekreducering mellan 40 och 70 % för alla behandlade substrat. Efter behandling med hydrodynamisk kavitation, i jämförelse med obehandlad biomassa, ökade metanproduktionens hastighetskonstant (K) för matavfall (+65%), makroalgen S. latissima (+3%), gräs (+16 %) samtidigt som den minskade för A. nodosum (-17 %). Förbehandlingen med ångexplosion ökade hastighetskonstanten för S. latissima (+50 %) och A. nodosum (+65 %) medan den minskade för gräs (-37 %), i jämförelse med obehandlad biomassa. Vad gäller BMP värden, orsakade hydrodynamisk kavitation små variationer där endast A. nodosum visade en ökning efter behandling (+44 %) i jämförelse med obehandlad biomassa. Biomassa förbehandlade med ångexplosion visade en ökning för A .nodosum (+86 %), gräs (14 %) och S. latissima (4 %). Sammantaget visar hydrodynamisk kavitation potential som en effektiv behandling före rötning och kapabel att konkurrera med den traditionella ångexplosionen gällande kinetik och energibalans (+14%) samt metanutbytet för A. nodosum.

The development of analytical methods for emerging contaminants creates many unique challenges for analytical chemists. By their nature, emerging contaminants have inherent data gaps related to their environmental occurrence, fate, and impact. This dissertation is a compilation of three studies related to method development for the structural identification of emerging contaminants, the detection and quantification of chemicals used in unprecedented quantities and applications, and the extraction of compounds from complex matrices where the solvent-solute-matrix interactions are not completely understood. The three studies present analytical methods developed for emerging contaminants in complex matrices, including: fluorochemical surfactants in aqueous film-forming foams, oil dispersant surfactants in seawater, and fullerene nanomaterials in carbonaceous solids. Aqueous film-forming foams, used in military and commercial firefighting, represent environmentally-relevant commercial mixtures that contain a variety of fluorochemical surfactants. Combining the surfactant-selective ionization of fast atom bombardment mass spectrometry with high resolution mass spectrometry, chemical formulas for 11 different fluorochemical classes were identified. Then AFFF-related patents were used to determine the structures. Of the eleven classes of fluorochemicals, ten have little, if any, data on their environmental occurrence, fate, and potential impacts in the peer-reviewed literature. In addition, nine of the identified classes had either cationic or zwitterionic functionalities and are likely to have different transport properties compared to the well-studied anionic fluorochemicals, such as perfluorooctanoate. After the Deepwater Horizon oil spill in the summer of 2010, one of the emergency response methods for the mitigation of the oil's environmental impact was the use of unprecedented amounts of oil dispersant to break down the oil slick and encourage biodegradation. This event illustrated the need for rapid analytical method development in order to respond to the potential environmental disaster in a timely manner. Using large volume injection liquid chromatography with tandem mass spectrometry, an analytical method was developed for the trace analysis of the multiple dispersant surfactant classes and the potential degradation products of the primary surfactant. Limits of detection ranged from 49 ��� 3,000 ng/L. The method provided excellent recovery (86 ��� 119%) and precision (10 ��� 23% RSD), while also accommodating for the high salinity of seawater samples and analyte contamination. Despite the fact that fullerene nanomaterials have been studied for almost three decades, research is still being conducted to fully understand the environmental properties of these materials. Previous studies to extract fullerenes from environmental matrices have resulted in low efficiency, high variability, or the extraction efficiencies have gone unreported. Extraction by ultrasonication with toluene and 1-methylnaphthalene increased the recovery 5-fold of a spiked, isotopically-labeled C������ surrogate from carbon lampblack as compared to that of the conventional approach of extracting with 100% toluene. The study revealed the importance of evaluating experimental variables such as extraction solvent composition and volume, and sample mass, as they have a significant impact on the quantitative extraction of fullerenes from environmental matrices. / Graduation date: 2013 / Access restricted to the OSU Community at author's request from Aug. 15, 2012 - Aug. 15, 2013

This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.