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.

With the rapidly growing computational power of modern computers, physically based rendering has found its way into real world applications. Real-time simulations and renderings of fire and smoke had become one major research interest in modern video game industry, and will continue being one important research direction in computer graphics. To visually recreate realistic dynamic fire and smoke is a complicated problem. Furthermore, to solve the problem requires knowledge from various areas, ranged from computer graphics and image processing to computational physics and chemistry. Even though most of the areas are well-studied separately, when combined, new challenges will emerge. This thesis focuses on three aspects of the problem, dynamic, real-time and realism, to propose a solution in form of a GPGPU pipeline, along with its implementation. Three main areas with application in the problem are discussed in detail: fluid simulation, volumetric radiance estimation and volumetric rendering. The weights are laid upon the first two areas. The results are evaluated around the three aspects, with graphical demonstrations and performance measurements. Uniform grids are used with Finite Difference (FD) discretization scheme to simplify the computation. FD schemes are easy to implement in parallel, especially with ComputeShader, which is well supported in Unity engine. The whole implementation can easily be integrated into any real-world applications in Unity or other game engines that support DirectX 11 or higher.

Dans cette thèse, nous nous intéressons à l'étude de quatre équations d'évolution non-locales. Les solutions de ces quatre équations peuvent exploser en temps fini. Dans la théorie des équations d'évolution non-linéaires, une solution est qualifiée de globale si elle est définie pour tout temps positif. Au contraire, si une solution existe seulement sur un intervalle de temps [0; T) borné, elle est dite locale. Dans ce dernier cas et quand le temps maximal d'existence est relié à une alternative d'explosion, on dit aussi que la solution explose en temps fini. Dans un premier travail, nous considérons l'équation de Schrödinger non-linéaire avec une puissance fractionnaire du laplacien, et nous obtenons l'explosion de la solution en temps fini Tmax > 0 pour toute condition initiale positive et non-triviale dans le cas d'exposant sous-critique. Ensuite, nous étudions une équation des ondes amorties avec un potentiel d'espace-temps et un terme non-linéaire et non-local en temps. Nous obtenons un résultat d'existence locale d'une solution dans l'espace d'énergie sous des conditions restrictives sur les données initiales, la dimension de l'espace et la croissance du terme non-linéaire. De plus, nous obtenons l'explosion de la solution en temps fini pour toute condition initiale de moyenne strictement positive. De plus, nous étudions un problème de Cauchy pour l'équation d'évolution avec un p- Laplacien avec une non linéarité non-locale en temps. Dans ce cadre, nous nous intéressons à l'étude de l'existence locale d'une solution de cette équation ainsi qu'un résultat de non-existence de solution globale. Finalement, nous étudions l'intervalle maximal d'existence des solutions de l'équation des milieux poreux avec un terme non-linéaire non-local en temps. / In this thesis, we study four non-local evolution equations. The solutions of these four equations can blow up in finite time. In the theory of nonlinear evolution equations, a solution is qualified as global if it isdefined for any time. Otherwise, if a solution exists only on a bounded interval [0; T), it is called local solution. In this case and when the maximum time of existence is related to a blow up alternative, we say that the solution blows up in finite time. First, we consider the nonlinear Schröodinger equation with a fractional power of the Laplacien operator, and we get a blow up result in finite time Tmax > 0 for any non-trivial non-negative initial condition in the case of sub-critical exponent. Next, we study a damped wave equation with a space-time potential and a non-local in time non-linear term. We obtain a result of local existence of a solution in the energy space under some restrictions on the initial data, the dimension of the space and the growth of nonlinear term. Additionally, we get a blow up result of the solution in finite time for any initial condition positive on average. In addition, we study a Cauchy problem for the evolution p-Laplacien equation with nonlinear memory. We study the local existence of a solution of this equation as well as a result of non-existence of global solution. Finally, we study the maximum interval of existence of solutions of the porous medium equation with a nonlinear non-local in time term.

Les Etudes Probabilistes de Sûreté (EPS) de niveau 2 en centrale nucléaire visent à identifier les séquences d’événements pouvant correspondre à la propagation d’un accident d’un endommagement du cœur jusqu’à une perte potentielle de l’intégrité de l’enceinte, et à estimer la fréquence d’apparition des différents scénarios possibles.<p>Ces accidents sévères dépendent non seulement de défaillances matérielles ou d’erreurs humaines, mais également de l’occurrence de phénomènes physiques, tels que des explosions vapeur ou hydrogène. La prise en compte de tels phénomènes dans le cadre booléen des arbres d’événements s’avère difficile, et les méthodologies dynamiques de réalisation des EPS sont censées fournir une manière plus cohérente d’intégrer l’évolution du processus physique dans les changements de configuration discrète de la centrale au long d’un transitoire accidentel.<p>Cette thèse décrit l’application d’une des plus récentes approches dynamiques des EPS – la Théorie de la Dynamique Probabiliste basée sur les Stimuli (SDTPD) – à différents modèles de déflagration d'hydrogène ainsi que les développements qui ont permis cette applications et les diverses améliorations et techniques qui ont été mises en oeuvre.<p><p>Level-2 Probabilistic Safety Analyses (PSA) of nuclear power plants aims to identify the possible sequences of events corresponding to an accident propagation from a core damage to a potential loss of integrity of the containment, and to assess the frequency of occurrence of the different scenarios.<p>These so-called severe accidents depend not only on hardware failures and human errors, but also on the occurrence of physical phenomena such as e.g. steam or hydrogen explosions. Handling these phenomena in the classical Boolean framework of event trees is not convenient, and dynamic methodologies to perform PSA studies are expected to provide a more consistent way of integrating the physical process evolution with the discrete changes of plant configuration along an accidental transient.<p>This PhD Thesis presents the application of one of the most recently proposed dynamic PSA methodologies, i.e. the Stimulus-Driven Theory of Probabilistic Dynamics (SDTPD), to several models of hydrogen explosion in the containment of a plant, as well as the developed methods and improvements.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Nanotechnology is expected to play a major role in many technology areas including electronics, materials, and defense. One of the most popular tools for nanoscale surface analysis is the atomic force microscope (AFM). AFM can be used for surface manipulation along with surface imaging. The primary motivation for this research is to demonstrate AFM-based lithography on thin films using cantilevers with integrated heaters. These thermal cantilevers can control the temperature at the end of the tip, and hence they can be used for local in-situ thermal analysis. This research directly addresses applications like nanoscale electrical circuit fabrication/repair and thermal analysis of thin-films. In this study, an investigation was performed on two thin-film materials. One of them is co-polycarbonate, a variant of a polymer named polycarbonate, and the other is an energetic material called pentaerythritol tetranitrate (PETN). Experimental methods involved in the lithography process are discussed, and the results of lithographic experiments performed on co-polycarbonate and PETN are reported. Effects of dominant parameters during lithography experiments like time, temperature, and force are investigated. Results of simulation of the interface temperature between thermal cantilever tip and thin film surface, at the beginning of the lithography process, are also reported.

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Derek Parfit är kanske en av vår tids mest kända moralfilosofer. Parfit inleder sin första bok Reasons and Persons med att ställa frågan: vad har vi mest skäl att göra? Hans fråga berör vad som egentligen har betydelse, en fråga som han fortsätter att beröra i sin andra bok On What Matters. Filosofen Toby Ord argumenterar i sin bok The Precipice för att den utmaning som definierar vår tid, och bör ha en central prioritering, är utmaningen att skydda mänskligheten emot så kallade existentiella risker. En existentiell risk är en typ av risk som hotar att förstöra, eller förhindra, mänsklighetens långsiktiga potential. Ord menar att vi idag befinner oss vid en kritisk tidpunkt i mänsklighetens historia som kan vara helt avgörande för om det ens kommer existera en framtid för mänskligheten. Men om vi bör skydda mänskligheten emot existentiella risker, så kan en lämplig följdfråga vara i vilken ordning vi bör prioritera olika existentiella risker. Den svenske filosofen Nick Bostrom har liksom Ord länge förespråkat att existentiella risker bör tas på allvar. Han menar att preventiva åtgärder bör vidtas. I sin bok Superintelligens argumenterar Bostrom, både omfattande och väl, för att den existentiella risk som kan te sig som mest brådskande, och kanske allvarligast, är artificiell intelligens. Bostrom menar att vi har goda skäl att tro att utveckling av artificiell intelligens kan eskalera till den grad att mänsklighetens öde kan hamna bortom vår egen kontroll. Det han syftar på är att människan just nu är den dominerande agenten på jorden och därför innehar en stor kontroll, men att så inte alltid behöver vara fallet. Bostroms tes kunde te sig som okonventionell då den presenterades, men kan även te sig så idag vid en första anblick. Han har dock fått explicit medhåll av personer som Bill Gates, Stephen Hawking, Elon Musk, Yuval Noah Harari och Max Tegmark, som antingen håller med eller resonerar i liknande banor. Även jag själv finner Bostroms antaganden välgrundade. Slutsatsen som många drar är därför att vi bör betrakta artificiell intelligens som en existentiell risk som ska prioriteras högt. Jag kommer dock i denna text att argumentera för tesen att vi inte bör betrakta artificiell intelligens som en existentiell risk. Tesen följer från en invändning som jag kommer att kalla för AI-paradoxen. Det tycks enligt invändningen som att artificiell intelligens inte kan leda till en existentiell katastrof givet vissa premisser som flera i debatten om artificiell intelligens tycks acceptera. Texten i uppsatsen är strukturerad på följande sätt. I avsnitt 2 kommer jag att återge det övergripande argumentet som cirkulerar i debatten om artificiell intelligens som ett hot. I avsnittet kommer jag också förklara några viktiga termer och begrepp. I avsnitt 3 börjar jag med att titta på den första premissen i argumentet, samt resonera om dess rimlighet. I avsnitt 4 går jag sedan vidare till den andra premissen i argumentet och gör samma sak med den. Väl i avsnitt 5 så väljer jag att presentera min egen idé som jag kallar för AI-paradoxen, vilket är en invändning mot argumentet. I avsnitt 6 diskuterar jag sedan AI-paradoxens implikationer. Avslutningsvis, i avsnitt 7, så ger jag en övergripande sammanfattning och en slutsats, samt några sista reflektioner. / Derek Parfit is perhaps one of the most famous moral philosophers of our time. Parfit begins his first book Reasons and Persons by asking the question: what do we have most reason to do? His question touches upon what really matters, a question he continues to touch upon in his second book On What Matters. The philosopher Toby Ord argues in his book The Precipice that the challenge that defines our time, and should have a central priority, is the challenge of safeguarding humanity from so-called existential risks. An existential risk is a type of risk that threatens to destroy, or prevent, humanity’s longterm potential. Ord means that today we are at a critical time in the history of humanity that can be absolutely decisive for whether there will even exist a future for humanity. But if we are to safeguard humanity from existential risks, then an appropriate question may be in what order we should prioritize different existential risks. The Swedish philosopher Nick Bostrom, like Ord, has long advocated that existential risks should be taken seriously. He believes that preventive measures should be taken. In his book Superintelligence Bostrom argues, both extensively and well, that the existential risk that may seem most urgent, and perhaps most severe, is artificial intelligence. Bostrom believes that we have good reason to believe that the development of artificial intelligence can escalate to the point that the fate of humanity can end up beyond our own control. What he is referring to is that humans are currently the dominant agent on earth and therefore has great control, but that this does not always have to be the case. Bostrom's thesis may have seemed unconventional when it was presented, but it can also seem so today at first glance. However, he has been explicitly supported by people like Bill Gates, Stephen Hawking, Elon Musk, Yuval Noah Harari and Max Tegmark, who either agree or reason similarly. I myself also find Bostrom's assumptions well-founded. The conclusion that many draw is therefore that we should regard artificial intelligence as an existential risk that should be given a high priority. However, in this text I will argue for the thesis that we should not regard artificial intelligence as an existential risk. The thesis follows from an objection of my own, which I call the AI ​​paradox. According to the objection, it seems that artificial intelligence cannot lead to an existential catastrophe given certain premises that many in the debate about artificial intelligence as a threat seem to accept. The text in the essay is structured as follows. In section 2 I will present the main argument circulating in the debate about artificial intelligence as a threat. In the section I will also explain some important terms and concepts. In section 3 I begin by looking at the first premise in the argument, and also reason about its plausibility. In section 4 I proceed to the second premise in the argument and examine it similarly. Once in section 5 I choose to present my own idea, which I call the AI ​​paradox, which is an objection to the argument. In section 6 I discuss the implications of the AI ​​paradox. Finally, in section 7, I give an overall summary and a conclusion, as well as some last reflections.