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PhD Thesis / The superconductivity in heavy-fermion compounds, iron pnictides and cuprates has been intensively studied for over thirty years. Amongst some of these materials, the common denominator is the presence of strong antiferromagnetic fluctuations in their normal state, signaling an underlying quantum phase transition between a paramagnetic metal and a metal with antiferromagnetic long-range order. Although the quantum critical point is experimentally inaccessible due to the presence of superconducting order, it determines the physical properties of the normal state of the metal in a wide range of temperatures. In this thesis we study the low-energy theory for the critical metallic state that arises at the aforementioned quantum critical point. We present a nonperturbative study of the theory in spatial dimensions between two and three. We pay special attention to two dimensions where we show that our physical predictions are in qualitative agreement with experiments in electron-doped cuprates. We further develop a field theoretic functional renormalization group scheme that is analytically tractable. It provides a general framework to study the low-energy theory of metallic states with or without a quasiparticle description. Within this formalism we characterize the single-particle properties of the antiferromagnetic quantum critical metal. This allows one to study the superconducting instability triggered by critical antiferromagnetic quantum fluctuations quantitatively. / Thesis / Doctor of Science (PhD)

Real-time computing systems are those that are designed to achieve computing goals by certain deadlines. Real-time computing systems are present in everything from cars to airplanes, pacemakers to industrial-control systems, and other pieces of critical infrastructure. With the increasing interconnectivity of these systems, system security issues and the constant threat of manipulation by malicious external attackers that have plagued general computing systems, now threaten the integrity and safety of real-time systems. This dissertation discusses three different defense techniques that focuses on the role that real-time scheduling theory can play to reduce runtime cost, and guarantee correctness when applying these defense strategies to real-time systems. The first work introduces a novel timing aware defense strategy for the CAN bus that utilizes TrustZone on state-of-the-art ARMv8-M microcontrollers. The second reduces the runtime cost of control-flow integrity (CFI), a popular system security defense technique, by correctly modeling when a real-time system performs I/O, and exploiting the model to schedule CFI procedures efficiently. Finally, the third studies and provides a lightweight mitigation strategy for a recently discovered vulnerability within mixed criticality real-time systems. / Doctor of Philosophy / Real-time computing systems are those that are designed to achieve computing goals within certain timing constraints. Real-time computing systems are present in everything from cars to airplanes, pacemakers to industrial-control systems, and other pieces of critical infrastructure. With the increasing interconnectivity of these systems, system security issues and the constant threat of manipulation by malicious external attackers that have plagued general computing systems, now threaten the integrity and safety of real-time systems. This dissertation discusses three different defense techniques that focuses on the role that real-time scheduling theory can play to reduce runtime cost, and guarantee correctness when applying these defense strategies to real-time systems. The first work introduces a novel timing aware defense strategy for the Controller Area Network (CAN). CAN is a popular communication system that is at the heart of every modern passenger vehicle and is indispensable for the safe operation of various components such as the engine and transmission systems, and due to its simplicity, may be vulnerable to a variety of attacks. We leverage security advancements in modern processor design to provide a lightweight and predictable (in terms of time taken to perform the operation) defense technique for some of these vulnerabilities. The second work applies a technique called Control-Flow Integrity (CFI) to real-time systems. CFI is a general-purpose defense technique to prevent attackers from modifying software execution, and applying such techniques to real-time systems, particularly those with limited hardware capabilities, may be infeasible. By applying real-time scheduling theory, we propose a strategy to apply CFI to such systems, while reducing its overhead, or cost, without compromising the security guarantees CFI inherently provides. Finally, safety-critical systems may consist of a mix of operations, each having a different level of importance (criticality) with respect to the safe operation of the system. However, due to the complexity of modeling such systems, the models themselves may be vulnerable to attacks. Through simulations we study one such vulnerability and propose a modification to mitigate it.

A análise de segurança de criticalidade nuclear é uma atividade mandatória sob o ponto de vista de licenciamento de uma instalação que manipula qualquer quantidade de material físsil. Este trabalho apresenta uma metodologia de análise para uma instalação fabril que processa e estoca ligas de urânio enriquecido. Trata-se da verificação da instalação para que se evite qualquer evento de acidente nuclear, seja por um equipamento inseguro, seja por um arranjo inseguro dos materiais. Todo o ciclo do urânio, principalmente as instalações envolvidas na fabricação do combustível nuclear, é avaliado quanto à segurança contra a criticalidade nuclear. A disponibilidade de informações relacionadas à segurança das instalações para combustíveis de reatores de potência comerciais (PWR e BWR, das siglas em inglês para reator de água pressurizada e reator de água fervente, respectivamente) utilizando o dióxido de urânio (UO2) com baixo nível de enriquecimento são amplamente compartilhadas. No entanto, informações sobre parâmetros seguros de criticalidade nuclear voltadas para combustíveis à base de ligas de urânio com nível de enriquecimento médio (até 20%) são raras na literatura. Dessa forma, o trabalho proposto visa suprir essa carência ao desenvolver um método de análise de criticalidade voltada para uma instalação destinada à fabricação de combustível nuclear, utilizando ligas metálicas urânio com 20% de enriquecimento. / Nuclear Criticality Safety analysis is a mandatory licensing activity for a facility that handles a certain amount of fissile material. This work presents an analysis methodology for a plant which processes and stores uranium alloys enriched. It is the verification of the facility in order to avoid any nuclear accident event, either by unsafe equipament or by an unsafe arrangement of materials. The whole uranium cycle, mainly the facilities involved in manufacturing of nuclear fuel is evaluated for safety against nuclear criticality. The availability of information related to facilities safety for fuel of commercial power reactors facilites (PWR and BWR, Pressurized Water Reactor and Boiling Water Reactor respectively) using the mixed oxide of uranium (UO2) with low enrichment level are widely shared. However, information of safe parameters focused on the nuclear criticality of uranium alloys based fuels with average enrichment level (up to 20%) are scarse in the literature. Thus, the proposed work aims to fill this need by developing a criticality analysis method focused on a facility dedicated to the manufacture of nuclear fuel using uranium alloys with 20% degree of enrichment.

A análise de segurança de criticalidade nuclear é uma atividade mandatória sob o ponto de vista de licenciamento de uma instalação que manipula qualquer quantidade de material físsil. Este trabalho apresenta uma metodologia de análise para uma instalação fabril que processa e estoca ligas de urânio enriquecido. Trata-se da verificação da instalação para que se evite qualquer evento de acidente nuclear, seja por um equipamento inseguro, seja por um arranjo inseguro dos materiais. Todo o ciclo do urânio, principalmente as instalações envolvidas na fabricação do combustível nuclear, é avaliado quanto à segurança contra a criticalidade nuclear. A disponibilidade de informações relacionadas à segurança das instalações para combustíveis de reatores de potência comerciais (PWR e BWR, das siglas em inglês para reator de água pressurizada e reator de água fervente, respectivamente) utilizando o dióxido de urânio (UO2) com baixo nível de enriquecimento são amplamente compartilhadas. No entanto, informações sobre parâmetros seguros de criticalidade nuclear voltadas para combustíveis à base de ligas de urânio com nível de enriquecimento médio (até 20%) são raras na literatura. Dessa forma, o trabalho proposto visa suprir essa carência ao desenvolver um método de análise de criticalidade voltada para uma instalação destinada à fabricação de combustível nuclear, utilizando ligas metálicas urânio com 20% de enriquecimento. / Nuclear Criticality Safety analysis is a mandatory licensing activity for a facility that handles a certain amount of fissile material. This work presents an analysis methodology for a plant which processes and stores uranium alloys enriched. It is the verification of the facility in order to avoid any nuclear accident event, either by unsafe equipament or by an unsafe arrangement of materials. The whole uranium cycle, mainly the facilities involved in manufacturing of nuclear fuel is evaluated for safety against nuclear criticality. The availability of information related to facilities safety for fuel of commercial power reactors facilites (PWR and BWR, Pressurized Water Reactor and Boiling Water Reactor respectively) using the mixed oxide of uranium (UO2) with low enrichment level are widely shared. However, information of safe parameters focused on the nuclear criticality of uranium alloys based fuels with average enrichment level (up to 20%) are scarse in the literature. Thus, the proposed work aims to fill this need by developing a criticality analysis method focused on a facility dedicated to the manufacture of nuclear fuel using uranium alloys with 20% degree of enrichment.

Mass balance processes in glaciers are important for determining the growth or retreat of ice. Calving, the mechanical breakage of ice bergs from a glacier front, is a poorly understood phenomenon. This process has great importance to the mass balance of many glaciers, for example on Antarctica and in the Arctic. A recent paper by Åström et al. (2014) compare calving fronts to Self-Organized Critical (SOC) systems, especially the Abelian sand pile model, meaning that the calving front will stay at a critical state at all times. Fluctuations in external conditions will cause the glacier front to either retreat or advance. The calving frequency and size distribution of Tunabreen, a tidewater glacier in Svalbard, was studied during August and September, 2014, with the use of a time-lapse camera set up in front of the calving front. An 11-day period is studied in detail and compared to certain external factors, i.e. tide, air temperature, humidity, atmospheric pressure, wind speed and wind direction. The results are also compared to the relationships found by Åström et al. (2014). The results vary: tide relationships are found as the amplitude reaches above 1 meter, but seize to correlate as the tide falls off. Temperature trends are found for certain periods, but are of low credibility. Humidity, atmospheric pressure, wind speed and wind direction show low to no correlation with the calving size distribution. Fragment size distribution and calving rates show good correlation with the results from Åström et al. (2014). This helps to confirm the theory of SOC applied to calving fronts. Time-lapse photography is deemed as a good way to observe calving fronts, but have certain problems which are mostly related to the weather. Longer time periods would be needed to find better long term relationships between external conditions and calving frequencies, but data is hard to acquire and time consuming to process. The theory of SOC applied to calving fronts is promising and opens up new discussions for the research community. / Massbalansprocesser för glaciärer är viktiga för att bestämma om isen drar sig tillbaka eller avancerar. Den mekaniska brytningen av isberg från glaciärer kallas kalvning. Kalvning är väldigt viktig för ett flertal glaciärers massbalans, exempelvis för landisen på Antarktis och glaciärer i Arktis. Ny forskning visar att kalvande glaciärfronter alltid försöker befinna sig i ett kritiskt läge, liknande ett så kallat Self-Organized Critical (SOC) system. Detta kan liknas vid hur en sandhög försöker befinna sig vid sin kritiska sluttningsvinkel när ett konstant flöde av sandkorn adderas. Adderandet av sandkorn kan jämföras med hur externa förhållanden, så som temperatur och tidvatten, ändras. När dessa värden ändras med tid så kommer fronten kalva, mycket likt hur sandhögen rasar när sandkorn tillförs. Externa förhållanden kommer alltså styra om glaciären kalvar eller inte, och när.En time-lapse-kamera installerades framför Tunabreen, en tidvatten glaciär på Svalbard, under Augusti-September, 2014. Bilderna över Tunabreens kalvningsfront, som varade över en 11-dagars period, användes för att ta ut varje enskild kalvingshändelse. Denna data jämfördes sedan med tidvatten, temperatur, luftfuktighet, atmosfäriskt tryck, vindhastighet och vindriktning. Resultaten jämfördes även med de förhållanden som visades i den nya studien som beskrevs tidigare.Resultaten är blandade. När tidvattnets amplitud var större än 1 meter så följer kalvningen tidvattnets mönster, men detta avtar när amplituden är mindre. Temperaturen visar viss korrelation, men endast för kortare perioder. Då temperaturens förhållande till kalvningen inte följer under de högsta och lägsta värden som fanns så bedöms temperaturen ha låg trovärdighet som kontrollerande faktor. Luftfuktighet, atmosfäriskt tryck, vindhastighet och vindriktning visar låg, till ingen, korrelation med kalvning. Storleksfördelningen av fragment och kalvningshastigheten har god korrelation med forskningen kring SOC, resultaten hjälper till att bekräfta denna teori. Time-lapse-fotografi bedöms som en bra metod för att observera kalvningsfronter, men har ett flertal problem som relaterar till det lokala vädret.Längre tidsperioder behövs för att bedöma om förhållanden stämmer på lång sikt. Data är svår att förvärva och tidskrävande att behandla. SOC stämmer bra in på kalvningsfronter vilket öppnar upp nya diskussioner inom forskningsvärlden.

This dissertation is an attempt at establishing a bridge between biology and physics leading naturally from the field of phase transitions in physics to the cooperative nature of living systems. We show that this aim can be realized by supplementing the current field of evolutionary game theory with a new form of self-organized temporal criticality. In the case of ordinary criticality, the units of a system choosing either cooperation or defection under the influence of the choices done by their nearest neighbors, undergo a significant change of behavior when the intensity of social influence has a critical value. At criticality, the behavior of the individual units is correlated with that of all other units, in addition to the behavior of the nearest neighbors. The spontaneous transition to criticality of this work is realized as follows: the units change their behavior (defection or cooperation) under the social influence of their nearest neighbors and update the intensity of their social influence spontaneously by the feedback they get from the payoffs of the game (environment). If units, which are selfish, get higher benefit with respect to their previous play, they increase their interest to interact with other units and vice versa. Doing this, the behavior of single units and the whole system spontaneously evolve towards criticality, thereby realizing a global behavior favoring cooperation. In the case when the interacting units are oscillators with their own periodicity, homeodynamics concerns, the individual payoff is the synchronization with the nearest neighbors (i.e., lowering the energy of the system), the spontaneous transition to criticality generates fluctuations characterized by the joint action of periodicity and crucial events of the same kind as those revealed by the current analysis of the dynamics of the brain. This result is expected to explain the efficiency of enzyme catalyzers, on the basis of a new non-equilibrium statistical physics. We argue that the results obtained apply to sociological and psychological systems as well as to elementary biological systems.

Criticality calculations are often performed in MCNP5 using the Shannon entropy as an indicator of source convergence for the given neutron transport problem. The Shannon entropy is a concept that comes from information theory. The Shannon entropy is calculated for each batch in MCNP5, and it has been shown that the Shannon entropy tends to converge to a single value as the source distribution converges. MCNP5 has its own criteria for when the Shannon entropy has converged and recommends a number for how many batches should be skipped; however, this value for how many batches should be skipped is often not very accurate and has room for improvement. This work will investigate an approach for using the Shannon entropy source distribution convergence information obtained in a shorter simulation to predict the required number of generations skipped in the reference case with desired statistical precision. In several test cases, it has been found that running a lesser number of particles per batch produces a similar Shannon entropy graph when compared to running more particles per batch. Then, by appropriate adjustment through a synthetic model, one is able to determine when the Shannon entropy will converge by running fewer particles, finding the point where it converges and then using this value to determine how many batches one should skip for a given problem. This reduces computational time and any "guessing" involved when deciding how many batches to skip. Thus, the purpose of this research is to develop a model showing how one can use this concept and produce a streamlined approach for applying this concept to a criticality problem.

Thesis (MSc)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: In this thesis we give an overview of self-organised criticality and its application to studying seismicity. We recall some of the basic models and techniques for studying self-organised critical systems. We discuss one of these, the sandpile model, in detail and show how various properties of the model can be calculated using a matrix formulation thereof. A correspondence between self-organised critical systems and seismicity is then proposed. Finally, we consider the timeevolution of the sandpile model by using a time-to-failure analysis, originally developed in the study of seismicity and obtain results for the sandpile model that show similarities with that of the analyses of seismic data. / AFRIKAANSE OPSOMMING: In hierdie tesis gee ons 'n oorsig van self-organiserende kritikaliteit en die toepassing daarvan in die studie van seismisiteit. Ons beskryf die basiese modelle en tegnieke vir die studie van self-organiserende kritiese sisteme. Ons bespreek een van hierdie, die sandhoopmodel, in besonderheid en wys hoe om verskeie eienskappe van die model te bereken deur gebruik te maak van 'n matriks-formulering daarvan. Ons stel dan 'n korrespondensie tussen self-organiserende kritiese sisteme en seismisiteit voor. Ter afsluiting ondersoek ons die tydontwikkeling van die sand hoopmodel deur gebruik te maak van 'n deurbreektyd analise wat oorspronklik in die bestudering seismiese data ontwikkel is. Die resultate vir die analise van die sandhoopmodel toon ooreenkomste met dit wat verkry word vir seismiese data.

Second-order phase transitions involve critical fluctuations just below and above the transition temperature. Macroscopically, they manifest in the power-law behaviour of many physical properties such as the susceptibility and the specific heat. The power-laws are predicted to be universal, i.e. the same exponents are expected for a certain class of transitions irrespective of the microscopic details of the system. The underlying commonality of such transitions is the divergence of the correlation length ξ and the correlation time ξ_τ of the critical fluctuations at the transition temperature. Both ξ and ξ_τ can be directly observed by neutron scattering experiments, making them an ideal tool for the study of critical phenomena. At classical phase transitions, the critical fluctuations will be thermal in nature. However, if a second-order transition occurs at T = 0, thermal fluctuations are frozen, and the transition is driven by quantum fluctuations instead. This is called a quantum critical point. The quantum nature of the fluctuations influences observable properties, also at finite temperatures, and causes unusual behaviour in the vicinity of the quantum critical point or the existence of exotic phases, e.g. unconventional superconductivity. Heavy-fermion compounds are a class of materials that is well suited for the study of quantum criticality. They frequently show second-order transitions into a magnetically ordered state at very low temperatures, which can easily be tuned to T = 0 by the application of pressure, magnetic fields or element substitution. In this thesis, fluctuations near a quantum critical point are investigated for three heavy-fermion systems. CeCu2Si2 shows unconventional superconductivity close to an antiferromagnetic quantum critical point. Results from single-crystal neutron spectroscopy and thermodynamic measurements are discussed and some details are also given about the synthesis of large single crystals. The focus of the study is the comparison of the inelastic response of magnetic and superconducting samples, which are found to be very similar for ΔE > 0.2 meV. CePdAl has an antiferromagnetic state with partial magnetic frustration. The ordering temperature can be suppressed by Ni substitution towards a quantum critical point. Single-crystal neutron diffraction experiments of three members of the substitution series were analysed. They revealed several unusual effects of the frustrated state in the pure sample, and show that magnetic order and frustration persist in the substituted samples. YbNi4P2 is a rare example of a compound with ferromagnetic quantum criticality, which has only been studied in the last few years. The aim of the powder neutron spectroscopy experiments presented here was to obtain an overview of the relevant energy scales, i.e. the crystal electric field, local magnetic fluctuations and ferromagnetic fluctuations. Simulations using the program McPhase were performed for a thorough understanding of the crystal electric field.