In an attempt to reach a better understanding of the properties and critical behavior of non-equilibrium systems, we investigate the steady state properties of three simple models, variations of the prototype, the driven Ising lattice gas. Our first system studied is the bilayer model, a stack of two driven Ising lattice gases allowed to interact. We study this model using a very simple analytic approximation, the high temperature expansion. Building on existing simulation data and field theory results, our goal is to test how faithfully the series expansion can reproduce the Monte Carlo phase diagram. We find that the agreement between our calculations and the already reported simulations results is remarkably good. Next, we investigate the critical behavior of a two-dimensional Ising lattice gas driven into a non-equilibrium steady state, subject to a local modification of the dynamics, namely, having anisotropic attempt frequencies for exchanges along different spatial directions. We employ both Monte Carlo simulation techniques and a high temperature expansion approximation and find the phase diagram of the system, perform a finite-size scaling study in order to determine the universality class of the model and compare our simulation results with the phase diagram obtained using the high temperature expansion. We conclude that the bias in the jump rates does not affect the universal critical properties of the system: the modified model is in the same universality class as the driven Ising lattice gas. Our last objective concerns a different inroad into the study of non-equilibrium steady states. Instead of investigating a non-equilibrium steady state via indirect observables, such as correlation functions and order parameters, we seek to compute the steady state probability distribution directly. This is feasible only for systems with a small number of degrees of freedom. We chose to study a one-dimensional version of the so-called two-temperature kinetic Ising model. We solve the master equation exactly for a 1x6 system, and compare the full configurational probability distribution with its equilibrium counterpart. / Ph. D.

Nesta dissertação discutimos a medida RAA desenvolvida para análise de observáveis de colisão núcleo-núcleo (AA), tendo em vista sua implementação em colisões próton-próton (pp). No contexto das colisões hadrônicas de altíssimas energias, o RAA compara quantidade de observáveis duros medidos em colisões AA com a quantidade do mesmo observável em colisões pp. As qualidades destas colisões são descritas pela teoria do modelo de Glauber, em que projeção analítica da produção esperada de quarks pesados (observável duro) é realizada para colisões nucleares por meio da sobreposição de colisões pp independentes. Esta projeção analítica é comparada no RAA à medida de quarks pesados em estado final de colisões AA, e desvios em relação à distribuição de momentos da seção de choque calculada teoricamente são interpretados como decorrentes da presença de plasma de quarks e glúons (PQG) na colisão medida. O plasma de quarks e glúons é o objeto de interesse do campo de estudos em que esta pesquisa se insere. Considerado presente em colisões AA centrais desde 2000, o plasma de quarks e glúons é o estado da matéria mais energético possível, em que os pártons produto da colisão se comportam livremente por breves instantes e sofrem expansão hidrodinâmica. Este processo acontece nos estágios inacessíveis da colisão. Algumas das medidas indiretas que indicam formação de plasma em colisões AA são detectadas em colisões de sistemas pequenos, pp e pA desde 2010. Ainda não foi medida supressão de provas duras no PQG. As tentativas de medir PQG em sistemas pequenos pelo método do RAA tem sido feitas por meio da comparação RpA, também definida pelo modelo de Glauber. Na presente pesquisa buscamos extrapolar o funcionamento do RAA para medidas em colisões pp. Como o núcleo em Glauber é formado por sobreposição de prótons, a resolução da descrição da colisão na teoria é discutida. Além disso verificamos que a concepção de que colisões pp não formam ambiente de PQG é importante para o estabelecimento da comparação RAA. Entendemos que as hipóteses sobre a física de estágios inacessíveis da colisão previstas pela teoria de Glauber são diferentes das hipóteses decorrentes de medidas de coletividade em sistemas pequenos. Propomos alternativamente comparações experimentais simples entre quantidades parecidas medidas em colisões pp que podem conter informações sobre supressão de observáveis duros em colisões pp de alta multiplicidade sem o uso de quantidades teóricas. / This master thesis adresses the measurement RAA, developed for the analysis of nucleus-nucleus (AA) collisions, aiming to implement the measure for proton-proton (pp) collisions. In the context of high energy hadronic collisions, RAA compares hard observables measured in AA collisions with the same observable measured in pp collisions. These collisions traits are described by the Glauber model, where an analitical projection of the expected heavy quark production (hard observable) is calculated through the superimposition of independent pp collisions. In RAA, that analitical projection is compared to the actual final state AA collisions measurements, and deviations with relation to the momentum distribution of the theoriticaly calculated cross section are regarded as arising from interaction of the heavy quark with a quark gluon plasma (QGP) formed in the measured collision. The quark gluon plasma is the fields object of interest in which this reasearch is undertaken. Since 2000, QGP is measured and presumed in central AA colissions.The quark gluon plasma is the most energetic state of nuclear matter, in which partons behave as deconfined matter and undergo hydrodynamic expansion. That happends in the first inaccessible stages of the collisions. Some of the indirect measurements that point to the formation of QGP in AA collisions have been detected small systems, pp and pA, since 2010. Is yet to be measured hard probes PQG supression in these systems. Current attempts to evaluate this supression have been made with the RpA comparison, also defined with the Glauber model. In this study, we attempt to extrapolate the RAA operation to pp collision measurements. As the nucleus in Glauber is modeled as a superimposition of pp collisions, the theory\'s resolutuon in describing AA collisions is discussed. We also notice that the concept of pp collisions not formimg QGP is relevant for RAA comparisons. We appreciate that the theoretical hipothesis on the physics of the inaccessible first stages of collisions as foreseen with the Glauber model are different than the hipothesis that stem from collectivity in small systems. We propose alternatively simple experimental comparisons between similar quantities measured in pp collisions without the use of theoretical quantities.

Um novo estado, o Plasma Quark-Gluon (QGP), é formado quando a matéria comum formada por hadrons é submetida a condições extremas de temperatura e/ou densidade. Acredita-se que esse estado esteja presente nos primeiros momentos do universo e que seja relevante para entender propriedades da cromodinâmica quântica. O QGP é criado e caracterizado em aceleradores de partículas por meio de colisões de íons pesados. No entanto, uma estrutura alongada em psedorapidez (\\textit{double ridge}) na distribuição da correlação angular entre duas partículas foi encontrada em sistemas pequenos, como pp e p--Pb. Essa estrutura assemelha-se àquela observada nas colisões com íons pesados, onde sua interpretação está ligada ao comportamento coletivo que gera uma anisotropia azimutal nos produtos finais das colisões. Essa estrutura não era esperada em sistemas pequenos e sua interpretação física ainda está em debate, em particular no que diz respeito ao papel da hidrodinâmica e das condições iniciais. Uma medida para este efeito com partículas provenientes de quarks pesados ainda não haviam sido realizadas no momento em que este trabalho foi iniciado e esta medida poderia esclarecer questões sobre as diferentes interpretações. Os quarks pesados são uma sonda interessante caso o QGP seja formado devido ao seu tempo de formação inicial, reagindo a toda a evolução do meio. Neste trabalho, os quarks pesados são estudados medindo-se os elétrons provenientes dos decaimentos semi-leptônicos de hádrons que contêm quarks \\textit{charm} ou \\textit{beauty} e outros quarks leves (\\textit{open heavy flavor}). Os hadrons não são reconstruídos e usa-se um método de extração de sinal para remover elétrons de outras fontes. As correlações angulares de elétrons de decaimento de hadrons de quarks pesados com partículas carregadas em colisões de p--Pb a $\\sqrt{s_{m NN}}$ = 5,02 TeV medidos com o experimento ALICE em rapidez central ($ | \\eta | <0,8 $) são apresentadas. As distribuições mostram sinais de anisotropias azimutais que são quantificadas pelo coeficiente $ v_2 $. O $ v_2 $ para elétrons provenientes de quarks pesados é positivo com mais de $ 5 \\sigma $ de significância, fornecendo uma forte indicação de anisotropias azimutais similares ao \\textit{double ridge} para partículas contendo quarks pesados em colisões de alta multiplicidade de p--Pb. Esta é a primeira medida do $ v_2 $ para elétrons vindos de quarks pesados em colisões p--Pb. / A new state of mater, the Quark-Gluon Plasma (QGP), is formed when the ordinary hadronic matter is put under extreme temperature and/or density conditions. This state is believed to be present in the first moments of the universe and it is relevant to understand properties of the quantum chromodynamics. The QGP is created and characterized in particle accelerators by colliding heavy ions. However, a double-ridge long-range structure in the two-particle azimuthal correlation distribution was found in small systems, such as pp and p--Pb. This structure resembles the one observed in heavy-ion collisions, where its interpretation is linked to collective behavior that generates an azimuthal anisotropy in the final products of the collisions. This structure was not expected in small systems and its physical interpretation is still in debate, in particular regarding the role of hydrodynamics and initial conditions. A measurement for this effect with particles coming from heavy quarks was not done by the time this work started and this measurement could shed light into the different interpretations. Heavy quarks are an interesting probe in case the QGP is formed due to their early formation time, experiencing the whole evolution of the medium. In this work, heavy quarks are examined by measuring electrons originating from the semi-leptonic decays of hadrons that contain a heavy quark (charm or beauty) and other light quarks (open heavy flavor). The hadrons are not reconstructed and a signal extraction method is used to remove electrons from other sources. The azimuthal angular correlations of heavy-flavour hadron decay electrons with charged particles in p--Pb collisions at $\\sqrt{s_{m NN}}$ = 5.02 TeV measured with ALICE detector at mid-rapidity ($|\\eta| < 0.8$) are studied. The distributions show signs of azimuthal anisotropies which are quantified by the $v_2$ coefficient. The $v_2$ for heavy-flavor electrons is found to be positive with more than $5\\sigma$ significance, providing very strong indication of long-range azimuthal anisotropies for heavy-flavour particles in high multiplicity p--Pb collisions. This is the first measurement of the $v_2$ for electrons coming from heavy-flavor hadron decays in p--Pb collisions.

Slow sand filtration is a proven and sustainable technology for drinking water treatment in small communities. The process, however, is sensitive to lower water temperatures that can lead to decreased biological treatment, and high raw water turbidity levels that can lead to premature clogging of the filter and frequent cleaning requirements, resulting in increased risk of pathogen breakthrough. Multistage filtration, consisting of roughing filtration followed by slow sand filtration, can overcome these treatment limitations and provide a robust treatment alternative for surface water sources of variable water quality in northern climates, which typically experience water temperatures ranging down to 2&deg;C. Prior to this study, however, multistage filtration had yet to be systematically challenged in colder climates, including testing of its performance under increased hydraulic loadings and elevated influent turbidity together with cold water conditions. The primary goal of this research was to demonstrate the reliability of multistage filtration for small communities in northern climates with reference to the Ontario Safe Drinking Water Act. In this research, testing was conducted on two different pilot multistage filtration systems and fed with water from the Grand River, a municipally and agriculturally impacted river in Southern Ontario. One system featured pre-ozonation and post-granular activated carbon (GAC) stages, and shallower bed depths in the roughing filter and slow sand filter. The other system featured deeper bed depths in the roughing filter and slow sand filter, two parallel roughing filters of different design for comparison, and a second stage of slow sand filtration for increased robustness. Removal of turbidity, total coliforms, and fecal coliforms under a range of influent turbidities (1 to >100 NTU), water temperatures (~2 to 20&deg;C), and hydraulic loading rates (0. 2 to 0. 8 m/h) were investigated. In addition, the slow sand filters in each pilot system were challenged with high concentrations (~10⁶ oocyst/L) of inactivated <i>Cryptosporidium parvum</i> oocysts. The performance of both pilot multistage filtration systems was highly dependent on the biological maturity of the system and its hydraulic loading rate. In a less mature system operating in cold water conditions (<5&deg;C), effluent turbidity was mostly below 0. 5 NTU during periods of stable influent turbidity (no runoff events) and a hydraulic loading of 0. 4 m/h, however, runoff events of high influent turbidity (>50 NTU), increased hydraulic loadings (0. 6 m/h), and filter cleaning occasionally resulted in effluent turbidity above 1 NTU. Furthermore, in a less mature system operating during runoff events of high turbidity, reducing the hydraulic loading rate to 0. 2 m/h was important for achieving effluent turbidity below 1 NTU. However, in a more mature system operating in warm water conditions (19-22&deg;C), effluent turbidity was consistently below 0. 3 NTU at a hydraulic loading rate of 0. 4 m/h, and below 0. 5 NTU at 0. 8 m/h, despite numerous events of high influent turbidity (>25 NTU). It remains to be seen whether this performance could be sustained in colder water temperatures with a fully mature filter. Removal of coliform bacteria was occasionally incomplete in a less mature multistage system, whereas, in a more mature system operating in warm water conditions (>9&deg;C), removal was complete in all measurements. Furthermore, the average removal of <i>Cryptosporidium</i> was greater than 2. 5 logs in both systems (with hydraulic loading rates ranging from 0. 4 to 0. 8 m/h) and improved with increased filter maturity. Each individual stage of the multistage system was an important treatment barrier in the overall process of turbidity and pathogen removal. The roughing filter was not only important for protecting the slow sand filter from solids loading and increasing its run length, but was also a significant contributor to coliform removal when the system was less mature. Removal of turbidity was significantly improved when the roughing filter was more mature, suggesting that biological treatment was an important treatment mechanism in the roughing filter. Although pre-ozonation was used mainly for the removal of organic carbon and colour, it achieved complete removal of coliform bacteria and was also suspected to be important for enhanced removal of turbidity. The second slow sand filter in series provided additional robustness to the process by reducing effluent turbidity to below 1 NTU during cold water runoff events of high turbidity and increased hydraulic loadings (0. 6 m/h), while achieving effluent below 0. 3 NTU during normal periods of operation. It also provided additional removals of coliforms under challenging operating conditions, and contributed an additional average removal of <i>Cryptosporidium</i> of 0. 8 logs, which resulted in cumulative removal of 3. 7 logs, approximately 1 log greater than all the other challenge tests. Collectively, the entire multistage system performed well with water temperatures ranging down to 2&deg;C, limited filter maturity, elevated raw water turbidities, and increased hydraulic loading rates. Its ability to meet the current Ontario turbidity regulations and greater than 2 log removal of <i>Cryptosporidium</i> over a range of operating conditions, with little or no process adjustment, is a testament to the robustness and minimal maintenance requirements of the process, which are desirable attributes for small water systems that are often located in rural areas. While this research demonstrated the performance of multistage filtration using pilot scale testing, it is important to note that full-scale plants tend to produce significantly better results than pilot facilities, due to long term biological maturation of the system. Overall, multistage filtration is a sustainable and cost-effective technology that, through this research, appears to be a safe, reliable, and robust treatment alternative for small and non-municipal water systems in North America and the developing world. Further, based on its performance with challenging influent water quality and cold water conditions, multistage filtration holds particular promise for small communities in northern climates that are required to meet safe drinking water regulations, but are dependent on surface water sources of variable water quality and temperatures.

Slow sand filtration is a proven and sustainable technology for drinking water treatment in small communities. The process, however, is sensitive to lower water temperatures that can lead to decreased biological treatment, and high raw water turbidity levels that can lead to premature clogging of the filter and frequent cleaning requirements, resulting in increased risk of pathogen breakthrough. Multistage filtration, consisting of roughing filtration followed by slow sand filtration, can overcome these treatment limitations and provide a robust treatment alternative for surface water sources of variable water quality in northern climates, which typically experience water temperatures ranging down to 2&deg;C. Prior to this study, however, multistage filtration had yet to be systematically challenged in colder climates, including testing of its performance under increased hydraulic loadings and elevated influent turbidity together with cold water conditions. The primary goal of this research was to demonstrate the reliability of multistage filtration for small communities in northern climates with reference to the Ontario Safe Drinking Water Act. In this research, testing was conducted on two different pilot multistage filtration systems and fed with water from the Grand River, a municipally and agriculturally impacted river in Southern Ontario. One system featured pre-ozonation and post-granular activated carbon (GAC) stages, and shallower bed depths in the roughing filter and slow sand filter. The other system featured deeper bed depths in the roughing filter and slow sand filter, two parallel roughing filters of different design for comparison, and a second stage of slow sand filtration for increased robustness. Removal of turbidity, total coliforms, and fecal coliforms under a range of influent turbidities (1 to >100 NTU), water temperatures (~2 to 20&deg;C), and hydraulic loading rates (0. 2 to 0. 8 m/h) were investigated. In addition, the slow sand filters in each pilot system were challenged with high concentrations (~10⁶ oocyst/L) of inactivated <i>Cryptosporidium parvum</i> oocysts. The performance of both pilot multistage filtration systems was highly dependent on the biological maturity of the system and its hydraulic loading rate. In a less mature system operating in cold water conditions (<5&deg;C), effluent turbidity was mostly below 0. 5 NTU during periods of stable influent turbidity (no runoff events) and a hydraulic loading of 0. 4 m/h, however, runoff events of high influent turbidity (>50 NTU), increased hydraulic loadings (0. 6 m/h), and filter cleaning occasionally resulted in effluent turbidity above 1 NTU. Furthermore, in a less mature system operating during runoff events of high turbidity, reducing the hydraulic loading rate to 0. 2 m/h was important for achieving effluent turbidity below 1 NTU. However, in a more mature system operating in warm water conditions (19-22&deg;C), effluent turbidity was consistently below 0. 3 NTU at a hydraulic loading rate of 0. 4 m/h, and below 0. 5 NTU at 0. 8 m/h, despite numerous events of high influent turbidity (>25 NTU). It remains to be seen whether this performance could be sustained in colder water temperatures with a fully mature filter. Removal of coliform bacteria was occasionally incomplete in a less mature multistage system, whereas, in a more mature system operating in warm water conditions (>9&deg;C), removal was complete in all measurements. Furthermore, the average removal of <i>Cryptosporidium</i> was greater than 2. 5 logs in both systems (with hydraulic loading rates ranging from 0. 4 to 0. 8 m/h) and improved with increased filter maturity. Each individual stage of the multistage system was an important treatment barrier in the overall process of turbidity and pathogen removal. The roughing filter was not only important for protecting the slow sand filter from solids loading and increasing its run length, but was also a significant contributor to coliform removal when the system was less mature. Removal of turbidity was significantly improved when the roughing filter was more mature, suggesting that biological treatment was an important treatment mechanism in the roughing filter. Although pre-ozonation was used mainly for the removal of organic carbon and colour, it achieved complete removal of coliform bacteria and was also suspected to be important for enhanced removal of turbidity. The second slow sand filter in series provided additional robustness to the process by reducing effluent turbidity to below 1 NTU during cold water runoff events of high turbidity and increased hydraulic loadings (0. 6 m/h), while achieving effluent below 0. 3 NTU during normal periods of operation. It also provided additional removals of coliforms under challenging operating conditions, and contributed an additional average removal of <i>Cryptosporidium</i> of 0. 8 logs, which resulted in cumulative removal of 3. 7 logs, approximately 1 log greater than all the other challenge tests. Collectively, the entire multistage system performed well with water temperatures ranging down to 2&deg;C, limited filter maturity, elevated raw water turbidities, and increased hydraulic loading rates. Its ability to meet the current Ontario turbidity regulations and greater than 2 log removal of <i>Cryptosporidium</i> over a range of operating conditions, with little or no process adjustment, is a testament to the robustness and minimal maintenance requirements of the process, which are desirable attributes for small water systems that are often located in rural areas. While this research demonstrated the performance of multistage filtration using pilot scale testing, it is important to note that full-scale plants tend to produce significantly better results than pilot facilities, due to long term biological maturation of the system. Overall, multistage filtration is a sustainable and cost-effective technology that, through this research, appears to be a safe, reliable, and robust treatment alternative for small and non-municipal water systems in North America and the developing world. Further, based on its performance with challenging influent water quality and cold water conditions, multistage filtration holds particular promise for small communities in northern climates that are required to meet safe drinking water regulations, but are dependent on surface water sources of variable water quality and temperatures.

PIP3 dynamics observed in membranes are responsible for the protruding edge formation in cancer and amoeboid cells. The mechanisms that maintain those PIP3 domains in three-dimensional space remain elusive, due to limitations in observation and analysis techniques. Recently, a strong relation between the cell geometry, the spatial confinement of the membrane, and the excitable signal transduction system has been revealed by Hörning and Shibata (2019) using a novel 3D spatiotemporal analysis methodology that enables the study of membrane signaling on the entire membrane (Hörning and Shibata, 2019). Here, using 3D spatial fluctuation and phase map analysis on actin polymerization inhibited Dictyostelium cells, we reveal a spatial asymmetry of PIP3 signaling on the membrane that is mediated by the contact perimeter of the plasma membrane—the spatial boundary around the cell-substrate adhered area on the plasma membrane. We show that the contact perimeter guides PIP3 waves and acts as a pinning site of PIP3 phase singularities, that is, the center point of spiral waves. The contact perimeter serves as a diffusion influencing boundary that is regulated by a cell size- and shape-dependent curvature. Our findings suggest an underlying mechanism that explains how local curvature can favor actin polymerization when PIP3 domains get pinned at the curved protrusive membrane edges in amoeboid cells.