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

Industries (food, beverage, petrochemical, etc.) normally use various gravitational separation echniques in their processes. Such separation processes often suffer from the deposition of undesirable material on the active surfaces of the process equipment, e.g. a high-speed separator or decanter, causing a slew of problems with the process or product quality. To restore operational efficiencies, additional cleaning steps using both water and chemicals are required, making the process more expensive and less environmentally friendly. Other than operating time and concentration of the process fluid there are several factors such as surface nature, surface roughness, type of material, surface charge, etc which influence the fouling deposition of surfaces. Fouling on the surfaces can grow following different mechanisms. The goal of this research work is to learn more about the nature of foulant interactions with stainless steel surfaces and eventually design some antifouling methodology. It is too difficult to study foulingfor all kinds of solutions and industries, so we tried to investigate the organic deposition in dairy and brewery industries by using lab-scale synthesized milk and beer solutions, For quantitative and statistical examination of these characteristics, several experimental approaches (FTIR, percent weight change, surface roughness, surface energy) were used. It was confirmed that fouling grows on the surfaces in a non-linear fashion irrespective of the time and concentration of the solution. The fouling of surfaces can be improved by producing more hydrophilic surfaces or by reducing surface roughness. Steric hindrance, electrostatic charge, and water barrier or hydration layer theories can be used to modify the surface nature and hence the fouling deposition. For antifouling purposes, PMMA (organic) and tungsten oxide (inorganic) coatings were employed. The PMMA was deposited using a dip-coating technique using (6%,10%, and 12%) PMMA solution, and the tungsten oxide coating was carried out by using a standard two electrode electrochemical system under different voltage (3.5V and 4.5V) and time (5min, 10 min, and 20 min) conditions. The coatings were characterized by using different techniques and their antifouling effects were studied in model milk and model beer solutions / Vid industriella processer (livsmedel, petrokemisk etc.) används ofta olika tekniker för separation med hjälp av gravitation. Sådana separationsprocesser drabbas ofta av oönskade beläggningar och påväxt på processutrustningens aktiva ytor så som t.ex. i en separator eller en dekanter, vilket orsakar problem med processen eller produktkvaliteten. För att återställa driftseffektivitet krävs särskilda rengöringssteg med både vatten och kemikalier vilket gör processen dyrare och mindre miljövänlig. Förutom drifttid och processvätskans sammansättning finns det flera faktorer såsom ytbeskaffenhet, ytjämnhet, materialtyp, ytladdning m.m. som påverkar mängden oönskade beläggningar på ytor. Föroreningarna på ytor kan tillväxa med olika mekanismer. Målet med detta forskningsarbete är att studera interaktionen mellan olika former av påväxt och ytan på rostfritt stål och senare utforma metoder för att förhindra bildandet av sådana oönskade beläggningar. Det är en stor utmaning att studera olika typer av påväxt för alla typer av flöden och industrier. I studien undersöktes organisk påväxt inom mejeri- och bryggeriindustrin genom att använda syntetiserade mjölk- och ölprodukter i laboratorieskala, för kvantitativa och statistiska undersökningar av dessa egenskaper. Flera olika experimentella metoder användes (FTIR, viktförändring, ytjämnhet, ytenergi). Det bekräftades att tillväxten på ytorna var olinjärt oavsett tid och lösningens koncentration. Bildandet och tillväxt av oönskade beläggningar kan minskas med hjälp av mera hydrofila ytor eller genom att minska ytans ojämnhet. Steriska hinder, elektrostatisk laddning och vattenbarriär eller hydratiseringsskal kan användas för att modifiera ytan och därmed fördröja bildandet av oönskade beläggningar. För att förhindra påväxt belades ytan med PMMA (organisk) och volframoxid (oorganisk). PMMA deponerades genom en doppbeläggningsteknik med användning av (6%, 10% och 12%) PMMA-lösning och volframoxidbeläggningen utfördes med ett elektrokemiskt tvåelektrodssystem med olika spänningar (3,5V och 4,5V) och tider (5min, 10min och 20min). Ytbeläggningarna karakteriserades genom att använda olika tekniker och deras förmåga att förhindra snabb påväxt studerades i modellösningar av mjölk och öl.