Mott insulators are materials in which strong correlations among the electrons induce an unconventional insulating state. Rich interplay between the structural, magnetic, and electronic degrees of freedom resulting from the electron correlation can lead to unusual complexity of Mott materials on the atomic scale, such as microscopically heterogeneous phases or local structural correlations that deviate significantly from the average structure. Such behavior must be studied by suitable experimental techniques, i.e. "local probes", that are sensitive to this local behavior rather than just the bulk, average properties. In this thesis, I will present results from our studies of multiple families of Mott insulators using two such local probes: muon spin relaxation (muSR), a probe of local magnetism; and pair distribution function (PDF) analysis of x-ray and neutron total scattering, a probe of local atomic structure. In addition, I will present the development of magnetic pair distribution function analysis, a novel method for studying local magnetic correlations that is highly complementary to the muSR and atomic PDF techniques. We used muSR to study the phase transition from Mott insulator to metal in two archetypal Mott insulating systems: RENiO₃ (RE = rare earth element) and V₂O₃. In both of these systems, the Mott insulating state can be suppressed by tuning a nonthermal parameter, resulting in a "quantum" phase transition at zero temperature from the Mott insulating state to a metallic state. In RENiO₃, this occurs through variation of the rare-earth element in the chemical composition; in V₂O₃, through the application of hydrostatic pressure. Our results show that the metallic and Mott insulating states unexpectedly coexist in phase-separated regions across a large portion of parameter space near the Mott quantum phase transition and that the magnitude of the ordered antiferromagnetic moment remains constant across the phase diagram until it is abruptly destroyed at the quantum phase transition. Taken together, these findings point unambiguously to a first-order quantum phase transition in these systems. We also conducted x-ray and neutron PDF experiments, which suggest that the distinct atomic structures associated with the insulating and metallic phases similarly coexist near the quantum phase transition. These results have significant implications for our understanding of the Mott metal-insulator quantum phase transition in real materials. The second part of this thesis centers on the derivation and development of the magnetic pair distribution function (mPDF) technique and its application to the antiferromagnetic Mott insulator MnO. The atomic PDF method involves Fourier transforming the x-ray or neutron total scattering intensity from reciprocal space into real space to directly reveal the local atomic correlations in a material, which may deviate significantly from the average crystallographic structure of that material. Likewise, the mPDF method involves Fourier transforming the magnetic neutron total scattering intensity to probe the local correlations of magnetic moments in the material, which may exist on short length scales even when the material has no long-range magnetic order. After deriving the fundamental mPDF equations and providing a proof-of-principle by recovering the known magnetic structure of antiferromagnetic MnO, we used this technique to investigate the short-range magnetic correlations that persist well into the paramagnetic phase of MnO. By combining the mPDF measurements with ab initio calculations of the spin-spin correlation function in paramagnetic MnO, we were able to quantitatively account for the observed mPDF. We also used the mPDF data to evaluate competing ab initio theories, thereby resolving some longstanding questions about the magnetic exchange interactions in MnO.

Yip Kin Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 101-104). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- The Distribution of Fluctuations in Financial Data --- p.5 / Chapter 2.1 --- Empirical Statistics --- p.5 / Chapter 2.2 --- Data analyzed --- p.8 / Chapter 2.3 --- Levy Distribution --- p.10 / Chapter 2.4 --- Returns Distribution and Scaling Properties --- p.12 / Chapter 2.5 --- Volatility Clustering --- p.19 / Chapter 2.6 --- Conclusion --- p.21 / Chapter 3 --- Models of Herd behaviour in Financial Markets --- p.22 / Chapter 3.1 --- Cont and Bouchaud's model --- p.22 / Chapter 3.2 --- The Model of Egiuluz and Zimmerman --- p.24 / Chapter 3.3 --- EZ Model with Size-Dependent Dissociation Rates --- p.28 / Chapter 3.4 --- Democratic and Dictatorship Self-Organized Model --- p.31 / Chapter 3.5 --- Effect of Size-Dependent Fragmentation and Coagulation Prob- abilities --- p.33 / Chapter 3.6 --- Extensions of EZ model --- p.35 / Chapter 3.7 --- Conclusion --- p.39 / Chapter 4 --- Review on the Minority Game(MG) --- p.42 / Chapter 4.1 --- The Model and Results --- p.42 / Chapter 4.2 --- Crowd-anticrowd Theory and Phase Transition --- p.46 / Chapter 4.3 --- Market Efficiency --- p.48 / Chapter 5 --- MG with biased strategy pool --- p.52 / Chapter 5.1 --- The Model --- p.53 / Chapter 5.2 --- Numerical Results and Discussion --- p.53 / Chapter 5.3 --- Theory: MG with Biased Strategy Pool --- p.61 / Chapter 5.4 --- Conclusion --- p.69 / Chapter 6 --- MG with Randomly Participating Agents --- p.71 / Chapter 6.1 --- The Model with One RPA --- p.71 / Chapter 6.2 --- Results for q = 0.5 --- p.72 / Chapter 6.3 --- Inefficiency and Success Rate --- p.76 / Chapter 6.4 --- Results for q ≠ 0.5 --- p.82 / Chapter 6.5 --- Many RPAs --- p.85 / Chapter 6.6 --- Conclusion --- p.86 / Chapter 7 --- A Model on Coupled Minority Games --- p.88 / Chapter 7.1 --- The Model --- p.89 / Chapter 7.2 --- Results and Discussion。 --- p.90 / Chapter 7.3 --- Conclusion --- p.95 / Chapter 8 --- Conclusion --- p.97 / Bibliography --- p.101 / Chapter A --- Solving Cluster Size distribution in EZ model --- p.105

Yuen Yung Hui. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese. / Yuen Yung Hui.

Sung, Siu Chung = 鎂矽酸鹽(MgSiO₃)在核幔邊界條件下的第一性原理研究 / 宋紹聰. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 110-115). / Abstracts in English and Chinese. / Sung, Siu Chung = Mei xi suan yan (MgSiO₃) zai he man bian jie tiao jian xia de di yi xing yuan li yan jiu / Song Shaocong. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review on MgSiO3 --- p.5 / Chapter 2.1 --- Interior of the Earth --- p.5 / Chapter 2.1.1 --- The importance of MgSiO3 in geosciences --- p.6 / Chapter 2.1.2 --- "Anomalies in lower mantle, D"" layer and the core-mantle boundary" --- p.7 / Chapter 2.2 --- Review on experimental and theoretical studies on MgSiO3 --- p.9 / Chapter 2.2.1 --- The perovskite structure --- p.9 / Chapter 2.2.2 --- MgSiO3 pv --- p.12 / Chapter 2.3 --- ppv structure --- p.14 / Chapter 2.3.1 --- MgSiO3 ppv --- p.15 / Chapter 2.3.2 --- MgSiO3 liquid --- p.18 / Chapter 3 --- Physical quantities in geoscience and molecular dynamics sim- ulations --- p.20 / Chapter 3.1 --- Equation of state --- p.21 / Chapter 3.2 --- Gruneisen parameter --- p.22 / Chapter 3.3 --- Thermoelasticity --- p.22 / Chapter 3.4 --- Phase transition --- p.24 / Chapter 3.5 --- Correlation function --- p.25 / Chapter 3.5.1 --- Pair Distribution function --- p.25 / Chapter 3.5.2 --- Coordination number --- p.27 / Chapter 3.5.3 --- Time correlation function and mean square displacement --- p.27 / Chapter 3.6 --- Seismic velocities --- p.28 / Chapter 4 --- Theoretical Methods --- p.30 / Chapter 4.1 --- Density Functional Theory --- p.30 / Chapter 4.2 --- Approximating exchange-correlation energy functional --- p.33 / Chapter 4.3 --- Car-Parrinello Molecular Dynamics --- p.34 / Chapter 4.4 --- Variable cell dynamics --- p.36 / Chapter 4.5 --- Nose-Hoover Thermostat --- p.37 / Chapter 5 --- Simulation method and details --- p.39 / Chapter 5.1 --- Structure at 0 K --- p.40 / Chapter 5.1.1 --- Initialization of simulation cells --- p.40 / Chapter 5.1.2 --- Convergence test --- p.41 / Chapter 5.1.3 --- "Electronic minimization, fictitious electronic mass and time step" --- p.42 / Chapter 5.2 --- Electronic and ionic minimization --- p.43 / Chapter 5.3 --- Cell optimization and structure at 0 K --- p.44 / Chapter 5.3.1 --- Optimized simulation cell of pv and ppv --- p.44 / Chapter 5.4 --- Equation of state and stability of solid --- p.46 / Chapter 5.5 --- Melting --- p.48 / Chapter 5.6 --- Statistical average --- p.50 / Chapter 6 --- MgSiO3 perovskite and post-perovskite at CMB conditions --- p.51 / Chapter 6.1 --- Equations of state of pv and ppv at 0 K --- p.51 / Chapter 6.2 --- Enthalpy of pv and ppv at 0 K --- p.54 / Chapter 6.3 --- Equations of state of pv and ppv at different temperatures --- p.55 / Chapter 6.4 --- Fluctuation of stress components of pv and ppv --- p.59 / Chapter 6.5 --- Pair distribution function of pv and ppv --- p.61 / Chapter 6.5.1 --- Pair distribution function at different temperatures with similar cell volume --- p.61 / Chapter 6.5.2 --- Pair distribution function at 4000 K and different volumes --- p.66 / Chapter 6.5.3 --- Pair distribution function at 6000 K and different volumes --- p.70 / Chapter 6.5.4 --- Coordination numbers --- p.74 / Chapter 7 --- Liquid structure at CMB conditions --- p.78 / Chapter 7.1 --- Equations of state of liquid --- p.78 / Chapter 7.2 --- Stress components of liquid --- p.80 / Chapter 7.3 --- Pair distribution function of liquid --- p.83 / Chapter 7.4 --- Coordination numbers of liquid --- p.88 / Chapter 7.4.1 --- Mean square displacement --- p.88 / Chapter 8 --- Phase diagram of MgSiO3 --- p.92 / Chapter 8.1 --- Pressure-temperature relations --- p.92 / Chapter 8.1.1 --- Enthalpy --- p.94 / Chapter 8.2 --- Internal energy --- p.96 / Chapter 8.3 --- Phase boundaries and phase diagram --- p.99 / Chapter 9 --- Discussions --- p.105 / Chapter 9.1 --- Phase diagram --- p.105 / Chapter 9.2 --- LDA vs GGA --- p.107 / Chapter 9.3 --- Pv and ppv at low pressure --- p.107 / Chapter 9.4 --- Two-phase method --- p.108 / Bibliography --- p.110 / Chapter A --- Rotation and shape optimization --- p.116

ii ABSTRACT Percolation phenomena involving the electrical conductivity, dielectric constant, Hall coefficient, magnetoconductivity, relative magnetoresistivity, 1/ f noise and thermoelectric power are investigated in graphite (G) and hexagonal boron-nitride (BN) powder mixtures. Two kinds of systems are used in the experiments: highly compressed discs and parallelepipeds, cut from these discs, as well as 50%G-50%BN and 55%G-45%BN powder mixtures undergoing compression. The measured DC conductivities follow the power-laws 0"( <p, 0) ex: (<p-<Pc)t (<p > <Pc) and O"(<p, 0) ex: (<Pc-<Pti (<p < <Pc), and the low frequency (lOOHz & 1000Hz) dielectric constant varies as c( <p, W ~ 0) ex: (<Pc - <P )-S( <P < <Pc), where <Pc is the percolation threshold, t and s are the conductivity exponents, and s is the dielectric exponent. Near the percolation threshold and at high frequencies, the AC conductivity varies with frequency as 0"( <p, w) ex: WX and the AC dielectric constant varies as c( <p, w) ex: w-Y, where the exponents x and y satisfy the scaling relation x + y = 1. The crossover frequency We scales with DC conductivity as Wc ex: O"q( <p, 0) (<p > <Pc), while on the insulating side, Wc ~ 1, resulting in q ~O for the three G-BN systems. The loss tangent tan t5( <p, w) (<p < <Pc) is found to have a global minimum, in contrary to the results of computer simulations. The Hall constant could not be measured using existing instrumentation. The measured magnetoconductivity and relative magnetoresistivity follow the power-laws - 6. 0" ex: (<p - <Pc)3.08 and 6.R/ R ex: (<p - <Pc)O.28 respectively. These two exponents, iii 3.08 and 0.28, are not in agreement with theory. The 1/ f noise was measured for the conducting discs and parallelepipeds. The normalized 1/ f noise power varies as Sv I V2 ex RW with the exponents w = 1.47 and 1.72 for the disc and parallelepiped samples respectively. Furthermore, the normalized noise power near the percolation threshold is, for the first time, observed to vary inversely with the square-root of sample volume. Based on the Milgrom-Shtrikman-Bergman-Levy (MSBL) formula, thermoelectric power of a binary composite is shown to be a linear function of the WiedemanFranz ratio. A scaling scheme for the Wiedeman-Franz ratio for percolation systems is proposed, which yields power-law behavior for the thermoelectric power. The proposed power-laws for the thermoelectric power can be written as (Sm - Md ex (<p - <Pc)h 1 for <P > <Pc and as (Sm - /~1d ex (<Pc - <p)-h2 for <p < <Pc, where Sm is the thermoelectric power for the composites, Afl is a constant for a given percolation system, and hI and h2 are the two critical exponents. The experimental thermoelectric power data for the G-BN conducting parallelepipeds was fitted to the above powerlaw for <p > <Pc. A least squares fit yielded the exponent hI = -1.13 and parameter MI =9.511l V I I< respectively.

A Thermal Energy Storage (TES) system is meant for holding thermal energy in the form of hot or cold materials for later utilization. A TES system is an important technological system in providing energy savings as well as efficient and optimum energy use. The main types of a TES system are sensible heat and latent heat. A latent heat storage is a very efficient method for storing or releasing thermal energy due to its high energy storage density at constant temperatures, and a latent heat storage material can store 5-14 times more heat per unit volume than a sensible heat storage material can. Phase Change Materials (PCMs) are called latent heat storage materials. PCMs can save thermal energy, and use energy efficiently because PCMs can absorb thermal energy in the solid state, and the thermal energy can be released in the liquid state. Therefore, PCMs as new materials for saving energy can be applied into building applications. PCMs have been widely researched, but the current issues are lack of accurate and detailed information about thermophysical properties of PCMs to apply to buildings and inaccurate materials properties measured by existing methodology. The objective of this study is to develop a methodology and procedure to accurately determine the thermophysical properties of PCMs based on salt hydrates. TES systems of PCMs are measured and analyzed by various methods, such as DSC method and heat flow method. In addition, this study demonstrates to design a building roof with PCMs to save energy using Finite Element Analysis (FEA). The developed methodology is designed based on ASTM C1784-14, Standard Test Method for Using a Heat Flow Meter Apparatus for Measuring Thermal Storage Properties of Phase Change Materials and Products, for measuring the thermal energy storage properties of PCMs. The thermophysical properties and thermal stabilities are evaluated by using a Differential Scanning Calorimetry (DSC), which is made with DSC Q 200 equipment from TA Instruments and DSC STA 8000 equipment from Perkin Elmer Company. The thermal conductivities are assessed by heat flow meter, which is FOX 314 equipment from TA Instruments, and the enthalpy changes of the PCMs are determined by DSC method and heat flow method. Numerical FEA to evaluate potential energy savings is conducted using ABAQUS software. Four types of Phase Change Materials (PCMs), which have phase changes at 21ºC, 23ºC, 26ºC, and 30ºC, respectively, are used for measuring the thermophysical properties. The onset/peak temperature, the enthalpy, the heat flow, and the heat capacity of the PCMs are measured to assess the thermal energy storage system under the dynamic DSC mode. The results obtained using DSC equipment have a higher melting temperature than their own temperatures, which are known theoretically. The freezing temperatures of the PCMs are decreased by about 30ºC ~ 40ºC compare to their theoretical freezing temperatures. It is speculated that supercooling happens during the solidification. The enthalpy change curves as a function of temperature, which are determined by DSC method and heat flow method, are indicated to assess thermal energy storage system of the PCMs. During the phase change, the energy is increased. This is the reason why the energy is utilized to loosen or break apart the molecular or atomic bond structures of the PCMs by the latent heat. Moreover, the enthalpy change curves determined by heat flow method show more precise results than the curves by DSC method, because various factors lead to a temperature gradient in the PCM and the heat flux signal peak being shifted toward high temperatures. Regarding the thermal conductivities results of the PCMs, the thermal conductivities of the PCMs in the solid state are higher than those of the PCMs in the liquid state. This phenomenon happens due to the effect of the microstructure changing from the orderly solid structure in the solid state to the disorderly liquid structure in the liquid state. The numerical Finite Element Analysis (FEA) is conducted to evaluate potential energy savings of a roof. The results, such as the temperature variations from the outdoor to indoor measured under step 1 (the daytime) condition, show that the outdoor temperatures are higher than the indoor temperatures. This is due to the low thermal conductivity of the PCM in the liquid state. The low thermal conductivity of the PCM reduces the heat transmission to the indoor that in turn increases the outdoor temperature. This study shows the developed methodology and procedure, the accurate material information for the newly developed PCM, and the numerical FEA to analyze the TES systems with much more precision in the area of the PCMs.

During the operation of phase-change ink-jet printers a bubble formation phenomenon often occurs. These bubbles are detrimental to the operation of the printer and substantial efforts are made to remove them. The objective of this research was 1: to develop a fundamental understanding of how bubble or void formation occurs during the phase-change process, and, 2: to develop a simple computer model to simulate this behavior which can then be used as a tool for better design of print-head geometries. Preliminary experimental work indicated the void formation to be a result of the density change accompanying the phase-change process. The commercial numerical code, Flow 3-D, was used to model the phase-change process in print-head geometries and substantiate certain simplifying assumptions. These assumptions included the effect of convection on the process and the effect of the varying material properties. For channel sizes less than 0.5 cm the phase-change process was found to be a pure conduction process. Convection effects are thus negligible and can be eliminated from the model. The variability of density, specific heat and thermal conductivity must be included in the model, as they affect the phase-change process dramatically. Specific heat is the most influential of the properties and determines, along with the conductivity, the rate at which the phase change takes place. The density must be included since it is directly linked to the void formation. / Graduation date: 1994

In the living cell, the organization of the complex internal structure relies to a large extent on molecular motors. Molecular motors are proteins that are able to convert chemical energy from the hydrolysis of adenosine triphosphate (ATP) into mechanical work. Being about 10 to 100 nanometers in size, the molecules act on a length scale, for which thermal collisions have a considerable impact onto their motion. In this way, they constitute paradigmatic examples of thermodynamic machines out of equilibrium. This study develops a theoretical description for the energy conversion by the molecular motor myosin V, using many different aspects of theoretical physics. Myosin V has been studied extensively in both bulk and single molecule experiments. Its stepping velocity has been characterized as a function of external control parameters such as nucleotide concentration and applied forces. In addition, numerous kinetic rates involved in the enzymatic reaction of the molecule have been determined. For forces that exceed the stall force of the motor, myosin V exhibits a 'ratcheting' behaviour: For loads in the direction of forward stepping, the velocity depends on the concentration of ATP, while for backward loads there is no such influence. Based on the chemical states of the motor, we construct a general network theory that incorporates experimental observations about the stepping behaviour of myosin V. The motor's motion is captured through the network description supplemented by a Markov process to describe the motor dynamics. This approach has the advantage of directly addressing the chemical kinetics of the molecule, and treating the mechanical and chemical processes on equal grounds. We utilize constraints arising from nonequilibrium thermodynamics to determine motor parameters and demonstrate that the motor behaviour is governed by several chemomechanical motor cycles. In addition, we investigate the functional dependence of stepping rates on force by deducing the motor's response to external loads via an appropriate Fokker-Planck equation. For substall forces, the dominant pathway of the motor network is profoundly different from the one for superstall forces, which leads to a stepping behaviour that is in agreement with the experimental observations. The extension of our analysis to Markov processes with absorbing boundaries allows for the calculation of the motor's dwell time distributions. These reveal aspects of the coordination of the motor's heads and contain direct information about the backsteps of the motor. Our theory provides a unified description for the myosin V motor as studied in single motor experiments. / Die hier vorgelegte Arbeit entwickelt unter Verwendung vieler verschiedener Aspekte der statistischen Physik eine Theorie der chemomechanischen Kopplung für den Energieumsatz des molekularen Motors Myosin V. Das Myosin V ist sowohl in chemokinetischen wie in Einzelmolekülexperimenten grundlegend untersucht worden. Seine Schrittgeschwindigkeit ist in Abhängigkeit verschiedener externer Parameter, wie der Nukleotidkonzentration und einer äußeren Kraft, experimentell bestimmt. Darüber hinaus ist eine große Anzahl verschiedener chemokinetischer Raten, die an der enzymatischen Reaktion des Moleküls beteiligt sind, quantitativ erfasst. Unter der Wirkung externer Kräfte, die seine Anhaltekraft überschreiten, verhält sich der Motor wie eine Ratsche: Für Kräfte, die entlang der Schrittbewegung des Motors wirken, hängt seine Geschwindigkeit von der ATP-Konzentration ab, für rückwärts angreifende Kräfte jedoch ist die Bewegung des Motors unabhängig von ATP. Auf der Grundlage der chemischen Zustände des Motors wird eine Netzwerktheorie aufgebaut, die die experimentellen Beobachtungen des Schrittverhaltens für Myosin V einschließt. Diese Netzwerkbeschreibung dient als Grundlage für einen Markovprozess, der die Dynamik des Motors beschreibt. Die Verwendung diskreter Zustände bietet den Vorteil der direkten Erfassung der chemischen Kinetik des Moleküls. Darüber hinaus werden chemische und mechanische Eigenschaften des Motors in gleichem Maße im Modell berücksichtigt. Durch die Erfassung der Enzymkinetik mittels eines stochastischen Prozesses lässt sich die Motordynamik mit Hilfe des stationären Zustands der Netzwerkdarstellung beschreiben. Um diesen zu bestimmen, verwenden wir eine graphentheoretische Methode, die auf Kirchhoff zurückgreift. Wir zeigen in Einklang mit den Gesetzen der Thermodynamik für Nichtgleichgewichtssysteme, dass das Schrittverhalten des Motors von mehreren chemomechanischen Zyklen beeinflusst wird. Weiterhin untersuchen wir das funktionale Verhalten mechanischer Schrittraten in Abhängigkeit der äußeren Kraft unter Verwendung einer geeigneten Fokker-Planck-Gleichung. Hierfür wird auf die Theorie einer kontinuierlichen Beschreibung von molekularen Methoden zurückgegriffen. Wir berechnen Größen wie die mittlere Schrittgeschwindigkeit, das Verhältnis von Vorwärts- und Rückwärtsschritten, und die Lauflänge des Motors in Abhängigkeit einer äußeren angreifenden Kraft sowie der Nukleotidkonzentration, und vergleichen diese mit experimentellen Daten. Für Kräfte, die kleiner als die Anhaltekraft des Motors sind, unterscheidet sich der chemomechanische Zyklus grundlegend von demjenigen, der für große Kräfte dominiert. Diese Eigenschaft resultiert in einem Schrittverhalten, das mit den experimentellen Beobachtungen übereinstimmt. Es ermöglicht weiterhin die Zerlegung des Netzwerks in einzelne Zyklen, die die Bewegung des Motors für verschiedene Bereiche externer Kräfte erfassen. Durch die Erweiterung unseres Modells auf Markovprozesse mit absorbierenden Zuständen können so die Wartezeitenverteilungen für einzelne Zyklen des Motors analytisch berechnet werden. Sie erteilen Aufschluss über die Koordination des Motors und enthalten zudem direkte Informationen über seine Rückwärtsschritte, die experimentell nicht erfasst sind. Für das gesamte Netzwerk werden die Wartezeitenverteilungen mit Hilfe eines Gillespie-Algorithmus bestimmt. Unsere Theorie liefert eine einheitliche Beschreibung der Eigenschaften von Myosin V, die in Einzelmolekülexperimenten erfasst werden können.

Phase transitions and their critical scaling properties, especially in systems with disorder, are important both for our theoretical understanding of our environment, but also for their practical use in applications and materials in our everyday life. This thesis presents results from finite size scaling analysis of critical phenomena in systems with disorder, using high-precision Monte Carlo simulations and state of the art numerical methods. Specifically, theoretical models suitable for simulations in the presence of uncorrelated or correlated disorder are studied. Uncorrelated strong disorder, as present in the two dimensional gauge glass model to study the vortex glass phase of high temperature superconductors in an applied magnetic field is shown to lack a finite temperature phase transition. Further, results from dynamic quantities, such as resistance and autocorrelation functions, indicate the existence of two distinct diverging correlation times, one associated with local relaxation and one associated with vortex phase slips. Correlated disorder is studied both in the superfluid transition of helium-4 and in the anisotropic critical scaling of a transverse Meissner-like transition in an experimental setup of a high temperature superconductor. For the superfluid helium transition, it is shown that the presence of fractally correlated disorder presumably alters the universality class of the pure model. Also, a comparison with experimental data suggests that the critical scaling theory describing the heat capacity of helium-4 may need to be modified in the presence of the disorder. In the case of superconductors, analyzing experimental data from resistance measurements in a system with columnar defects together with an anisotropy in the applied magnetic field, reveals a fully anisotropic scaling regime. Finally, a data analysis is presented from simulations of a charged particle gas system in three dimensions, where the normal Coulomb interaction between charges is changed into a logarithmic interaction. Previous work indicates the possibility of a transition similar to the Kosterlitz-Thouless transition in certain two dimensional systems. On the contrary, our simulations seem to favor a system whose critical scaling behavior is consistent with a transition occurring only at zero critical temperature. Overall, disorder in the model systems studied leads to important modifications of the critical scaling properties of pure systems, and thereby also to possible changes of the corresponding universality classes. This results in interesting predictions with experimentally relevant consequences. / QC 20100811

Complex systems are neither perfectly regular nor completely random. They consist of a multitude of players who, in many cases, playtogether in a way that makes their combined strength greater than the sum of their individual achievements. It is often very effective to represent these systems as networks where the actual connections between the players take on a crucial role.Networks exist all around us and are an important part of our world, from the protein machinery inside our cells to social interactions and man-madecommunication systems. Many of these systems have developed over a long period of time and are constantly undergoing changes driven by complicated microscopic events. These events are often too complicated for us to accurately resolve, making the world seem random and unpredictable. There are however ways of using this unpredictability in our favor by replacing the true events by much simpler stochastic rules giving effectively the same outcome. This allows us to capture the macroscopic behavior of the system, to extract important information about the dynamics of the system and learn about the reason for what we observe. Statistical mechanics gives the tools to deal with such large systems driven by underlying random processes under various external constraints, much like how intracellular networks are driven by random mutations under the constraint of natural selection.This similarity makes it interesting to combine the two and to apply some of the tools provided by statistical mechanics on biological systems.In this thesis, several null models are presented, with this view point in mind, to capture and explain different types of structural properties of real biological networks. The most recent major transition in evolution is the development of language, both spoken and written. This thesis also brings up the subject of quantitative linguistics from the eyes of a physicist, here called linguaphysics. Also in this case the data is analyzed with an assumption of an underlying randomness. It is shown that some statistical properties of books, previously thought to be universal, turn out to exhibit author specific size dependencies. A meta book theory is put forward which explains this dependency by describing the writing of a text as pulling a section out of a huge, individual, abstract mother book. / Komplexa system är varken perfekt ordnade eller helt slumpmässiga. De består av en mängd aktörer, som i många fall agerar tillsammans på ett sådant sätt att deras kombinerade styrka är större än deras individuella prestationer. Det är ofta effektivt att representera dessa system som nätverk där de faktiska kopplingarna mellan aktörerna spelar en avgörande roll. Nätverk finns överallt omkring oss och är en viktig del av vår värld , från proteinmaskineriet inne i våra celler till sociala samspel och människotillverkade kommunikationssystem.Många av dessa system har utvecklats under lång tid och genomgår hela tiden förändringar som drivs på av komplicerade småskaliga händelser.Dessa händelser är ofta för komplicerade för oss att noggrant kunna analysera, vilket får vår värld att verka slumpmässig och oförutsägbar. Det finns dock sätt att använda denna oförutsägbarhet till vår fördel genom att byta ut de verkliga händelserna mot mycket enklare regler baserade på sannolikheter, som ger effektivt sett samma utfall. Detta tillåter oss att fånga systemets övergripande uppförande, att utvinna viktig information om systemets dynamik och att få kunskap om anledningen till vad vi observerar. Statistisk mekanik hanterar stora system pådrivna av sådana underliggande slumpmässiga processer under olika restriktioner, på liknande sätt som nätverk inne i celler drivs av slumpmässiga mutationer under restriktionerna från naturligt urval. Denna likhet gör det intressant att kombinera de två och att applicera de verktyg som ges av statistisk mekanik på biologiska system. I denna avhandling presenteras flera nollmodeller som, baserat på detta synsätt, fångar och förklarar olika typer av strukturella egenskaper hos verkliga biologiska nätverk. Den senaste stora evolutionära övergången är utvecklandet av språk, både talat och skrivet. Denna avhandling tar också upp ämnet om kvantitativ linguistik genom en fysikers ögon, här kallat linguafysik. även i detta fall så analyseras data med ett antagande om en underliggande slumpmässighet. Det demonstreras att vissa statistiska egenskaper av böcker, som man tidigare trott vara universella, egentligen beror på bokens längd och på författaren. En metaboksteori ställs fram vilken förklarar detta beroende genom att beskriva författandet av en text som att rycka ut en sektion ur en stor, individuell, abstrakt moderbok.