Lattice simulations are a popular tool for studying the non-perturbative physics of nonlinear field theories. To perform accurate lattice simulations, a careful account of the discretization error is necessary. Spatial discretization error as a result of lattice spacing dependence in Langevin simulations of anisotropic (2 + 1)-dimensional classical scalar field theories is studied. A transfer integral operator (TIO) method and a one-loop renormalization (1LR) procedure are used to formulate effective potentials. The effective potentials contain counterterms which are intended to suppress the lattice spacing dependence. The two effective potentials were tested numerically in the case of a phi-4 model. A high accuracy modified Euler method was used to evolve a phenomenological Langevin equation. Large scale Langevin simulations were performed in parameter ranges determined to be appropriate. Attempts at extracting correlation lengths as a means of determining effectiveness of each method were not successful. Lattice sizes used in this study were not of a sufficient size to obtain an accurate representation of thermal equilibrium. As an alternative, the initial behaviour of the ensemble field average was observed. Results for the TIO method showed that it was successful at suppressing lattice spacing dependence in a mean field limit. Results for the 1LR method showed that it performed poorly.

Doctor of Philosophy / First part of the thesis is focused on experimental preparation of new hard quaternary amorphous materials Si-B-C-N with high thermal stability. Materials were prepared in the form of thin films using reactive magnetron sputtering. The technique used proved to be suitable for reproducible synthesis of these materials. The Si-B-C-N films were generally found to be amorphous with low compressive stress and good adhesion to silicon or glass substrates. The process and film characteristics were controlled by varying the sputter target composition, the Ar fraction in the N2–Ar gas mixture, the negative rf-induced substrate bias, and the substrate temperature. Main conclusions describe the relationships between process parameters, discharge and deposition characteristics and film properties (elemental composition, chemical bonding structure, material hardness, compressive stress or electrical conductivity of materials prepared). Second part of the thesis is focused on ab-initio simulations of structures of experimentally prepared Si-B-C-N materials. In the performed liquid-quench simulations, the Kohn-Sham equations for the valence electrons are expanded in a basis of plane wave functions, while core electrons were represented using Goedecker-type pseudopotentials. We simplified the ion bombardment process by assuming that the primary impact creates a localized molten region of high temperature and sufficiently short cooling time, commonly referred to as a thermal spike. Main conclusions deal with N2 formation in studied materials, effect of implanted Ar on structure and properties of prepared materials, ability of Si to relieve that part of compressive stress which is caused by implanted Ar, and ability of B to improve thermal stability of Si-B-C-N materials. The calculated results are compared with experiment.

Asymmetrical dispersal is when dispersal rates differ in opposite directions. This is expected to be common in natural populations. This work aims to study the symmetrical and asymmetrical dispersal through the use of a simulation program, simuPOP. The main questions were (i) "what are the differences between asymmetrical and symmetrical dispersal in relation to genetic differentiation and equilibrium?" and (ii) "Is it possible to identify asymmetrical dispersal structure from observed patterns of genetic differentiation between populations, and variation within populations?". To address these questions, simulations were conducted with two and three subpopulations subject by three different dispersal rate contrasts and several spatial patterns of dispersal. Variables were estimated at drift-dispersal equilibrium included genetic differentiation between subpopulations (θ) and heterozygosity. With pairwise θ for three subpopulations it was possible to determine whether the metapopulations were subject to symmetrical or asymmetrical dispersal and sometimes to identify the structure of dispersal. Equilibrium heterozygosities did not aid diagnosis of asymmetrical dispersal patterns. I also checked the applicability of two predictions originally made for symmetrical dispersal: Wright's expectations for θ at equilibrium, and Whitlock's expectations fro time to half of equilibrium θ. In most cases these expectations were not applicable. Study of asymmetrical dispersal on living organisms is strongly encouraged.

Η παρούσα εργασία μελετά τα θερμικά ανοίγματα της διπλής έλικας του βιοπολυμερούς DNA χρησιμοποιώντας προσομοιώσεις Monte Carlo σε θερμοκρασία 310 K. Οι υπολογισμοί βασίζονται στο φαινομενολογικό μοντέλο των Peyrand, Bishop και Dauxois καθώς και στον αλγόριθμο των Metropolis et al. Το πρώτο κεφάλαιο της εργασίας αφιερώνεται σε γενικές πληροφορίες γύρω από την δομή και τις λειτουργίες του γεννετικού υλικού. Επιπλέον περιέχει πληροφορίες γύρω από την μεταγραφή του DNA στα προκαρυωτικά κύτταρα. Επειδή σκοπός της εργασίας είναι η διερεύνηση της συσχέτισης μεταξύ μεγάλων θερμικών ανοιγμάτων και θέσεων του βακτηριακού DNA που εμφανίζουν βιολογική λειτουργία (σημεία πρόσδεσης της RNA-πολυμεράσης και διαφόρων βοηθητικών μεταγραφικών παραγόντων) σε διάφορους υποκινητές οπερονίων του βακτηρίου της E.coli, γίνεται μια πιο λεπτομερής συζήτηση για τον τρόπο με τον οποίο τα οπερόνια αυτά επιτυγχάνουν τον έλεγχο της εκφρασής τους. Το δεύτερο κεφάλαιο αναφέρεται στο θεωρητικό υπόβαθρο της εργασίας. Γίνεται μια εκτεταμένη συζήτηση γύρω από τις προσομοιώσεις Monte Carlo και πιο συγκεκριμένα του κριτηρίου των Metropolis et al. Στο ίδιο κεφάλαιο γίνεται παρουσίαση του μοντέλου των Peyrand, Bishop και Dauxois. Στο μοντέλο αυτό η δυναμική ενέργεια του συστήματος αποτελείται από δυο όρους. Ο ένας αναφέρεται στην αλληλεπίδραση μεταξύ των βάσεων ενός ζεύγους βάσης, ενώ ο άλλος στην αλληλεπίδραση μεταξύ των γειτονικών ζευγών βάσεων εξαιτίας της επικάλυψης των π μοριακών τροχιακών κάθε ζεύγους. Το μοντέλο επικεντρώνεται στον πιο προφανή βαθμό ελευθερίας του συστήματος: τη θερμικά ευαίσθητη (εξαιτίας των δεσμών υδρογόνου) απομάκρυνση μεταξύ των βάσεων ενός ζεύγους βάσης. Το τρίτο κεφάλαιο συγκροτείται από τα αποτελέσματα των υπολογισμών και τον σχολιασμό τους. Αρχικά παρουσιάζονται αποτελέσματα για απλούστερα συστήματα ταλαντωτών που αποτελούν οριακές περιπτώσεις του μοντέλου που περιγράφει το πρόβλημα των ανοιγμάτων της διπλής έλικας του DNA, όπως τα συστήματα των μονοδιάστατων ασύνδετων και συνδεδεμένων αρμονικών ταλαντωτών και το μονοδιάστατο σύστημα ανεξάρτητων ταλαντωτών Morse. Ακόμη παρουσιάζονται αποτελέσματα προσομοιώσεων σε τυχαίες αλληλουχίες DNA που δεν σχετίζονται με κανέναν υποκινητή. Το κύριο μέρος του κεφαλαίου αυτού αφιερώνεται στην παράθεση και στον σχολιασμό των αποτελεσμάτων των προσομοιώσεων για τους υποκινητές των τεσσάρων οπερονίων του βακτηρίου E.coli που εξετάστηκαν: της λακτόζης, της τρυπτοφάνης, της γαλακτόζης και της πρωτείνης recA. Επίσης εξετάζονται και οι υποκινητές των γονιδίων AdMLP και AAV P5 αδενοιών. Στο τελευταίο κεφάλαιο της εργασίας αυτής παρουσιάζονται τα συμπεράσματα που εξήχθησαν. / This essay concentrates on studying thermal openings of biopolymer DNA using Monte Carlo simulations based on a microscopic model proposed by Peyrand, Bishop and Dauxois. The fist part of this work includes a brief discussion about the structure of the double helix of DNA and it’s main functions. Moreover in the same part of the assay the transcription regulation of the operons that are studied in our calculations is discussed. The used Peyrand, Bishop, and Dauxois model takes into account only the transverse stretching of the hydrogen bonds connecting complementary bases of the double stranded DNA. The potential energy of the model includes the potential energy between complementary bases and the stacking interactions between successive base-pairs. The Metropolis algorithm is used to produce equilibrium configurations of the double strand at temperature of 310 K. The Peyrand, Bishop and Dauxois model and the Metropolis method are described in the second chapter of this thesis. After equilibration, several other realizations (with numerous Monte Carlo steps, based on the Metropolis algorithm) are performed in order to measure the local probabilities for large openings and compare them with functional positions in specific promoter segments of biological interest (e.g. transcription starting sites, binding sites for regulatory proteins). The main goal of this project is to investigate several bacterial DNA gene promoter segments and to examine whether large openings occur with higher probability at biological functional sites. In particular we have examined the following operons: lac, tryptophane, gal, recA and the viral promoters AdMPL and AAV P5. Our results are compared with the binding sites of the RNA-polymerase and the regulatory proteins of each promoter. In addition, the results for the viral promoters have been compared with other theoretical results and experimental data. The presentation of our results takes place in the third chapter of the dissertation. Apart from the results that refer to the E.coli operons and the viral promoters, we also present calculations in simpler systems such as one dimensional chains of harmonic or Morse oscillators. Finally in the fourth chapter we present our conclusions.

abstract: Thin films of ever reducing thickness are used in a plethora of applications and their performance is highly dependent on their microstructure. Computer simulations could then play a vital role in predicting the microstructure of thin films as a function of processing conditions. FACET is one such software tool designed by our research group to model polycrystalline thin film growth, including texture evolution and grain growth of polycrystalline films in 2D. Several modifications to the original FACET code were done to enhance its usability and accuracy. Simulations of sputtered silver thin films are presented here with FACET 2.0 with qualitative and semi-quantitative comparisons with previously published experimental results. Comparisons of grain size, texture and film thickness between simulations and experiments are presented which describe growth modes due to various deposition factors like flux angle and substrate temperature. These simulations provide reasonable agreement with the experimental data over a diverse range of process parameters. Preliminary experiments in depositions of Silver films are also attempted with varying substrates and thickness in order to generate complementary experimental and simulation studies of microstructure evolution. Overall, based on the comparisons, FACET provides interesting insights into thin film growth processes, and the effects of various deposition conditions on thin film structure and microstructure. Lastly, simple molecular dynamics simulations of deposition on bi-crystals are attempted for gaining insight into texture based grain competition during film growth. These simulations predict texture based grain coarsening mechanisms like twinning and grain boundary migration that have been commonly reported in FCC films. / Dissertation/Thesis / Ph.D. Materials Science and Engineering 2011

In this thesis we employ computer simulations and statistical physics to understand the origin of liquid-liquid phase transitions and their relationship with anomalies typical of liquid water. Compared with other liquids, water has many anomalies. For example the density anomaly: when water is cooled below 4 C the density decreases rather than increases. This and other anomalies have also been found to occur in a few other one-component liquids, sometimes in conjunction with the existence of a liquid-liquid phase transition (LLPT) between a low-density liquid (LDL) and a high-density liquid (HDL). Using simple models we explain how these anomalies arise from the presence of two competing length scales. As a specific example we investigate the cut ramp potential, where we show the importance of "competition" in this context, and how one length scale can sometimes be zero. When there is a clear energetic preference for either LDL or HDL for all pressures and temperatures, then there is insufficient competition between the two liquid structures and no anomalies occur. From the simple models it also follows that anomalies can occur without the presence of a LLPT and vice versa. It remains therefore unclear if water has a LLPT that ends in a liquid-liquid critical point (LLCP), a hypothesis that was first proposed based on simulations of the ST2 water model. We confirm the existence of a LLCP in this model using finite size scaling and the Challa-Landau-Binder parameter, and show that the LLPT is not a liquid-crystal transition, as has recently been suggested. Previous research has indicated the possible existence of a LLCP in liquid silica. We perform a detailed analysis of two different silica models (WAC and BKS) at temperatures much lower than was previously simulated. Within the accessible temperature range we find no LLCP in either model, although in the case of WAC potential it is closely approached. We compare our results with those obtained for other tetrahedral liquids and conclude that insufficient "stiffness" in the Si-O-Si bond angle might be responsible for the absence of a LLCP.

Modern DNA analysis is possible due to the discovery of repeating microsatellite regions in DNA and successful implementation of the polymerase chain reaction (PCR) in laboratories. PCR amplification chemistries that contain short tandem repeat (STR) loci are sensitive. As a result, the discrimination power within human identification sciences has increased in recent years. Despite these advances, cellular admixtures are commonly collected, and the resultant “DNA mixture profile” is difficult to interpret as it is often encumbered by low-signals and allele drop-out. Regularly detected PCR artifacts can further complicate interpretation. One commonly encountered artifact is stutter, the result of strand slippage during PCR. Stutter can be of two types: forward and reverse. Reverse stutter (or back stutter) is the most prevalent and is one repeat unit shorter (n - 1) than the template strand. In contrast, forward stutter is one repeat unit longer (n + 1). If a reverse stutter amplicon is produced there is the distinct possibility that a stutter product of stutter may occur. This artifact is usually referred to as double-back stutter (DBS) or n - 2 stutter. Recently there has been renewed interest in examining signal approaching baseline levels. As the sensitivity of the process improves, so does the probability of detecting DBS. Therefore, studies that examine the peak height distributions, rarity, stutter signal-to-noise distances and the general impact of DBS on the signal are warranted. Models simulating PCR, and the entire forensic DNA process, have been created by this laboratory. The work presented herein builds upon a preexisting model; specifically, the dynamic model was extended such that DNA profiles consisting of 21 autosomal STRs, consistent with the GlobalFilerTM multiplex, are simulated. Furthermore, this expansion incorporated a three-type Galton-Watson branching process allowing DBS to be added to the simulated electropherogram (EPG). The in silico model was used to simulate the amplification of a 1:43 and 1:73 mixture at a total DNA concentration of 0.3 and 0.5 ng, respectively. We chose these extreme mixture ratios because the signal from these minor contributors would be most susceptible to DBS effects from the major contributor. A total of 1200 alleles from each contributor were simulated at each target, and effects of DBS on the signal from the minor contributor were characterized. At 0.3 and 0.5 ng both the noise and stutter signal histograms are right-skewed and a Kolmogorov-Smirnov (KS) test indicates that the noise and DBS were significantly different (p-value < 4x10-6). The average peak height of DBS for all loci in both scenarios were less than 50 RFU (Relative Fluorescence Units), and the DBS ratios ranged from 0.29 to 2.15% of the main allele, with the median ratios less than 0.5%. A per locus analytical threshold (AT) was calculated for both the 0.3 and 0.5 ng targets using two k-values: 3 and 4. The k-value is chosen based on the Type I risk assessment, wherein increasing the k-value increases AT. The percentage of DBS peaks greater than AT when k = 3 for the mixtures amplified at 0.3 and 0.5 ng ranged from 0 to 7.08% and 0 to 10.50%, respectively. Interestingly, when k = 4 the percentage of DBS peaks greater than AT for 0.3 and 0.5 ng reduced to 0 to 1.08% and 0 to 0.17%, respectively. This suggests that modeling DBS in continuous systems may not be necessary if the laboratory continues to rely on a system that requires an AT of sufficient strength. However, with the advent of Bayesian or machine learning-based approaches to analyzing EPGs, thus removing AT in its entirety, a complete understanding of the prevalence of DBS is necessary. This work shows that DBS from an extreme major using our laboratory protocols is not likely to be in the same signal regime as the signal from alleles; however, it does show that signal from DBS is significantly different from noise. Therefore, the software expert pair should be carefully considered during the validation stage and laboratories should consider DBS during interpretation, especially if enhanced post-PCR parameters are implemented into the forensic laboratory process.

This thesis considers various topics and open questions in galaxy formation during the epoch of reionization and presents multiple new computational techniques developed specifically to study this era. This work naturally divides into two main sections: 1) The formation of the first massive black holes and 2) Interpreting ALMA observations of galaxy formation during the epoch of reionization. The first topic addresses the existence of super massive black holes (SMBHs) with $M_{\rm BH} > 10^9$M$_{\odot}$ at $z > 6$. It is well established that stellar mass black holes are very unlikely to be able to accrete matter efficiently enough to grow to this mass at this redshift. For this reason, many alternative channels have been proposed for black hole formation that produce objects with significantly larger initial masses. In this thesis, I consider a mechanism whereby runaway stellar collisions in dense primordial star clusters form a very massive star that is likely to collapse to an intermediate mass black hole (IMBH) with $M_{\rm BH} > 10^3$M$_{\odot}$. In order to test this scenario, I added 12 species non-equilibrium chemistry to the massively parallel adaptive mesh refinement code RAMSES, and simulated, at sub-pc resolution, the collapse of the first metal-enriched halo which is likely to host a Population II star cluster. The properties of the central gas cloud in the collapsing halo were then extracted from the simulation and used to create initial conditions for the direct N-body integrator, NBODY6. These star clusters were simulated for 3.5Myr (until the first supernova is expected to occur) and it was determined that the properties of the gas clouds that form in cosmological simulations were indeed suitable to form a very massive star by collisional runaway. This suggests that this mechanism is a promising channel for forming the seeds of SMBHs at high redshift. The second topic of this thesis aims to help interpret the plethora of recent and upcoming ALMA observations of star forming galaxies during the epoch of reionization. These observations target far-infrared lines such as [CII] and [OIII] which directly probe the interstellar medium (ISM) of these $z > 6$ galaxies. In order to study this epoch, I employ the RAMSES-RT code, which allows for the computation of multifrequency radiative transfer on-the-fly. I modified this code in a number of ways so that it can handle radiation-coupled H$_2$ non-equilibrium chemistry (including Lyman-Werner band radiation) and I developed the variable speed of light approximation which changes the speed of light in the simulation depending on the density of gas so that ionisation fronts propagate at the correct speed in all gas phases. Cosmological boxes were initialised to include galaxies with masses comparable to the observations of Maiolino et al. (2015) and run at various resolutions to test convergence properties. One of the major goals of this study was to identify the physical mechanism responsible for the spatial offset observed between [CII] and UV/Lyα in many high-redshift galaxies.

Maps of chosen areas in Chicago, San José, London and Shibuya, areimported from Open Street Map into matlab in order to run LTE networksimulations for various scenarios. Firstly, two path loss models arecompared, the empirically based WINNER model and a set of sitespecificmodel. Secondly, low load network simulations are runseparately at two different carrier frequencies, 700MHz and 2GHz, forcity specific base station deployments. Simulation results show thatuser performance is quite unique for each city and that deploymentstrategies and city environments are strongly influencing path gain,SINR and throughput. In general, user performance in UL issignificantly worse at 2GHz than at 700MHz, whereas DL performance isnot as affected by the change in carrier frequency.

Undoubtedly, water is the most abundant and important molecular liquid and is likely the most necessary for life on Earth. The pursuit of understanding water's properties and behaviors has placed it in a unique scientific and even mythical position throughout human history. It is no surprise that much scientific research today centers around this molecule and its interactions with others. The interfacial region between liquid water solutions and other phases is still poorly understood, and only recently have experiments developed to where we can probe this unique environment. Water surfaces exist throughout the Earth's atmosphere and oceans but also make up many of the microscopic interfaces necessary for metabolic processes within living cells. Yet, the influence of water surfaces on the chemistry that drives life and terrestrial processes is still largely unknown, and many research efforts today are attempting to gain insight to this critically important frontier. This dissertation documents several unique computational studies aimed to further our understanding of the complex interactions within a water system and between water and simple, common solutes. Reported herein are the results of molecular dynamics (MD) simulations and computational analysis of interfacial aqueous systems of small hydrated acids, ionic aqueous salt solutions interfaced with a liquid oil, and gas molecules adsorbing onto water surfaces. The composition of the systems chosen for the studies reported in this dissertation reflect environmentally relevant interfaces and also complement recent experimental efforts by the Richmond laboratory. Classical and quantum ab initio MD techniques were used for simulation of the molecular systems and the subsequent analyses provided new information regarding molecular interactions, geometries, orientations, and surface behaviors of water and hydrated interfacial solute molecules. This dissertation includes both previously published and unpublished co-authored material.