No description available.

QCD at non-zero baryon density is expected to have a critical point where the finite temperature crossover at zero density turns into a first order phase transition. To identify this point, we use the canonical ensemble approach to scan the temperaturedensity plane through lattice QCD simulations with Wilson-type fermions. In order to scan a wide range of the phase diagram, we develop an algorithm, the ”winding number expansion method” (WNEM) to fix the numerical instability problem due to the discrete Fourier transform for calculating the projected determinant. For a given temperature, we measure the chemical potential as a function of the baryon number and look for the signal of a first order phase transition. We carry out simulations using clover fermions with mπ ≈ 800MeV on 63 × 4 lattices. As a benchmark, we run simulations for the four degenerate flavor case where we observe a clear signal of the first order phase transition. In the two flavor case we do not see any signal for temperatures as low as 0.83 Tc. To gauge the discretization errors, we also run a set of simulations using Wilson fermions and compare the results to those from the clover fermion. The three flavor case is close to realistic QCD with two light u and d quarks and one heavier s quark. Any hint of the existence of the first order phase transition and, particularly, its critical end point will be valuable for the planned relativistic heavy-ion experiments to search for such a point. In the three flavor case we found a clear signal for the first order phase transition, the critical point is located at a temperature of 0.93(2) Tc and a baryon chemical potential of 3.25(7) Tc. Since the quark mass in our present simulation is relatively heavy, we would like to repeat it with lighter quark masses and larger volumes.

We introduce an efficient thermodynamically consistent technique to extrapolate and interpolate normalized Canonical NVT ensemble averages like pressure and energy for Lennard-Jones (L-J) fluids. Preliminary results show promising applicability in oil and gas modeling, where accurate determination of thermodynamic properties in reservoirs is challenging. The thermodynamic interpolation and thermodynamic extrapolation schemes predict ensemble averages at different thermodynamic conditions from expensively simulated data points. The methods reweight and reconstruct previously generated database values of Markov chains at neighboring temperature and density conditions. To investigate the efficiency of these methods, two databases corresponding to different combinations of normalized density and temperature are generated. One contains 175 Markov chains with 10,000,000 MC cycles each and the other contains 3000 Markov chains with 61,000,000 MC cycles each. For such massive database creation, two algorithms to parallelize the computations have been investigated. The accuracy of the thermodynamic extrapolation scheme is investigated with respect to classical interpolation and extrapolation. Finally, thermodynamic interpolation benefiting from four neighboring Markov chains points is implemented and compared with previous schemes. The thermodynamic interpolation scheme using knowledge from the four neighboring points proves to be more accurate than the thermodynamic extrapolation from the closest point only, while both thermodynamic extrapolation and thermodynamic interpolation are more accurate than the classical interpolation and extrapolation. The investigated extrapolation scheme has great potential in oil and gas reservoir modeling.That is, such a scheme has the potential to speed up the MCMC thermodynamic computation to be comparable with conventional Equation of State approaches in efficiency. In particular, this makes it applicable to large-scale optimization of L-J model parameters for hydrocarbons and other important reservoir species. The efficiency of the thermodynamic dependent techniques is expected to make the Markov chains simulation an attractive alternative in compositional multiphase flow simulation.

No description available.

<p>Premelting is the formation of a thin, thermodynamically stable, liquid-like film at an interface for temperatures below the equilibrium melting temperature. Using a Monte Carlo technique, the underlying short range structural forces for premelting at the grain boundary can be directly calculated. This technique is applied to a (i) Σ9 ⟨115⟩ 120^o twist boundary and a (ii) Σ9 ⟨011⟩ {411} symmetric tilt boundary in an embedded atom model of Aluminum-Magnesium alloy. Both grain boundaries exhibit disordered structures near the melting point that depend on the concentration of Magnesium. The behavior is described quantitatively with sharp interface thermodynamics, involving an interfacial free energy that depends on width of the grain boundary, referred to as the disjoining potential. The disjoining potential calculated for boundary (i) displays a decreasing exponential dependence on width of the grain boundary, while the disjoining potential of (ii) features a weak attractive minimum. This work is discussed in relation to a previous study using pure Nickel, results of which can be useful to the theoretical study of thermodynamic forces underlying grain boundary premelting in an alloy.</p> / Master of Science (MSc)

L'adsorption de CO dans la faujasite échangée au CuI et au Na+ a été modélisée à l'aide des approches quantiques (DFT) et classiques (Monte Carlo). Grâce à l'approche DFT, la surface d'énergie potentielle de la faujasite a été explorée. Différents types d'interactions de CO avec les cations ont été identifiés, pour chacune les effets induits par l'adsorption de CO aux niveaux structural et énergétique ont été analysés, et le calcul de la fréquence de vibration de CO a été réalisé. Grâce aux valeurs obtenues, une nouvelle attribution des spectres d'adsorption de CO dans CuY et NaY a été établie. D'un autre côté, grâce aux simulations Monte Carlo dans l'ensemble Grand Canonique, les propriétés d'adsorption (isothermes et enthalpies) de la faujasite vis-à-vis de CO ont été modélisées, et le mécanisme microscopique d'adsorption de CO a été établi. La mise en œuvre de ces simulations a nécessité de paramétrer un nouveau champ de force destiné à décrire les interactions CO/faujasite et CO/CO. / CO adsorption in CuI and Na+ exchanged faujasite has been modeled by mean of quantum (DFT) and classical (Monte Carlo) approaches. By mean of the DFT calculations, faujasite potential energy surface has been explored. Different types of CO interactions with the cations have been highlighted, for each one of them CO adsorption effects on the structural and energetic parameters have been analyzed, and calculations of the CO stretching frequency have been performed. Thanks to our calculated values, a new attribution of CO adsorption spectra in CuY and NaY has been established. On another side, by mean of Monte Carlo simulations in the Grand Canonical ensemble, faujasite adsorption properties regarding CO (isotherms and enthalpies) have been modeled, and the CO adsorption mechanism has been established at the microscopic level. The implementation of these simulations has required the derivation of a new force field describing the CO/faujasite and CO/CO interactions.

La simulación molecular presenta la ventaja de ofrecer un marco teórico importante para predecir propiedades termodinámicas y de transporte de fluidos con aplicaciones industriales. En este trabajo, se explotó está ventaja para predecir el equilibrio líquido vapor de agua, compuestos aromáticos y sus mezclas a condiciones tanto sub- como supercríticas. Se realizó una comparación de diferentes potenciales intermoleculares conocidos mediante el cálculo de propiedades termodinámicas de sistemas puros que sirvió de punto de partida para llevar a cabo una optimización de parámetros transferibles para un potencial intermolecular de agua y compuestos aromáticos. En el caso de agua, se llevo a cabo el análisis y evaluación de propiedades termodinámicas de un modelo simple de agua. En este modelo, las contribuciones electrostáticas se aproximan mediante interacciones de corto alcance en vez de las típicas fuerzas de Coulomb de largo alcance. En general, se han encontrado grandes desviaciones con respecto a los datos experimentales, tal como un valor de temperatura crítica de 360K, valor 50% alejado del valor experimental. Debido a que estos resultados nos indican la importancia de incluir las fuerzas de Coulomb en el modelo molecular empleado para reproducir correctamente las propiedades de agua, el trabajo de investigación se ha enfocado en la optimización de los parámetros de los potenciales TIP4P y SPC/E. Los resultados obtenidos muestran que es posible encontrar una mejor aproximación al punto crítico experimental a partir de la optimización del modelo SPC/E. Sin embargo, el buen acuerdo con los experimentos del modelo original a condiciones ambiente se pierde usando los parámetros del modelo optimizado. Por otro lado, la estimación de propiedades de compuestos aromáticos esta de acuerdo con los datos experimentales permitiendo la reproducción de la densidad de líquido saturado, presión de saturación y entalpía de vaporización para compuestos puros. Finalmente, en el caso de mezclas se ha aplicado el conjunto de parámetros obtenidos para aromáticos. Las propiedades termodinámicas de la mezcla binaria aromático-aromático y aromático agua son analizadas en un amplio rango de temperaturas y presiones. Las desviaciones encontradas entre los valores calculados y los experimentales sugieren aplicar un mejor método de optimización para sistemas puros o por otro lado, promover un potencial de interacción intermolecular más sofisticado. Las estimaciones a condiciones cercanas al punto crítico están en buen acuerdo con los datos experimentales. / La simulació molecular presenta l'avantatge d'oferir un marc teòric important per a cercar propietats termodinàmiques i de transport de fluids amb aplicacions industrials. En aquest treball es va explotar aquesta avantatge per predir l'equilibri líquid vapor d'aigua, components aromàtics i les seves mescles, tant a condicions sub com supercrítiques. Es va realitzar una comparació de diferents potencials intermoleculars, coneguts mitjançant el càlcul de propietats termodinàmiques de sistemes purs, que ha servit de punt de sortida per portar a terme una optimització de paràmetres transferibles per a un potencial intermolecular de propietats termodinàmiques d'un model simple d'aigua. En aquest model, les contribucions electrostàtiques s'aproximen mitjançant interaccions de curt abast en lloc de les típiques forces de Coulomb de llarg abast. En general, s'ha trobat grans desviacions respecte a les dades experimentals, tal com un valor de temperatura crítica de 360K, valor 50% allunyat del valor experimental. Degut a que aquests resultats ens indiquen la importància d'incloure les forces de Coulomb en el model molecular emprat per reproduir correctament les propietats d'aigua, el treball d'investigació s'ha enfocat en l'optimització dels paràmetres dels potencials TIP4P i SPC/E. Els resultats obtinguts mostren que és possible trobar una millor aproximació al punt crític experimental a partir de l'optimització del model SPC/E. No obstant, el bon acord amb els experiments del model original a condicions ambientals es perden usant els paràmetres del model optimitzat. Per altre banda, l'estimació de propietats de compostos aromàtics esta d'acord amb les dades experimentals permetent la reproducció de la densitat de líquid saturat, pressió de saturació i entalpia de vaporització per a compostos purs mitjançant el potencial AUA-Aromátics proposat. Finalment, en el cas de mescles s'ha aplicat el conjunt de paràmetres obtinguts per aromàtics. Les propietats termodinàmiques de la mescla binària aromàtic-aromàtic i aromàtic-aigua són analitzades en un ample rang de temperatures i pressions. Les desviacions trobades entre els valors calculats i els experimentals suggereixen aplicar un millor mètode d'optimització per a sistemes purs o, per altre banda, promoure un potencial d'interacció intermolecular més sofisticat. Les estimacions en condicions properes al punt crític tenen un bon acord amb les dades experimentals. / Molecular simulation presents the advantage of providing a unified theoretical framework to model fluid properties for industrial applications. In this work we exploit this advantage to predict thermodynamic properties of pure water and aromatics and their mixtures at sub- and supercritical conditions. A comprehensive comparison of different intermolecular potentials has been carried out in order to analyze model predictions for pure component properties. In addition, an optimization of transferable parameters has been performed for an intermolecular potential for aromatics and water. In the case of water, an analysis and evaluation of the thermodynamic properties of a simple model has been performed. In this model, the electrostatic contributions are approximated by short-range interactions instead of the typical long-range Coulombic forces. On the whole, we found huge deviations with experimental data, such as a critical temperature value of 360K, 50% far away from the experimental value. Since, these calculations indicate the importance of including the electrostatic contribution in order to correctly model water, we also focus on reproducing critical properties from an optimization of the well known TIP4P and SPC/E water model parameters. Results obtained show that a better approximation to the critical point prediction is possible from the optimization of the SPC/E parameters, however, the good agreement with experiments for the original model at room conditions vanishes using the optimized parameters. On the other hand, thermodynamic property estimations of aromatic molecules are in good agreement with experimental data and we are able to reproduce saturation liquid densities, saturation pressures, vaporization enthalpies and liquid structure for pure compounds. Finally, in the case of mixtures, we applied the optimized set of parameters obtained for aromatics. The thermodynamic properties of binary aromatic-aromatic and aromatic water mixtures are analyzed over a wide range of temperatures and pressures. Deviations between the predicted and experimental values are found at low temperatures and high densities suggesting that a better optimization process needs to be performed for the pure systems or a more sophisticated intermolecular interaction potential is needed. Nevertheless, the estimations close to critical conditions are in good agreement with experimental data.

Simulations of particle systems at constant temperature may be used to estimate several of the system’s physical properties, and some require integration over very long time to be accurate. To achieve sufficient accuracy in finite time the choice of numerical scheme is important and we suggest to use the symplectic Euler method combined with a step in an Ornstein-Uhlenbeck process. This scheme is computationally very cheap and is often used in applications of molecular dynamics. This thesis strives to motivate the usage of the scheme due to the lack of theoretical results and comparisons to alternative methods. We conduct three numerical experiments to evaluate the scheme. The design of each experiment aims to expose weaknesses or strengths of the method. For both model problems and more realistic experiments are the results positive in favor of the method; the symplectic Euler method combined with an Ornstein- Uhlenbeck step does perform well over long times. / Simuleringar av partikelsystem vid konstant temperatur kan användas för att uppskatta flera av systemets fysiska egenskaper. Vissa klasser av egenskaper kräver integration över väldigt lång tid för att uppnå hög noggrannhet och för att uppnå detta i ändlig tid är valet av numerisk metod viktigt. Vi föreslår att använda den symplektiska Euler-metoden i kombination med ett implicit steg i en Ornstein-Uhlenbeck-process. Detta stegschema kräver låg beräkning jämfört med andra scheman och används redan i olika applikationer av molekyldynamik. Detta examensarbete eftersträvar att än mer motivera användandet av schemat, eftersom teoretiska resultat som stödjer metoder är få, och avsaknaden av tidigare liknande studier är betydlig. Vi genomför tre numeriska experiment för att pröva schemat. Under utformningen av experimenten har vi försökt att inkorporera olika fenomen som kan orsaka svårigheter för metoden för att exponera svagheter eller styrkor hos den. För båda modellproblem och för ett mer realistiskt experiment är resultaten positiva till schemats fördel; metoden att kombinera ett symplektisk Euler-steg med ett steg i Ornstein-Uhlenbeck-processen presterar bra över lång tid.

Thermostated time evolutions are on a firm ground and widely used in classical molecular dynamics (MD) simulations. Hamilton´s equations of motion are supplemented by time-dependent pseudofriction terms that convert the microcanonical isoenergetic time evolution into a canonical isothermal time evolution, thus permitting the calculation of canonical ensemble averages by time averaging. However, similar methods for quantum MD schemes are still lacking. Given the rich dynamical behavior of ultracold trapped quantum gases depending on the value of the s-wave scattering length, it is timely to investigate how classical thermostating methods can be combined with powerful approximate quantum dynamics schemes to deal with interacting quantum systems at finite temperature. In this work, the popular method of Nose and Hoover to create canonically distributed positions and momenta in classical MD simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum harmonic oscillator, the equations of motion in terms of coherent states may be modified in a Nose-Hoover manner to mimic the coupling of the system to a thermal bath and create a quantum canonical ensemble. The method is developed initially for a single particle and then generalized to the case of an arbitrary number of identical quantum particles, involving entangled distribution functions. The resulting isothermal equations of motion for bosons and fermions contain additional terms leading to Bose-attraction and Pauli-blocking, respectively. Questions of ergodicity are discussed for different coupling schemes. In the many-particle case, the superiority of the Nose-Hoover technique to a Langevin approach is demonstrated. In addition, the work contains an investigation of the Grilli-Tosatti thermostating method applied to the harmonic oscillator, and calculations for quantum wavefunctions moving with a time-invariant shape in a harmonic potential.

Ziel dieser Arbeit ist zunächst die Entwicklung einer Vergleichsgrundlage, auf Basis derer Algorithmen zur Berechnung der Zustandsdichte verglichen werden können. Darauf aufbauend wird ein bestehendes übergangsmatrixbasiertes Verfahren für das großkanonisch Ensemble um ein neues Auswerteverfahren erweitert. Dazu werden numerische Untersuchungen verschiedener Monte-Carlo-Algorithmen zur Berechnung der Zustandsdichte durchgeführt. Das Hauptaugenmerk liegt dabei auf Verfahren, die auf Übergangsmatrizen basieren, sowie auf dem Verfahren von Wang und Landau. Im ersten Teil der Forschungsarbeit wird ein umfassender Überblick über Monte-Carlo-Methoden und Auswerteverfahren zur Bestimmung der Zustandsdichte sowie über verwandte Verfahren gegeben. Außerdem werden verschiedene Methoden zur Berechnung der Zustandsdichte aus Übergangsmatrizen vorgestellt und diskutiert. Im zweiten Teil der Arbeit wird eine neue Vergleichsgrundlage für Algorithmen zur Bestimmung der Zustandsdichte erarbeitet. Dazu wird ein neues Modellsystem entwickelt, an dem verschiedene Parameter frei gewählt werden können und für das die exakte Zustandsdichte sowie die exakte Übergangsmatrix bekannt sind. Anschließend werden zwei weitere Systeme diskutiert für welche zumindest die exakte Zustandsdichte bekannt ist: das Ising Modell und das Lennard-Jones System. Der dritte Teil der Arbeit beschäftigt sich mit numerischen Untersuchungen an einer Auswahl der vorgestellten Verfahren. Auf Basis der entwickelten Vergleichsgrundlage wird der Einfluss verschiedener Parameter auf die Qualität der berechneten Zustandsdichte quantitativ bestimmt. Es wird gezeigt, dass Übergangsmatrizen in Simulationen mit Wang-Landau-Verfahren eine wesentlich bessere Zustandsdichte liefern als das Verfahren selbst. Anschließend werden die gewonnenen Erkenntnisse genutzt um ein neues Verfahren zu entwickeln mit welchem die Zustandsdichte mittels Minimierung der Abweichungen des detaillierten Gleichgewichts aus großen, dünnbesetzten Übergangsmatrizen gewonnen werden kann. Im Anschluss wird ein Lennard-Jones-System im großkanonischen Ensemble untersucht. Es wird gezeigt, dass durch das neue Verfahren Zustandsdichte und Dampfdruckkurve bestimmt werden können, welche qualitativ mit Referenzdaten übereinstimmen.