Atomistic simulations of bulk and free standing film smectics

In questa tesi viene descritto lo studio delle fasi liquido-cristalline del 4-n-ottil-4-cianobifenile eseguito tramite simulazioni al calcolatore molecular dynamics, sia per campioni bulk che per film smectici sottili. Impiegando un campo di forze "molecular mechanics" precedentemente usato con successo per studiare sistemi composti da 250 molecole della serie degli n-cianobifenili (nCB, con n pari a 4-8 atomi di carbonio nella catena alifatica), si è simulato il comportamento di un sistema bulk di 750 molecole e di un film smectico di 1500 molecole. Nel primo caso, sottoponendo il campione a un graduale raffreddamento, si è osservata la formazione spontanea di fasi ordinate quali quella nematica e quella smectica. Nel secondo caso, invece, si è studiata l'influenza dell'interfaccia con il vuoto sull'ordine posizionale e orientazionale di film sottili di diverso spessore e temperatura. Si sono confrontate le proprietà di entrambi i sistemi simulati con i dati sperimentali disponibili in letteratura, confermando la bontà del modello nel riprodurre fedelmente le caratteristiche dei campioni reali.

Monte Carlo simulations of Potts glasses

A complete understanding of the glass transition isstill a challenging problem. Some researchers attributeit to the (hypothetical) occurrence of a static phasetransition, others emphasize the dynamical transitionof mode coupling-theory from an ergodic to a non ergodicstate. A class of disordered spin models has been foundwhich unifies both scenarios. One of these models isthe p-state infinite range Potts glass with p>4, whichexhibits in the thermodynamic limit both a dynamicalphase transition at a temperature T_D, and a static oneat T_0 < T_D. In this model every spins interacts withall the others, irrespective of distance. Interactionsare taken from a Gaussian distribution.In order to understand better its behavior forfinite number N of spins and the approach to thethermodynamic limit, we have performed extensive MonteCarlo simulations of the p=10 Potts glass up to N=2560.The time-dependent spin-autocorrelation function C(t)shows strong finite size effects and it does not showa plateau even for temperatures around the dynamicalcritical temperature T_D. We show that the N-andT-dependence of the relaxation time for T > T_D can beunderstood by means of a dynamical finite size scalingAnsatz.The behavior in the spin glass phase down to atemperature T=0.7 (about 60% of the transitiontemperature) is studied. Well equilibratedconfigurations are obtained with the paralleltempering method, which is also useful for properlyestablishing static properties, such as the orderparameter distribution function P(q). Evidence is givenfor the compatibility with a one step replica symmetrybreaking scenario. The study of the cumulants of theorder parameter does not permit a reliable estimation ofthe static transition temperature. The autocorrelationfunction at low T exhibits a two-step decay, and ascaling behavior typical of supercooled liquids, thetime-temperature superposition principle, is observed. Inthis region the dynamics is governed by Arrheniusrelaxations, with barriers growing like N^{1/2}.We analyzed the single spin dynamics down to temperaturesmuch lower than the dynamical transition temperature. We found strong dynamical heterogeneities, which explainthe non-exponential character of the spin autocorrelationfunction. The spins seem to relax according to dynamicalclusters. The model in three dimensions tends to acquireferromagnetic order for equal concentration of ferro-and antiferromagnetic bonds. The ordering has differentcharacteristics from the pure ferromagnet. The spinglass susceptibility behaves like chi_{SG} proportionalto 1/T in the region where a spin glass is predicted toexist in mean-field. Also the analysis of the cumulantsis consistent with the absence of spin glass orderingat finite temperature. The dynamics shows multi-scalerelaxations if a bimodal distribution of bonds isused. We propose to understand it with a model based onthe local spin configuration. This is consistent with theabsence of plateaus if Gaussian interactions are used.

Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.

Computer simulations of charged systems in partially periodic geometries

This work presents algorithms for the calculation of the electrostatic interaction in partially periodic systems. The framework for these algorithms is provided by the simulation package ESPResSo, of which the author was one of the main developers. The prominent features of the program are listed and the internal structure is described. In the following, algorithms for the calculation of the Coulomb sum in three dimensionally periodic systems are described. These methods are the foundations for the algorithms for partially periodic systems presented in this work. Starting from the MMM2D method for systems with one non-periodic coordinate, the ELC method for these systems is developed. This method consists of a correction term which allows to use methods for three dimensional periodicity also for the case of two periodic coordinates. The computation time of this correction term is neglible for large numbers of particles. The performance of MMM2D and ELC are demonstrated by results from the implementations contained in ESPResSo. It is also discussed, how different dielectric constants inside and outside of the simulation box can be realized. For systems with one periodic coordinate, the MMM1D method is derived from the MMM2D method. This method is applied to the problem of the attraction of like-charged rods in the presence of counterions, and results of the strong coupling theory for the equilibrium distance of the rods at infinite counterion-coupling are checked against results from computer simulations. The degree of agreement between the simulations at finite coupling and the theory can be characterized by a single parameter gamma_RB. In the special case of T=0, one finds under certain circumstances flat configurations, in which all charges are located in the rod-rod plane. The energetically optimal configuration and its stability are determined analytically, which depends on only one parameter gamma_z, similar to gamma_RB. These findings are in good agreement with results from computer simulations.

Simulations of physics and chemistry of polar stratospheric clouds with a general circulation model

A polar stratospheric cloud submodel has been developed and incorporated in a general circulation model including atmospheric chemistry (ECHAM5/MESSy). The formation and sedimentation of polar stratospheric cloud (PSC) particles can thus be simulated as well as heterogeneous chemical reactions that take place on the PSC particles. For solid PSC particle sedimentation, the need for a tailor-made algorithm has been elucidated. A sedimentation scheme based on first order approximations of vertical mixing ratio profiles has been developed. It produces relatively little numerical diffusion and can deal well with divergent or convergent sedimentation velocity fields. For the determination of solid PSC particle sizes, an efficient algorithm has been adapted. It assumes a monodisperse radii distribution and thermodynamic equilibrium between the gas phase and the solid particle phase. This scheme, though relatively simple, is shown to produce particle number densities and radii within the observed range. The combined effects of the representations of sedimentation and solid PSC particles on vertical H2O and HNO3 redistribution are investigated in a series of tests. The formation of solid PSC particles, especially of those consisting of nitric acid trihydrate, has been discussed extensively in recent years. Three particle formation schemes in accordance with the most widely used approaches have been identified and implemented. For the evaluation of PSC occurrence a new data set with unprecedented spatial and temporal coverage was available. A quantitative method for the comparison of simulation results and observations is developed and applied. It reveals that the relative PSC sighting frequency can be reproduced well with the PSC submodel whereas the detailed modelling of PSC events is beyond the scope of coarse global scale models. In addition to the development and evaluation of new PSC submodel components, parts of existing simulation programs have been improved, e.g. a method for the assimilation of meteorological analysis data in the general circulation model, the liquid PSC particle composition scheme, and the calculation of heterogeneous reaction rate coefficients. The interplay of these model components is demonstrated in a simulation of stratospheric chemistry with the coupled general circulation model. Tests against recent satellite data show that the model successfully reproduces the Antarctic ozone hole.

Molekulardynamiksimulationen zur Untersuchung des Mischalkali-Effektes in silikatischen Gläsern

In der vorliegenden Arbeit wird mittels Molekulardynamik(MD)-Computersimulationen die Dynamik von verschiedenen Alkalisilikaten in der Schmelze und im Glas untersucht. Es ist bekannt, daß diese Systeme ionenleitend sind, was auf eine hohe Mobilität der Alkaliionen im Vergleich zu den glasbildenden Komponenten Si und O zurückzuführen ist. Im Mittelpunkt des Interesses steht der sog. Mischalkalieffekt (MAE), der in ternären Mischungen aus Siliziumdioxid mit zwei Alkalioxiden auftritt. Gegenüber Mischungen mit nur einer Alkaliionensorte weisen letztere Systeme eine signifikante Verlangsamung der Alkaliionendiffusion auf. Zunächst werden zwei binäre Alkalisilikate simuliert, nämlich Lithiumdisilikat (LS2) und Kaliumdisilikat (KS2). Die Simulationen zeigen, daß der Ursprung der hohen Mobilität der Alkaliionen in der Struktur begründet ist. KS2 und LS2 weisen auf intermediären Längenskalen Ordnung auf, die in partiellen statischen Strukturfaktoren durch Prepeaks reflektiert ist. Die den Prepeaks zugrundeliegende Struktur erklärt sich durch perkolierende Netzwerke aus alkalioxidreichen Kanälen, die als Diffusionskanäle für die mobilen Alkaliionen fungieren. In diesen Kanälen bewegen sich die Ionen mittels Sprüngen (Hopping) zwischen ausgezeichneten Plätzen. In der Simulation beobachtet man für die hohen Temperaturen (4000K>=1500K) eine ähnliche Aktivierungsenergie wie im Experiment. Im Experiment findet allerdings unterhalb von ca.1200K ein Crossover in ein Arrheniusverhalten mit höherer Aktivierungsenergie statt, welches von der Simulation nicht nachvollzogen wird. Das kann mit der in der Simulation nicht im Gleichgewicht befindlichen Si-O-Matrix erklärt werden, bei der Alterungseffekte beobachtet werden. Am stärksten ist der MAE für eine Alkalikomponente, wenn deren Konzentrationsanteil in einem ternären Mischalkalisystem gegen 0 geht. Daher wird ein LS2-System untersucht, in dem ein Li-Ion gegen ein K-Ion getauscht wird. Der Einfluß des K-Ions ist sowohl lokal in den charakteristischen Abständen zu den ersten nächsten Nachbarn (NN) zu sehen, als auch in der ortsaufgelösten Koordinationszahlverteilung bis zu Längenskalen von ca. 8,5 Angstrom. Die Untersuchung der Dynamik des eingesetzten K-Ions zeigt, daß die Sprungwahrscheinlichkeit nicht mit der Lokalisierung, einem Maß für die Bewegung eines Teilchens um seine Ruheposition, korreliert ist, aber daß eine chemische Umgebung mit wenig Li- und vielen O-NN oder vielen Li- und wenig O-NN ein Sprungereignis begünstigt. Zuletzt wird ein ternäres Alkalisilikat (LKS2) untersucht, dessen Struktur alle charakteristischen Längenskalen von LS2 und KS2 aufweist. Es stellt sich also eine komplexe Struktur mit zwei perkolierenden Subnetzwerken für Alkaliionen ein. Die Untersuchung der Dynamik zeigt eine geringe Wahrscheinlichkeit dafür auf, daß Ionen in ein Subnetzwerk andersnamiger Ionen springen. Auch kann gezeigt werden, daß das Modellpotential den MAE reproduzieren kann, daß also die Diffusionskonstanten in LKS2 bei bis zu einer Größenordnung langsamer sind als in KS2 bzw. LS2. Der beobachtete Effekt stellt sich zudem vom funktionalen Verlauf her so dar, wie er beim MAE erwartet wird. Es wurde auch festgestellt, daß trotz der zeitlichen Verzögerung in den dynamischen Größen die Anzahl der Sprünge pro Zeit nicht geringer ist und daß für niedrige Temperaturen (d.h.im Glas) Sprünge auf den Nachbarplatz mit anschließendem Rücksprung auf die vorherige Position deutlich wahrscheinlicher sind als bei hohen Temperaturen (also in der Schmelze). Die vorliegenden Resultate geben Aufschluß über die Details der Mechanismen mikroskopischer Ionenleitung in binären und ternären Alkalisilikaten sowie dem MAE.

Computer simulations of two-dimensional colloidal crystals in confinement

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two ``walls'' providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-) long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y-direction along the walls then crosses over from the logarithmic increase (characteristic for $d=2$) to a linear increase (characteristic for d=1). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising- and XY-models is made

Atomistic simulations of cosolvent/water mixtures

In this thesis, atomistic simulations are performed to investigate hydrophobic solvation and hydrophobic interactions in cosolvent/water binary mixtures. Many cosolvent/water binary mixtures exhibit non-ideal behavior caused by aggregation at the molecular scale level although they are stable and homogenous at the macroscopic scale. Force-field based atomistic simulations provide routes to relate atomistic-scale structure and interactions to thermodynamic solution properties. The predicted solution properties are however sensitive to the parameters used to describe the molecular interactions. In this thesis, a force field for tertiary butanol (TBA) and water mixtures is parameterized by making use of the Kirkwood-Buff theory of solution. The new force field is capable of describing the alcohol-alcohol, water-water and alcohol-water clustering in the solution as well as the solution components’ chemical potential derivatives in agreement with experimental data. With the new force field, the preferential solvation and the solvation thermodynamics of a hydrophobic solute in TBA/water mixtures have been studied. First, methane solvation at various TBA/water concentrations is discussed in terms of solvation free energy-, enthalpy- and entropy- changes, which have been compared to experimental data. We observed that the methane solvation free energy varies smoothly with the alcohol/water composition while the solvation enthalpies and entropies vary nonmonotonically. The latter occurs due to structural solvent reorganization contributions which are not present in the free energy change due to exact enthalpy-entropy compensation. It is therefore concluded that the enthalpy and entropy of solvation provide more detailed information on the reorganization of solvent molecules around the inserted solute. Hydrophobic interactions in binary urea/water mixtures are next discussed. This system is particularly relevant in biology (protein folding/unfolding), however, changes in the hydrophobic interaction induced by urea molecules are not well understood. In this thesis, this interaction has been studied by calculating the free energy (potential of mean force), enthalpy and entropy changes as a function of the solute-solute distance in water and in aqueous urea (6.9 M) solution. In chapter 5, the potential of mean force in both solution systems is analyzed in terms of its enthalpic and entropic contributions. In particular, contributions of solvent reorganization in the enthalpy and entropy changes are studied separately to better understand what are the changes in interactions in the system that contribute to the free energy of association of the nonpolar solutes. We observe that in aqueous urea the association between nonpolar solutes remains thermodynamically favorable (i.e., as it is the case in pure water). This observation contrasts a long-standing belief that clusters of nonpolar molecules dissolve completely in the presence of urea molecules. The consequences of our observations for the stability of proteins in concentrated urea solutions are discussed in the chapter 6 of the thesis.

Characterization of geothermal reservoirs’ parameters by inverse problem resolution and geostatistical simulations

BTES (borehole thermal energy storage)systems exchange thermal energy by conduction with the surrounding ground through borehole materials. The spatial variability of the geological properties and the space-time variability of hydrogeological conditions affect the real power rate of heat exchangers and, consequently, the amount of energy extracted from / injected into the ground. For this reason, it is not an easy task to identify the underground thermal properties to use when designing. At the current state of technology, Thermal Response Test (TRT) is the in situ test for the characterization of ground thermal properties with the higher degree of accuracy, but it doesn’t fully solve the problem of characterizing the thermal properties of a shallow geothermal reservoir, simply because it characterizes only the neighborhood of the heat exchanger at hand and only for the test duration. Different analytical and numerical models exist for the characterization of shallow geothermal reservoir, but they are still inadequate and not exhaustive: more sophisticated models must be taken into account and a geostatistical approach is needed to tackle natural variability and estimates uncertainty. The approach adopted for reservoir characterization is the “inverse problem”, typical of oil&gas field analysis. Similarly, we create different realizations of thermal properties by direct sequential simulation and we find the best one fitting real production data (fluid temperature along time). The software used to develop heat production simulation is FEFLOW 5.4 (Finite Element subsurface FLOW system). A geostatistical reservoir model has been set up based on literature thermal properties data and spatial variability hypotheses, and a real TRT has been tested. Then we analyzed and used as well two other codes (SA-Geotherm and FV-Geotherm) which are two implementation of the same numerical model of FEFLOW (Al-Khoury model).

Hydrodynamical simulations of galaxy clusters in dark energy cosmologies

In this work we investigate the influence of dark energy on structure formation, within five different cosmological models, namely a concordance $\Lambda$CDM model, two models with dynamical dark energy, viewed as a quintessence scalar field (using a RP and a SUGRA potential form) and two extended quintessence models (EQp and EQn) where the quintessence scalar field interacts non-minimally with gravity (scalar-tensor theories). We adopted for all models the normalization of the matter power spectrum $\sigma_{8}$ to match the CMB data. For each model, we perform hydrodynamical simulations in a cosmological box of $(300 \ {\rm{Mpc}} \ h^{-1})^{3}$ including baryons and allowing for cooling and star formation. We find that, in models with dynamical dark energy, the evolving cosmological background leads to different star formation rates and different formation histories of galaxy clusters, but the baryon physics is not affected in a relevant way. We investigate several proxies for the cluster mass function based on X-ray observables like temperature, luminosity, $M_{gas}$, and $Y_{X}$. We confirm that the overall baryon fraction is almost independent of the dark energy models within few percentage points. The same is true for the gas fraction. This evidence reinforces the use of galaxy clusters as cosmological probe of the matter and energy content of the Universe. We also study the $c-M$ relation in the different cosmological scenarios, using both dark matter only and hydrodynamical simulations. We find that the normalization of the $c-M$ relation is directly linked to $\sigma_{8}$ and the evolution of the density perturbations for $\Lambda$CDM, RP and SUGRA, while for EQp and EQn it depends also on the evolution of the linear density contrast. These differences in the $c-M$ relation provide another way to use galaxy clusters to constrain the underlying cosmology.

Testing future weak lensing surveys through simulations of observations

Weak lensing experiments such as the future ESA-accepted mission Euclid aim to measure cosmological parameters with unprecedented accuracy. It is important to assess the precision that can be obtained in these measurements by applying analysis software on mock images that contain many sources of noise present in the real data. In this Thesis, we show a method to perform simulations of observations, that produce realistic images of the sky according to characteristics of the instrument and of the survey. We then use these images to test the performances of the Euclid mission. In particular, we concentrate on the precision of the photometric redshift measurements, which are key data to perform cosmic shear tomography. We calculate the fraction of the total observed sample that must be discarded to reach the required level of precision, that is equal to 0.05(1+z) for a galaxy with measured redshift z, with different ancillary ground-based observations. The results highlight the importance of u-band observations, especially to discriminate between low (z < 0.5) and high (z ~ 3) redshifts, and the need for good observing sites, with seeing FWHM < 1. arcsec. We then construct an optimal filter to detect galaxy clusters through photometric catalogues of galaxies, and we test it on the COSMOS field, obtaining 27 lensing-confirmed detections. Applying this algorithm on mock Euclid data, we verify the possibility to detect clusters with mass above 10^14.2 solar masses with a low rate of false detections.

First principle study of ions in water and ionic liquids

Die beiden in dieser Arbeit betrachteten Systeme, wässrige Lösungen von Ionen und ionische Flüssigkeiten, zeigen vielfältige Eigenschaften und Anwendungsmöglichkeiten, im Gegensatz zu anderen Systemen. Man findet sie beinahe überall im normalen Leben (Wasser), oder ihre Bedeutung wächst (ioinische Flüssigkeiten). Der elektronische Anteil und der atomare Anteil wurden getrennt voneinander untersucht und im Zusammenhang analysiert. Mittels dieser Methode konnten die in dem jeweiligen System auftretenden Mechanismen genauer untersucht werden. Diese Methode wird "Multiscale Modeling" genannt, dabei werden die Untereinheiten eines Systems genauer betrachtet, wie in diesem Fall die elektronischen and atomaren Teilsystem. Die Ergebnisse, die aus den jeweiligen Betrachtungen hervorgehen, zeigen, dass, im Falle von hydratisierten Ionen die Wasser-Wasser Wechselwirkungen wesentlich stärker sind als die elektrostatischen Wechselwirkung zwischen Wasser und dem Ion. Anhand der Ergebnisse ergibt sich, dass normale nicht-polarisierbare Modelle ausreichen, um Ionen-Wasser Lösungen zu beschreiben. Im Falle der ionischen Flüssigkeiten betrachten wir die elektronische Ebene mittels sehr genauer post-Hartree-Fock Methoden und DFT, deren Ergebnisse dann mit denen auf molekularer Ebene (mithilfe von CPMD/klassischer MD) in Beziehung gesetzt werden. Die bisherigen Ergebnisse zeigen, dass die Wasserstoff-Brückenbindungen im Fall der ionischen Flüssigkeiten nicht vernachässigt werden können. Weiterhin hat diese Studie herausgefunden, dass die klassischen Kraftfelder die Elektrostatik (Dipol- und Quadrupolmomente) nicht genau genug beschreibt. Die Kombination des mikroskopischen Mechanismus und der molekularen Eigenschaften ist besonders sinnvoll um verschiedene Anhaltspunkte von Simualtionen (z.B. mit klassische Molekular-Dynamik) oder Experimenten zu liefern oder solche zu erklären.

Computer simulations of microstructures related to the olivine spinel transition

Tiefherd-Beben, die im oberen Erdmantel in einer Tiefe von ca. 400 km auftreten, werden gewöhnlich mit dem in gleicher Tiefe auftretenden druckabhängigen, polymorphen Phasenübergang von Olivine (α-Phase) zu Spinel (β-Phase) in Verbindung gebracht. Es ist jedoch nach wie vor unklar, wie der Phasenübergang mit dem mechanischen Versagen des Mantelmaterials zusammenhängt. Zur Zeit werden im Wesentlichen zwei Modelle diskutiert, die entweder Mikrostrukturen, die durch den Phasenübergang entstehen, oder aber die rheologischen Veränderungen des Mantelgesteins durch den Phasenübergang dafür verantwortlich machen. Dabei sind Untersuchungen der Olivin→Spinel Umwandlung durch die Unzugänglichkeit des natürlichen Materials vollständig auf theoretische Überlegungen sowie Hochdruck-Experimente und Numerische Simulationen beschränkt. Das zentrale Thema dieser Dissertation war es, ein funktionierendes Computermodell zur Simulation der Mikrostrukturen zu entwickeln, die durch den Phasenübergang entstehen. Des Weiteren wurde das Computer Modell angewandt um die mikrostrukturelle Entwicklung von Spinelkörnern und die Kontrollparameter zu untersuchen. Die Arbeit ist daher in zwei Teile unterteilt: Der erste Teil (Kap. 2 und 3) behandelt die physikalischen Gesetzmäßigkeiten und die prinzipielle Funktionsweise des Computer Modells, das auf der Kombination von Gleichungen zur Errechnung der kinetischen Reaktionsgeschwindigkeit mit Gesetzen der Nichtgleichgewichtsthermodynamik unter nicht-hydostatischen Bedingungen beruht. Das Computermodell erweitert ein Federnetzwerk der Software latte aus dem Programmpaket elle. Der wichtigste Parameter ist dabei die Normalspannung auf der Kornoberfläche von Spinel. Darüber hinaus berücksichtigt das Programm die Latenzwärme der Reaktion, die Oberflächenenergie und die geringe Viskosität von Mantelmaterial als weitere wesentliche Parameter in der Berechnung der Reaktionskinetic. Das Wachstumsverhalten und die fraktale Dimension von errechneten Spinelkörnern ist dabei in guter Übereinstimmung mit Spinelstrukturen aus Hochdruckexperimenten. Im zweiten Teil der Arbeit wird das Computermodell angewandt, um die Entwicklung der Oberflächenstruktur von Spinelkörnern unter verschiedenen Bedigungen zu eruieren. Die sogenannte ’anticrack theory of faulting’, die den katastrophalen Verlauf der Olivine→Spinel Umwandlung in olivinhaltigem Material unter differentieller Spannung durch Spannungskonzentrationen erklärt, wurde anhand des Computermodells untersucht. Der entsprechende Mechanismus konnte dabei nicht bestätigt werden. Stattdessen können Oberflächenstrukturen, die Ähnlichkeiten zu Anticracks aufweisen, durch Unreinheiten des Materials erklärt werden (Kap. 4). Eine Reihe von Simulationen wurde der Herleitung der wichtigsten Kontrollparameter der Reaktion in monomineralischem Olivin gewidmet (Kap. 5 and Kap. 6). Als wichtigste Einflüsse auf die Kornform von Spinel stellten sich dabei die Hauptnormalspannungen auf dem System sowie Heterogenitäten im Wirtsminerals und die Viskosität heraus. Im weiteren Verlauf wurden die Nukleierung und das Wachstum von Spinel in polymineralischen Mineralparagenesen untersucht (Kap. 7). Die Reaktionsgeschwindigkeit der Olivine→Spinel Umwandlung und die Entwicklung von Spinelnetzwerken und Clustern wird durch die Gegenwart nicht-reaktiver Minerale wie Granat oder Pyroxen erheblich beschleunigt. Die Bildung von Spinelnetzwerken hat das Potential, die mechanischen Eigenschaften von Mantelgestein erheblich zu beeinflussen, sei es durch die Bildung potentieller Scherzonen oder durch Gerüstbildung. Dieser Lokalisierungprozess des Spinelwachstums in Mantelgesteinen kann daher ein neues Erklärungsmuster für Tiefbeben darstellen.