Computer simulations of two-dimensional colloidal crystals under confinement and shear

In this thesis we are presenting a broadly based computer simulation study of two-dimensional colloidal crystals under different external conditions. In order to fully understand the phenomena which occur when the system is being compressed or when the walls are being sheared, it proved necessary to study also the basic motion of the particles and the diffusion processes which occur in the case without these external forces. In the first part of this thesis we investigate the structural transition in the number of rows which occurs when the crystal is being compressed by placing the structured walls closer together. Previous attempts to locate this transition were impeded by huge hysteresis effects. We were able to determine the transition point with higher precision by applying both the Schmid-Schilling thermodynamic integration method and the phase switch Monte Carlo method in order to determine the free energies. These simulations showed not only that the phase switch method can successfully be applied to systems with a few thousand particles and a soft crystalline structure with a superimposed pattern of defects, but also that this method is way more efficient than a thermodynamic integration when free energy differences are to be calculated. Additionally, the phase switch method enabled us to distinguish between several energetically very similar structures and to determine which one of them was actually stable. Another aspect considered in the first result chapter of this thesis is the ensemble inequivalence which can be observed when the structural transition is studied in the NpT and in the NVT ensemble. The second part of this work deals with the basic motion occurring in colloidal crystals confined by structured walls. Several cases are compared where the walls are placed in different positions, thereby introducing an incommensurability into the crystalline structure. Also the movement of the solitons, which are created in the course of the structural transition, is investigated. Furthermore, we will present results showing that not only the well-known mechanism of vacancies and interstitial particles leads to diffusion in our model system, but that also cooperative ring rotation phenomena occur. In this part and the following we applied Langevin dynamics simulations. In the last chapter of this work we will present results on the effect of shear on the colloidal crystal. The shear was implemented by moving the walls with constant velocity. We have observed shear banding and, depending on the shear velocity, that the inner part of the crystal breaks into several domains with different orientations. At very high shear velocities holes are created in the structure, which originate close to the walls, but also diffuse into the inner part of the crystal.

Variational Monte Carlo study of the hydrogen electronic structure at ultra-high pressure

Die causa finalis der vorliegenden Arbeit ist das Verständnis des Phasendiagramms von Wasserstoff bei ultrahohen Drücken, welche von nichtleitendem H2 bis hin zu metallischem H reichen. Da die Voraussetzungen für ultrahohen Druck im Labor schwer zu schaffen sind, bilden Computersimulationen ein wichtiges alternatives Untersuchungsinstrument. Allerdings sind solche Berechnungen eine große Herausforderung. Eines der größten Probleme ist die genaue Auswertung des Born-Oppenheimer Potentials, welches sowohl für die nichtleitende als auch für die metallische Phase geeignet sein muss. Außerdem muss es die starken Korrelationen berücksichtigen, die durch die kovalenten H2 Bindungen und die eventuellen Phasenübergänge hervorgerufen werden. Auf dieses Problem haben unsere Anstrengungen abgezielt. Im Kontext von Variationellem Monte Carlo (VMC) ist die Shadow Wave Function (SWF) eine sehr vielversprechende Option. Aufgrund ihrer Flexibilität sowohl lokalisierte als auch delokalisierte Systeme zu beschreiben sowie ihrer Fähigkeit Korrelationen hoher Ordnung zu berücksichtigen, ist sie ein idealer Kandidat für unsere Zwecke. Unglücklicherweise bringt ihre Formulierung ein Vorzeichenproblem mit sich, was die Anwendbarkeit limitiert. Nichtsdestotrotz ist es möglich diese Schwierigkeit zu umgehen indem man die Knotenstruktur a priori festlegt. Durch diesen Formalismus waren wir in der Lage die Beschreibung der Elektronenstruktur von Wasserstoff signifikant zu verbessern, was eine sehr vielversprechende Perspektive bietet. Während dieser Forschung haben wir also die Natur des Vorzeichenproblems untersucht, das sich auf die SWF auswirkt, und dabei ein tieferes Verständnis seines Ursprungs erlangt. Die vorliegende Arbeit ist in vier Kapitel unterteilt. Das erste Kapitel führt VMC und die SWF mit besonderer Ausrichtung auf fermionische Systeme ein. Kapitel 2 skizziert die Literatur über das Phasendiagramm von Wasserstoff bei ultrahohem Druck. Das dritte Kapitel präsentiert die Implementierungen unseres VMC Programms und die erhaltenen Ergebnisse. Zum Abschluss fasst Kapitel 4 unsere Bestrebungen zur Lösung des zur SWF zugehörigen Vorzeichenproblems zusammen.

Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.

Computer simulation methods to study interfacial tensions : from the Ising model to colloidal crystals

In condensed matter systems, the interfacial tension plays a central role for a multitude of phenomena. It is the driving force for nucleation processes, determines the shape and structure of crystalline structures and is important for industrial applications. Despite its importance, the interfacial tension is hard to determine in experiments and also in computer simulations. While for liquid-vapor interfacial tensions there exist sophisticated simulation methods to compute the interfacial tension, current methods for solid-liquid interfaces produce unsatisfactory results.rnrnAs a first approach to this topic, the influence of the interfacial tension on nuclei is studied within the three-dimensional Ising model. This model is well suited because despite its simplicity, one can learn much about nucleation of crystalline nuclei. Below the so-called roughening temperature, nuclei in the Ising model are not spherical anymore but become cubic because of the anisotropy of the interfacial tension. This is similar to crystalline nuclei, which are in general not spherical but more like a convex polyhedron with flat facets on the surface. In this context, the problem of distinguishing between the two bulk phases in the vicinity of the diffuse droplet surface is addressed. A new definition is found which correctly determines the volume of a droplet in a given configuration if compared to the volume predicted by simple macroscopic assumptions.rnrnTo compute the interfacial tension of solid-liquid interfaces, a new Monte Carlo method called ensemble switch method'' is presented which allows to compute the interfacial tension of liquid-vapor interfaces as well as solid-liquid interfaces with great accuracy. In the past, the dependence of the interfacial tension on the finite size and shape of the simulation box has often been neglected although there is a nontrivial dependence on the box dimensions. As a consequence, one needs to systematically increase the box size and extrapolate to infinite volume in order to accurately predict the interfacial tension. Therefore, a thorough finite-size scaling analysis is established in this thesis. Logarithmic corrections to the finite-size scaling are motivated and identified, which are of leading order and therefore must not be neglected. The astounding feature of these logarithmic corrections is that they do not depend at all on the model under consideration. Using the ensemble switch method, the validity of a finite-size scaling ansatz containing the aforementioned logarithmic corrections is carefully tested and confirmed. Combining the finite-size scaling theory with the ensemble switch method, the interfacial tension of several model systems, ranging from the Ising model to colloidal systems, is computed with great accuracy.

Molecular dynamics simulations of silicate and borate glasses and melts : structure, diffusion dynamics and vibrational properties

Molecular dynamics simulations of silicate and borate glasses and melts: Structure, diffusion dynamics and vibrational properties. In this work computer simulations of the model glass formers SiO2 and B2O3 are presented, using the techniques of classical molecular dynamics (MD) simulations and quantum mechanical calculations, based on density functional theory (DFT). The latter limits the system size to about 100−200 atoms. SiO2 and B2O3 are the two most important network formers for industrial applications of oxide glasses. Glass samples are generated by means of a quench from the melt with classical MD simulations and a subsequent structural relaxation with DFT forces. In addition, full ab initio quenches are carried out with a significantly faster cooling rate. In principle, the structural properties are in good agreement with experimental results from neutron and X-ray scattering, in all cases. A special focus is on the study of vibrational properties, as they give access to low-temperature thermodynamic properties. The vibrational spectra are calculated by the so-called ”frozen phonon” method. In all cases, the DFT curves show an acceptable agreement with experimental results of inelastic neutron scattering. In case of the model glass former B2O3, a new classical interaction potential is parametrized, based on the liquid trajectory of an ab initio MD simulation at 2300 K. In this course, a structural fitting routine is used. The inclusion of 3-body angular interactions leads to a significantly improved agreement of the liquid properties of the classical MD and ab initio MD simulations. However, the generated glass structures, in all cases, show a significantly lower fraction of 3-membered planar boroxol rings as predicted by experimental results (f=60%-80%). The largest boroxol ring fraction of f=15±5% is observed in the full ab initio quenches from 2300 K. In case of SiO2, the glass structures after the quantum mechanical relaxation are the basis for calculations of the linear thermal expansion coefficient αL(T), employing the quasi-harmonic approximation. The striking observation is a change change of sign of αL(T) going along with a temperature range of negative αL(T) at low temperatures, which is in good agreement with experimental results.

Numerical analysis of the relation between interactions and structure in a molecular fluid

Coarse graining is a popular technique used in physics to speed up the computer simulation of molecular fluids. An essential part of this technique is a method that solves the inverse problem of determining the interaction potential or its parameters from the given structural data. Due to discrepancies between model and reality, the potential is not unique, such that stability of such method and its convergence to a meaningful solution are issues.rnrnIn this work, we investigate empirically whether coarse graining can be improved by applying the theory of inverse problems from applied mathematics. In particular, we use the singular value analysis to reveal the weak interaction parameters, that have a negligible influence on the structure of the fluid and which cause non-uniqueness of the solution. Further, we apply a regularizing Levenberg-Marquardt method, which is stable against the mentioned discrepancies. Then, we compare it to the existing physical methods - the Iterative Boltzmann Inversion and the Inverse Monte Carlo method, which are fast and well adapted to the problem, but sometimes have convergence problems.rnrnFrom analysis of the Iterative Boltzmann Inversion, we elaborate a meaningful approximation of the structure and use it to derive a modification of the Levenberg-Marquardt method. We engage the latter for reconstruction of the interaction parameters from experimental data for liquid argon and nitrogen. We show that the modified method is stable, convergent and fast. Further, the singular value analysis of the structure and its approximation allows to determine the crucial interaction parameters, that is, to simplify the modeling of interactions. Therefore, our results build a rigorous bridge between the inverse problem from physics and the powerful solution tools from mathematics. rn

Regulatory mechanism of the light-activable allosteric switch LOV-TAP for the control of DNA binding: a computer simulation study

The spatio-temporal control of gene expression is fundamental to elucidate cell proliferation and deregulation phenomena in living systems. Novel approaches based on light-sensitive multiprotein complexes have recently been devised, showing promising perspectives for the noninvasive and reversible modulation of the DNA-transcriptional activity in vivo. This has lately been demonstrated in a striking way through the generation of the artificial protein construct light-oxygen-voltage (LOV)-tryptophan-activated protein (TAP), in which the LOV-2-Jα photoswitch of phototropin1 from Avena sativa (AsLOV2-Jα) has been ligated to the tryptophan-repressor (TrpR) protein from Escherichia coli. Although tremendous progress has been achieved on the generation of such protein constructs, a detailed understanding of their functioning as opto-genetical tools is still in its infancy. Here, we elucidate the early stages of the light-induced regulatory mechanism of LOV-TAP at the molecular level, using the noninvasive molecular dynamics simulation technique. More specifically, we find that Cys450-FMN-adduct formation in the AsLOV2-Jα-binding pocket after photoexcitation induces the cleavage of the peripheral Jα-helix from the LOV core, causing a change of its polarity and electrostatic attraction of the photoswitch onto the DNA surface. This goes along with the flexibilization through unfolding of a hairpin-like helix-loop-helix region interlinking the AsLOV2-Jα- and TrpR-domains, ultimately enabling the condensation of LOV-TAP onto the DNA surface. By contrast, in the dark state the AsLOV2-Jα photoswitch remains inactive and exerts a repulsive electrostatic force on the DNA surface. This leads to a distortion of the hairpin region, which finally relieves its tension by causing the disruption of LOV-TAP from the DNA.

The foundations of computer assisted surgery

Using navigation systems in general orthopaedic surgery and, in particular, knee replacement is becoming more and more accepted. This paper describes the basic technological concepts of modern computer assisted surgical systems. It explains the variation in currently available systems and outlines research activities that will potentially influence future products. In general, each navigation system is defined by three components: (1) the therapeutic object is the anatomical structure that is operated on using the navigation system, (2) the virtual object represents an image of the therapeutic object, with radiological images or computer generated models potentially being used, and (3) last but not least, the navigator acquires the spatial position and orientation of instruments and anatomy thus providing the necessary data to replay surgical action in real-time on the navigation system's screen.

Prosthetically driven, computer-guided implant planning for the edentulous maxilla: a model study

OBJECTIVES: To analyze computer-assisted diagnostics and virtual implant planning and to evaluate the indication for template-guided flapless surgery and immediate loading in the rehabilitation of the edentulous maxilla. MATERIALS AND METHODS: Forty patients with an edentulous maxilla were selected for this study. The three-dimensional analysis and virtual implant planning was performed with the NobelGuide software program (Nobel Biocare, Göteborg, Sweden). Prior to the computer tomography aesthetics and functional aspects were checked clinically. Either a well-fitting denture or an optimized prosthetic setup was used and then converted to a radiographic template. This allowed for a computer-guided analysis of the jaw together with the prosthesis. Accordingly, the best implant position was determined in relation to the bone structure and prospective tooth position. For all jaws, the hypothetical indication for (1) four implants with a bar overdenture and (2) six implants with a simple fixed prosthesis were planned. The planning of the optimized implant position was then analyzed as follows: the number of implants was calculated that could be placed in sufficient quantity of bone. Additional surgical procedures (guided bone regeneration, sinus floor elevation) that would be necessary due the reduced bone quality and quantity were identified. The indication of template-guided, flapless surgery or an immediate loaded protocol was evaluated. RESULTS: Model (a) - bar overdentures: for 28 patients (70%), all four implants could be placed in sufficient bone (total 112 implants). Thus, a full, flapless procedure could be suggested. For six patients (15%), sufficient bone was not available for any of their planned implants. The remaining six patients had exhibited a combination of sufficient or insufficient bone. Model (b) - simple fixed prosthesis: for 12 patients (30%), all six implants could be placed in sufficient bone (total 72 implants). Thus, a full, flapless procedure could be suggested. For seven patients (17%), sufficient bone was not available for any of their planned implants. The remaining 21 patients had exhibited a combination of sufficient or insufficient bone. DISCUSSION: In the maxilla, advanced atrophy is often observed, and implant placement becomes difficult or impossible. Thus, flapless surgery or an immediate loading protocol can be performed just in a selected number of patients. Nevertheless, the use of a computer program for prosthetically driven implant planning is highly efficient and safe. The three-dimensional view of the maxilla allows the determination of the best implant position, the optimization of the implant axis, and the definition of the best surgical and prosthetic solution for the patient. Thus, a protocol that combines a computer-guided technique with conventional surgical procedures becomes a promising option, which needs to be further evaluated and improved.

Mechanisms of Ligand–Protein Interaction in Sec-14-like Transporters Investigated by Computer Simulations

We review our recent work on protein-ligand interactions in vitamin transporters of the Sec-14-like protein. Our studies focused on the cellular-retinaldehyde binding protein (CRALBP) and the alpha-tocopherol transfer protein (alpha-TTP). CRALBP is responsible for mobilisation and photo-protection of short-chain cis-retinoids in the dim-light visual cycle or rod photoreceptors. alpha-TTP is a key protein responsible for selection and retention of RRR-alpha-tocopherol, the most active isoform of vitamin E in superior animals. Our simulation studies evidence how subtle chemical variations in the substrate can lead to significant distortion in the structure of the complex, and how these changes can either lead to new protein function, or be used to model engineered protein variants with tailored properties. Finally, we show how integration of computational and experimental results can contribute in synergy to the understanding of fundamental processes at the biomolecular scale.

Fully Automatic CT Segmentation for Computer-Assisted Pre-operative Planning of Hip Arthroscopy

Extraction of both pelvic and femoral surface models of a hip joint from CT data for computer-assisted pre-operative planning of hip arthroscopy is addressed. We present a method for a fully automatic image segmentation of a hip joint. Our method works by combining fast random forest (RF) regression based landmark detection, atlas-based segmentation, with articulated statistical shape model (aSSM) based hip joint reconstruction. The two fundamental contributions of our method are: (1) An improved fast Gaussian transform (IFGT) is used within the RF regression framework for a fast and accurate landmark detection, which then allows for a fully automatic initialization of the atlas-based segmentation; and (2) aSSM based fitting is used to preserve hip joint structure and to avoid penetration between the pelvic and femoral models. Validation on 30 hip CT images show that our method achieves high performance in segmenting pelvis, left proximal femur, and right proximal femur surfaces with an average accuracy of 0.59 mm, 0.62 mm, and 0.58 mm, respectively.

Knowledge-Based Task Structure Planning for an Information Gathering Agent

An effective solution to model and apply planning domain knowledge for deliberation and action in probabilistic, agent-oriented control is presented. Specifically, the addition of a task structure planning component and supporting components to an agent-oriented architecture and agent implementation is described. For agent control in risky or uncertain environments, an approach and method of goal reduction to task plan sets and schedules of action is presented. Additionally, some issues related to component-wise, situation-dependent control of a task planning agent that schedules its tasks separately from planning them are motivated and discussed.

Cerebellar mechanisms for motor learning: Testing predictions from a large-scale computer simulation

The cerebellum is the major brain structure that contributes to our ability to improve movements through learning and experience. We have combined computer simulations with behavioral and lesion studies to investigate how modification of synaptic strength at two different sites within the cerebellum contributes to a simple form of motor learning—Pavlovian conditioning of the eyelid response. These studies are based on the wealth of knowledge about the intrinsic circuitry and physiology of the cerebellum and the straightforward manner in which this circuitry is engaged during eyelid conditioning. Thus, our simulations are constrained by the well-characterized synaptic organization of the cerebellum and further, the activity of cerebellar inputs during simulated eyelid conditioning is based on existing recording data. These simulations have allowed us to make two important predictions regarding the mechanisms underlying cerebellar function, which we have tested and confirmed with behavioral studies. The first prediction describes the mechanisms by which one of the sites of synaptic modification, the granule to Purkinje cell synapses (gr → Pkj) of the cerebellar cortex, could generate two time-dependent properties of eyelid conditioning—response timing and the ISI function. An empirical test of this prediction using small, electrolytic lesions of the cerebellar cortex revealed the pattern of results predicted by the simulations. The second prediction made by the simulations is that modification of synaptic strength at the other site of plasticity, the mossy fiber to deep nuclei synapses (mf → nuc), is under the control of Purkinje cell activity. The analysis predicts that this property should confer mf → nuc synapses with resistance to extinction. Thus, while extinction processes erase plasticity at the first site, residual plasticity at mf → nuc synapses remains. The residual plasticity at the mf → nuc site confers the cerebellum with the capability for rapid relearning long after the learned behavior has been extinguished. We confirmed this prediction using a lesion technique that reversibly disconnected the cerebellar cortex at various stages during extinction and reacquisition of eyelid responses. The results of these studies represent significant progress toward a complete understanding of how the cerebellum contributes to motor learning. ^