08 Fakultät Mathematik und Physik

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9

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Open Access
Die Bedeutung perkolierender und nichtperkolierender Phasen bei Mehrphasenströmungen in porösen Medien auf Laborskala
(2011) Doster, Florian; Hilfer, Rudolf (Prof. Dr. Dr.)
Das Verständnis makroskopischer Phänomene bei Mehrphasenströmungen in porösen Medien ist sowohl von wissenschaftlicher Seite als auch für Anwendungen von großem Interesse. Obwohl seit über einem Jahrhundert intensiv daran geforscht wird und die Phänomene auf der Porenskala durch die Gleichungen der klassischen Hydrodynamik beschrieben werden, ist bis heute keine Theorie vorhanden, die auf Labor- und Feldskala Hysterese und residuale Fluidkonfigurationen bei Mehrphasenströmungen umfassend und physikalisch richtig beschreibt. Die Berücksichtigung der unterschiedlichen hydrodynamischen Eigenschaften von perkolierenden und nichtperkolierenden Fluidanteilen auf makroskopischen Skalen könnte der Schlüssel zu einem besseren Modell sein. Hilfer schlägt ein Modell vor (Phys. Rev. E. 73, 016307 (2006)), in welchem diese Unterschiede nicht ignoriert werden. Erste quasistationäre Lösungen dieses Modells geben Hoffnung, dass durch das Einbeziehen dieser Unterschiede in der Modellbildung Schwachpunkte traditioneller Ansätze behoben werden können. Weitergehende Untersuchungen dieses Modells und seiner Gleichungen bilden die Aufgabenstellung dieser Dissertation. Um die Gleichungen zu studieren, wurden Umformungen und Näherungen formuliert, die analytische Lösungen ermöglichen. Außerdem wurden Schließbedingungen formuliert, die die Lösung zeitabhängiger Fragestellungen erlauben. Vier Anfangs- und Randwertprobleme wurden analytisch bzw. quasianalytisch gelöst. Sie sind Verallgemeinerungen des Buckley-Leverett-Problems, der schwerkraftgetriebenen Umverteilung, des McWhorter-Sunada-Problems und des Philip-Problems. Ferner wurden vier numerische Algorithmen entwickelt, die Anfangs- und Randwertprobleme für unterschiedliche mathematische Formulierungen und physikalische Näherungen des Modells lösen. Mit diesen Algorithmen wurden Laborexperimente simuliert. Die Experimente können drei Klassen zugeordnet werden. Die erste Klasse bilden Experimente mit einer geschlossenen porösen Säule. In diesen Experimenten bewirken allein die Schwerkraft und Kapillar- und Grenzflächenkräfte eine Umverteilung der Fluide. Die Ergebnisse zeigen, dass das Modell hysteretisches Verhalten in Sättigungsverteilungen beschreiben kann. Sie illustrieren außerdem Gemeinsamkeiten und Unterschiede zu bestehenden Modellen. Die gewonnenen Aussagen können im Labor überprüft werden. Die zweite Klasse bilden Experimente, bei denen eine poröse Säule von einem von außen aufgeprägten Fluss durchströmt wird. Die Simulationen zeigen, dass die Beschreibung der Dynamik residualer Sättigungen mit diesem Modell möglich ist. Die dritte Klasse bilden Experimente mit Druckrandbedingungen. Solche Experimente werden im Labor zur Bestimmung und Überprüfung von Kapillardrucksättigungsbeziehungen durchgeführt. Die Simulation eines solchen Experiments stimmt gut mit Messwerten aus der Literatur überein. Die Ergebnisse dieser Dissertation zeigen, dass zumindest einige Schwächen traditioneller Ansätze durch die Berücksichtigung der unterschiedlichen hydrodynamischen Eigenschaften von perkolierenden und nichtperkolierenden Fluidanteilen behoben werden können. Für das neue Modell wurden analytische und quasianalytische Lösungen bestimmt und Verfahren entwickelt, numerische Lösungen zu berechnen. Einige der numerischen Lösungen wurden mit experimentellen Daten verglichen. Es konnte eine gute Übereinstimmung der Ergebnisse gezeigt werden. Die übrigen Lösungen dienen als Vorschlag für Experimentatoren. Eine Durchführung dieser Experimente im Labor würde wichtige Erkenntnisse zur Qualität des Modells liefern.
Open Access
A brief review of capillary number and its use in capillary desaturation curves
(2022) Guo, Hu; Song, Kaoping; Hilfer, R.
Capillary number, understood as the ratio of viscous force to capillary force, is one of the most important parameters in enhanced oil recovery (EOR). It continues to attract the interest of scientists and engineers, because the nature and quantification of macroscopic capillary forces remain controversial. At least 41 different capillary numbers have been collected here from the literature. The ratio of viscous and capillary force enters crucially into capillary desaturation experiments. Although the ratio is length scale dependent, not all definitions of capillary number depend on length scale, indicating potential inconsistencies between various applications and publications. Recently, new numbers have appeared and the subject continues to be actively discussed. Therefore, a short review seems appropriate and pertinent.
Open Access
CO2-induced drastic decharging of dielectric surfaces in aqueous suspensions
(2024) Vogel, Peter; Beyer, David; Holm, Christian; Palberg, Thomas
We study the influence of airborne CO2 on the charge state of carboxylate stabilized polymer latex particles suspended in aqueous electrolytes. We combine conductometric experiments interpreted in terms of Hessinger's conductivity model with Poisson-Boltzmann cell (PBC) model calculations with charge regulation boundary conditions. Without CO2, a minority of the weakly acidic surface groups are dissociated and only a fraction of the total number of counter-ions actually contribute to conductivity. The remaining counter-ions exchange freely with added other ions like Na+, K+ or Cs+. From the PBC-calculations we infer a corresponding pKa of 4.26 as well as a renormalized charge in reasonably good agreement with the number of freely mobile counter-ions. Equilibration of salt- and CO2-free suspensions against ambient air leads to a drastic de-charging, which exceeds by far the expected effects of to dissolved CO2 and its dissociation products. Further, no counter-ion-exchange is observed. To reproduce the experimental findings, we have to assume an effective pKa of 6.48. This direct influence of CO2 on the state of surface group dissociation explains our recent finding of a CO2-induced decrease of the ζ-potential and supports the suggestion of an additional charge regulation caused by molecular CO2. Given the importance of charged surfaces in contact with aqueous electrolytes, we anticipate that our observations bear substantial theoretical challenges and important implications for applications ranging from desalination to bio-membranes.
Open Access
Coarse grained hydrogels
(2017) Richter, Tobias; Holm, Christian (Prof. Dr.)
Open Access
Coarse-grained simulations of molecular catalysis in confined spaces
(2023) Tischler, Ingo; Holm, Christian (Prof. Dr.)
Open Access
Collective variables in data-centric neural network training
(2023) Nikolaou, Konstantin
Neural Networks have become beneficial tools for physics research. While they provide a powerful tool for data-driven modeling, their success is accompanied by a lack of interpretability. This thesis aims to add transparency to the opaque nature of NNs by means of collective variables, a concept well-known in the field of statistical physics. Three collective variables are introduced that emerge from the interactions between neurons and data. These observables enable one to capture holistic behavior of the network and are used to conduct an analysis of neural network training, focusing on data. Through the investigations, the collective variables are applied to selections from a novel sampling method: Random Network Distillation (RND). Besides studying collective variables, the investigation of Random Network Distillation as a data selection method composes the second part of this thesis. The method is analyzed and optimized with respect to its components, aiming to understand and improve the data selection process. It is shown that RND can be used to select data sets that are beneficial for neural network training, giving rise to its application in fields like active learning. The collective variables are leveraged to further investigate the selection method and its effect on neural network training, revealing previously unknown properties of RND-selected data sets. The potential of the collective variables is demonstrated and discussed from a data-centric perspective. They are shown to be discriminative towards the information content of data and give rise to novel insights into the nature of neural network training. In addition to fundamental research on neural networks, the collective variables offer several potential applications including the identification of adversarial attacks and facilitating neural architecture search.
Open Access
Conditional entropic approach to nonequilibrium complex systems with weak fluctuation correlation
(2023) Itto, Yuichi
A conditional entropic approach is discussed for nonequilibrium complex systems with a weak correlation between spatiotemporally fluctuating quantities on a large time scale. The weak correlation is found to constitute the fluctuation distribution that maximizes the entropy associated with the conditional fluctuations. The approach is illustrated in diffusion phenomenon of proteins inside bacteria. A further possible illustration is also presented for membraneless organelles in embryos and beads in cell extracts, which share common natures of fluctuations in their diffusion.
Open Access
Confined Ru‐catalysts in a two‐phase heptane/ionic liquid solution : modeling aspects
(2020) Kobayashi, Takeshi; Kraus, Hamzeh; Hansen, Niels; Fyta, Maria
A modeling approach for atomic‐resolution studies of sup‐ ported ionic liquid phase (SILP) catalytic systems in silica mesoporous confinement with surface hydroxyl and functional groups is proposed. First, a force field for the Ru‐based catalyst is developed. Second, its solvation behavior within a bulk two‐phase system of heptane and an IL is studied. Third, static and dynamic properties of the confined system are investigated. Using classical molecular dynamics simulations, experimentally inaccessible properties can thus be studied that are important for an optimization of a SILP system for performing a ring‐closing metathesis reaction.
Open Access
Contact Networks of Mobile Agents and Spreading Dynamics
(2006) González, Marta C.; Herrmann, Hans J. (Prof. Dr.)
The concept complex networks'' refers to a network that is often the representation of a complex system. In this context, a statistical physics approach has been exploited as a very convenient method because of its deep connection with graph theory and because of its ability to quantitatively characterize macroscopic phenomena in terms of the microscopic dynamics of the various systems. Our research focuses on the development of appropriate models of spreading dynamics, such as diffusion models of opinion formation and spreading of infections. Particularly, we present models of contact that differ from the traditional static graph modeling that is at the core of classical graph theory: We incorporate underlying agent interactions that generate dynamical contact networks. The network itself is the result of the interactions among nodes. Motivated by the close relations of the field with real world measurements, we collect and incorporate in the context of Statistical Physics literature new sets of social networks in order to test and validate the models here proposed.
Open Access
Convolution on distribution spaces characterized by regularization
(2023) Kleiner, Tillmann; Hilfer, Rudolf
Locally convex convolutor spaces are studied which consist of those distributions that define a continuous convolution operator mapping from the space of test functions into a given locally convex lattice of measures. The convolutor spaces are endowed with the topology of uniform convergence on bounded sets. Their locally convex structure is characterized via regularization and function‐valued seminorms under mild structural assumptions on the space of measures. Many recent generalizations of classical distribution spaces turn out to be special cases of the general convolutor spaces introduced here. Recent topological characterizations of convolutor spaces via regularization are extended and improved. A valuable property of the convolutor spaces in applications is that convolution of distributions inherits continuity properties from those of bilinear convolution mappings between the locally convex lattices of measures.
Open Access
Crystallization pathways and mechanisms of charged macromolecules at low supersaturations
(2014) Kratzer, Kai; Arnold, Axel (Jun.-Prof. Dr.)
In this work, we investigate the crystallization of charged macromolecules with Molecular Dynamics computer simulations. Thereby, the charged macromolecules are modeled by an effective pair potential, the Yukawa potential, which accounts for the electrostatic screening by neutralizing salt ions. The Yukawa potential can be used to model real colloidal systems like they are used in experiments. This has been shown during this work in collaboration with the 2nd Physical Institute of the University of Stuttgart. We found that at lower system densities the Yukawa potential fits very well to the interaction potentials obtained from the RDFs. At higher densities, the repulsive part of the interaction potential could be described by the Yukawa potential, while for large distances, three body interactions play a role. To study the crystal growth in detail, it is necessary to simulate near the coexistence line in the phase diagram, where the attachment rate of growth units is low, which leads to a high free energy barrier towards nucleation. Therefore, we use the Forward Flux Sampling (FFS) method, where the reaction path through phase space is partitioned by a set of interfaces. The efficiency of the FFS method depends mainly on the positions of the interfaces. We developed two methods to place these interfaces on-the-fly and at their optimized locations. Beyond the increase of efficiency, this leads to a tremendous simplification of the method: Only the initial state and the final state have to be defined in terms of the order parameter. Then, the simulation finds its way through phase space automatically and optimized. The backtracking of different crystallization pathways in the FFS scheme yields the successful crystallization paths. These pathways were analyzed in the post-processing for determining nucleation mechanisms and to identify possible precursors for the onset of crystal growth. We found that at the local position, where the critical cluster will be formed, a local structure of sixfold order can already been discovered in the fluid at an early stage. We did not find correlations with the fourfold symmetry or the local density. Depending on the pressure and contact energies of the potential, we arrive at different solid-like structures in the final state. For lower contact values and higher pressures the structure is an hcp/fcc-like lattice. In contrast, at higher contact values and lower pressures we obtained a bcc-like structure, which is not the stable structure according to the phase diagram. This can be explained by the fact that the crystallization process is a two-stage mechanism with two energy barriers involved. The first stage is the transition from the liquid phase to the metastable bcc-like phase, and the second stage is the transition from the bcc-like phase to the hcp/fcc-like phase. The energy barrier for the second transition is lower for smaller contact values of the Yukawa potential, and higher for larger contact values. This is the reason, why we could only observe the spontaneous transition to the stable phase for the low contact value case. In the simulation with the higher contact value, the second energy barrier could not be overcome spontaneously, but requires performing an additional FFS simulation, which optimizes for a higher number of fcc-like particles in the system. Moreover, the transition was only possible when starting from the critical clusters and not from the fully converted bcc-like system. Hence, a condition for the second transition is the existence of a liquid-bcc interface. The process of the transition is facilitated by hcp/fcc-like fluctuations at the surface of the crystal cluster. Thus, we observe a heterogeneous nucleation in the initially homogeneous system. With the help of analyzing stationary distributions of the order parameter it was possible to calculate the free energy landscape of crystallization. The free energy landscape fits well to CNT, if one allows a small shift for the cluster size. This is justified because the unknown real dimensions of the cluster depend on the (arbitrary) threshold for the solid particle detection in the local bond order parameter analysis. For both, high and low contact values, the shift was smaller than a particle’s diameter. CNT can be applied in both cases considering the first, metastable phase. This phase is always a bcc crystal, even if the thermodynamically stable phase is an fcc crystal. In this case, nucleation is a two-stage process, which however does not influence nucleation rates or the structure of the critical cluster. The nuclei are almost spherical, so that edges of the crystal play a minor role. Also, the crystal surface is fairly diffuse, which however is taken into account by the surface tension. Nucleation is mainly the formation of a sixfold symmetry, which can already be seen at the onset of crystallization in the supersaturated liquid.
Open Access
Dielectric effects in complex fluids
(2022) Zeman, Johannes; Holm, Christian (Prof. Dr.)
Open Access
Dielectric variations in simulations of charged soft matter
(2016) Fahrenberger, Florian; Holm, Christian (Prof. Dr.)
In this thesis, an algorithm to calculate electrostatic interactions in molecular dynamics simulations is extended to include spatial and temporal variations in the dielectric permittivity of the system. The algorithm is implemented, verified, and parallelized. It is then applied to a number of systems containing charged soft matter. Noticeable quantitative and qualitative differences are found between simulations including and excluding dielectric variations. Particularly for the effective charge of colloids, and for the conductivity of polyelectrolytes in aqueous solution, major behavioral changes are shown.
Open Access
Effective transport coefficients of anisotropic disordered materials
(2022) Hilfer, R.; Hauskrecht, J.
A novel effective medium theory for homogenized transport coefficients of anisotropic mixtures of possibly anisotropic materials is developed. Existing theories for isotropic systems cannot be easily extended, because that would require geometric characterizations of anisotropic connectivity. In this work anisotropic connectivity is characterized by introducing a tensor that is constructed from a histogram of local percolating directions. The construction is inspired by local porosity theory. A large number of known and unknown generalized effective medium approximations for anisotropic media are obtained as limiting special cases from the new theory. Among these limiting cases the limit of strong cylindrical anisotropy is of particular interest. The parameter space of the generalized theory is explored, and the advanced results are applied to experiment.
Open Access
Efficient algorithms for electrostatic interactions including dielectric contrasts
(2013) Arnold, Axel; Breitsprecher, Konrad; Fahrenberger, Florian; Kesselheim, Stefan; Lenz, Olaf; Holm, Christian
Coarse grained models of soft matter are usually combined with implicit solvent models that take the electrostatic polarizability into account via a dielectric background. In biophysical or nanoscale simulations that include water, this constant can vary greatly within the system. Performing molecular dynamics or other simulations that need compute exact electrostatic interactions between charges in those systems is computationally demanding. We review here several algorithms developped by us that perform exactly this task. For planar dielectric surfaces in partial periodic boundary conditions, the arising image charges can be either treated with the MMM2D algorithm in a very efficient and accurate way, or with the ELC term that enables the user to use his favorite 3D periodic Coulomb solver . Arbitrarily shaped interfaces can be dealt with using induced surface charges with the ICC algorithm. Finally, the local electrostatics algorithm MEMD (Maxwell Equations Molecular Dynamics) allows even to employ a smoothly varying dielectric constant in the systems. We introduce the concepts of these three algorithms, and an extension for the inclusion of boundaries that are to be held fixed at constant potential (metal conditions). For each method, we present a showcase application to highlight the importance of dielectric interfaces.
Open Access
Electrokinetic transport phenomena in soft-matter systems
(2018) Rempfer, Georg; Holm, Christian (Prof. Dr.)
Open Access
Electronic, adsorption, and transport properties of diamondoid-based complexes
(2017) Adhikari, Bibek; Fyta, Maria (Jun. Prof. Dr.)
Quantum simulation is an invaluable tool to researchers from various fields of scientific research. It allows the investigation of various complex condensed matter in the regimes of physics, chemistry, and biology. In this work, we focused our attention in unraveling the physical, chemical, electronic, transport, and optical properties of diamondoids and their complexes through quantum simulations. We have implemented a bottom-up approach where we move from the doping and functionalization of single diamondoids up to the diamondoid-based molecular devices. Naturally, diamondoids have been extracted from petroleum and also have been synthesized in the lab. These diamondoids are hydrogen terminated carbon cage-like structures which have lattice structure similar to diamond. As a result, they are found to be as rigid and stiff as diamonds and are comparable to the stiffness of graphite and carbon nanotubes. In addition to their strong physical properties, they are also the building blocks for important drugs. Furthermore, because they have a negative electron affinity, they are potentially useful in molecular electronics and electron-emitting devices.
Open Access
The electrophoretic mobility of bare and soft spherical colloids : a molecular dynamics study
(2014) Raafatnia, Shervin; Holm, Christian (Prof. Dr.)
In this work, the electrophoretic mobility of colloids in salt solutions are studied by means of coarse-grained Molecular Dynamics simulations. Two different types of colloids are considered; bare colloids and polyelectrolyte-grafted colloids. A novel model for simulation of large bare colloids in the presence of explicit ions is developed. Comparison of the results with experimental data helps gain a better understanding of the mechanisms responsible for the interesting phenomenon of mobility reversal. Furthermore, a hitherto unknown electrokinetic behavior of polyelectrolyte-grafted colloids is found from simulations including full hydrodynamic interactions. The validity of the existing theories is verified via comparison with simulation results.
Open Access
Entropic segregation of polymers under confinement
(2016) Minina, Elena; Holm, Christan (Prof. Dr.)
Overlapping polymers confined in a cylinder experience strong repulsion that drives them towards segregation. This has biological relevance to chromosome segregation in single-celled elongated bacteria such as Escherichia coli because in principle, chromosomes can segregate for purely entropic reasons without any help from active mechanisms. In this thesis, we investigated entropic segregation of polymers under cylindrical confinement of infinite length where the confining cylinder is so narrow that its diameter is significantly smaller than the radius of gyration of the unconfined polymers.
Open Access
Entwurf eines integrierten Systems zur Visualisierung von Ergebnissen numerischer Berechnungsverfahren für massiv parallele Rechnerarchitekturen
(2000) Schlageter, Hans-Ulrich; Rühle, Roland (Prof. Dr.-Ing.)
In dieser Arbeit wird ein Visualisierungsprogrammsystem, bestehend aus parallelen und interaktiven Komponenten vorgestellt. Das Anwendungsgebiet der Software ist neben der numerischen Strömungsmechanik vor allem die Strukturmechanik. Das Programmsystem erlaubt es, zahlreiche unabhängige Software-Einheiten (Moduln) individuell zu gruppieren und zu benutzerspezifischen Anwendungen zusammenzubinden. Die Software-Einheiten umfassen Eingabe, Ausgabe, Import und Export von Daten ebenso wie eine Bandbreite an Visualisierungstechniken zum sequentiellen und parallelen Gebrauch. Als Beispiele seien Kontur- und Isoflächen, Stromlinien, die Verfolgung von Partikeln, Flächen und Kugeln genannt. Das Modulpaket läuft auf einer leistungsfähigen UNIX-Graphik-Workstation unter dem Application Visualization System (AVS) und erlaubt die Anbindung eines Parallelrechners der MIMD-Klasse als Back-End, zum einen, um Berechnungsaufwände umzuverteilen und zu minimieren (Lastenausgleich ) und zum anderen, um visuelle Ergebnisdaten aus einer laufenden parallelen CFD-Simulation heraus zu erhalten. Ein besonderer Fokus liegt auf dem Austausch von Daten und Anweisungen über das Netzwerk zwischen verschiedenen Prozessen der wichtigsten Komponenten des Systems. Der Datenaustausch wird direkt über eine neuentwickelte, auf den Sockets der Interprozeßkommunikation basierende Transmitter-Software abgewickelt, die Punkt-zu-Punkt-Verbindungen auf Anforderung anbietet, die nicht bereits im Vorhinein spezifiziert und aufgebaut werden müssen.