Modelling and numerical analysis of energy-dissipating systems with nonlocal free energy

The broad objective of this thesis is to design finite-volume schemes for a family of energy-dissipating systems. All the systems studied in this thesis share a common property: they are driven by an energy that decreases as the system evolves. Such decrease is produced by a dissipation mechanism, which ensures that the system eventually reaches a steady state where the energy is minimised. The numerical schemes presented here are designed to discretely preserve the dissipation of the energy, leading to more accurate and cost-effective simulations. Most of the material in this thesis is based on the publications [16, 54, 65, 66, 243]. The research content is structured in three parts. First, Part II presents well-balanced first-, second- and high-order finite-volume schemes for a general class of hydrodynamic systems with linear and nonlinear damping. These well-balanced schemes preserve stationary states at machine precision, while discretely preserving the dissipation of the discrete free energy for first- and second-order accuracy. Second, Part III focuses on finite-volume schemes for the Cahn-Hilliard equation that unconditionally and discretely satisfy the boundedness of the phase eld and the free-energy dissipation. In addition, our Cahn-Hilliard scheme is employed as an image inpainting filter before passing damaged images into a classification neural network, leading to a significant improvement of damaged-image prediction. Third, Part IV introduces nite-volume schemes to solve stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. The main advantages of these schemes are the preservation of non-negative densities in the presence of noise and the accurate reproduction of the statistical properties of the physical systems. All these fi nite-volume schemes are complemented with prototypical examples from relevant applications, which highlight the bene fit of our algorithms to elucidate some of the unknown analytical results.Open Acces

Numerical Simulations of Directed Self-Assembly Methods in Di-block Copolymer Films for Efficient Manufacturing of Nanoscale Patterns with Long-Range Order

Directed self-assembly (DSA) of block copolymers (BCPs) has been shown as a viable method to achieve bulk fabrication of surface patterns with feature sizes smaller than those available through traditional photolithography. Under appropriate thermodynamic conditions, BCPs will self-assemble into ordered micro-domain morphologies, a desirable feature for many applications. One of the primary interests in this field of research is the application of thin-film BCPs to existing photolithography techniques. This “bottom-up” approach utilizes the self-assembled BCP nanostructures as a sacrificial templating layer in the lithographic process. While self-assembly occurs spontaneously, extending orientational uniformity over centimeter-length scales remains a critical challenge. A number of DSA techniques have been developed to enhance the long range order in an evolving BCP system during micro-phase separation. Of primary interest to this dissertation is the synergistic behavior between chemoepitaxial templating and cold-zone annealing. The first method involves pre-treating a substrate with chemical boundaries that will attract or repel one of the monomer blocks before application of the thin-film via spin-coating. The second method applies a mobile, thermal gradient to induce micro-phase separation in a narrow region within the homogeneous thin-film . Parametric studies have been performed to characterize the extent of long range order and defect densities obtained by applying various thermal zone velocities and template patterns. These simulations are performed by utilizing a Time-Dependent Ginzburg-Landau (TDGL) model and an optimized phase field (OPF) model. Parallel processing is implemented to allow large-scale simulations to be performed within a reasonable time period

Simulación atomística de superredes de aleaciones de FeCr.

Las aleaciones de hierro-cromo (FeCr) son materiales de gran interés tecnológico debido a que presentan excelentes propiedades mecánicas y de resistencia a la radiación y a la corrosión. En este trabajo, se ha explorado el comportamiento de superredes de aleaciones de hierro-cromo (FeCr) usando un modelo de interdifusión atomístico basado en Monte Carlo Cinético sin Red (OKMC), que presenta un esquema sin red y parte de una dependencia de la energía de mezcla basada en cálculos Ab initio. Además, cuantifica de forma simplificada las interacciones entre cajas adyacentes y ha demostrado ser eficaz para reproducir el engrosamiento y la coalescencia de las zonas precipitadas y, también, ha demostrado ser computacionalmente más eficiente que otros modelos utilizados. Este modelo OKMC, está implementado en el simulador MMONCA, y, debido a sus características, se ha considerado el simulador adecuado para nuestros intereses. Los ficheros de datos de salida proporcionados por MMONCA, han sido importados por MATLAB, una herramienta de software matemático, que, a su vez, nos ha proporcionado diferentes tipos de representaciones de los datos que nos han permitido estudiar y analizar los resultados obtenidos de las simulaciones. Se han realizado simulaciones de superredes de diferentes periodos a temperaturas de 500 0C y se han identificado una serie de estados en la evolución de estas superredes dependientes del periodo de la superred y del tiempo de recocido. Como parámetros interesantes para elucidar la fenomenología de las superredes se han estudiado la energía libre promedio y el volumen de las intercaras. También se ha recurrido a técnicas de procesado de imagen y análisis de Fourier para poder identificar los diferentes estados por los que pasa la superred hasta su desestabilización. Por último, se han comparado los resultados obtenidos en las simulaciones con los resultados experimentales sobre superredes de periodo ultracorto llevados a cabo recientemente. Se ha puesto de manifiesto que nuestro modelo reproduce cualitativamente, aunque no cuantitativamente, dichos resultados experimentales y se han analizado las causas de estas discrepancias.Ingeniería, Industria y Construcció

Low Energy Ion Beam Synthesis of SiNanocrystals for Nonvolatile Memories – Modeling and Process Simulations

es ist kein Abstrakt vorhanden

Low Energy Ion Beam Synthesis of Si Nanocrystals for Nonvolatile Memories - Modeling and Process Simulations

Metal-Oxide-Silicon Field-Effect-Transistors with a layer of electrically isolated Si nanocrystals (NCs) embedded in the gate oxide are known to improve conventional floating gate flash memories. Data retention, program and erase speeds as well as the memory operation voltages can be substantially improved due to the discrete charge storage in the isolated Si NCs. Using ion beam synthesis, Si NCs can be fabricated along with standard CMOS processing. The optimization of the location and size of ion beam synthesized Si NCs requires a deeper understanding of the mechanisms involved, which determine (i) the built-up of Si supersaturation by high-fluence ion implantation and (ii) NC formation by phase separation. For that aim, process simulations have been conducted that address both aspects on a fundamental level and, on the other hand, are able to avoid tedious experiments. The built-up of a Si supersaturation by high-fluence ion implantation were studied using dynamic binary collision calculations with TRIDYN and have lead to a prediction of Si excess depth profiles in thin gate oxides of a remarkable quality. These simulations include in a natural manner high fluence implantation effects as target erosion by sputtering, target swelling and ion beam mixing. The second stage of ion beam synthesis is modeled with the help of a tailored kinetic Monte Carlo code that combines a detailed kinetic description of phase separation on atomic level with the required degree of abstraction that is necessary to span the timescales involved. Large ensembles of Si NCs were simulated reaching the late stages of NC formation and dissolution at simulation sizes that allowed a direct comparison with experimental studies, e.g. with electron energy loss resolved TEM investigations. These comparisons reveal a nice degree of agreement, e.g. in terms of predicted and observed precipitate morphologies for different ion fluences. However, they also point clearly onto impact of additional external influences as, e.g., the oxidation of implanted Si by absorbed humidity, which was identified with the help of these process simulations. Moreover, these simulations are utilized as a general tool to identify optimum processing regimes for a tailored Si NC formation for NC memories. It is shown that key properties for NC memories as the tunneling distance from the transistor channel to the Si NCs, the NC morphology, size and density can be adjusted accurately despite of the involved degree of self-organization. Furthermore, possible lateral electron tunneling between neighboring Si NCs is evaluated on the basis of the performed kinetic Monte Carlo simulations

Multi-scale studies of molecular self-assembly in biology

Self-assembly of molecules into higher-order structures of specific shapes and sizes is central to biological organization. My graduate work is focused on understanding how molecular-scale interactions encode the emergent mesoscale properties in three model systems involving biomolecular condensates, viral genomic RNA packaging, and the septin cytoskeleton. Biomolecular condensates are formed when proteins and nucleic acids undergo phase separation coupled to percolation (PSCP) which allows for compartmentalization of biochemistry without the use of membranes. Studies to date have shown that oligomerization of phase separating proteins promotes PSCP. However, we have shown that the fungal protein Whi3 contains a transiently structured region which can promote oligomerization and opposes PSCP. Stabilizing structure in this region increases dilute phase oligomerization and reduces the concentration of Whi3 in condensates. Both trends are reversed when structure formation is abrogated. Further, condensates with low dense phase protein concentrations experience an accelerated dynamical arrest, while condensates with higher proteins concentrations coarsen over longer periods of time. The relationships between dilute phase oligomerization and PSCP have implications for myriad systems, including the packaging of viral RNA genomes.Viruses must package their genomes into nascent virions while excluding unwanted cellular and viral molecules. Recent work has shown that viral packaging proteins can undergo PSCP with and on viral genomes. The Gladfelter lab previously demonstrated that the 5 and 3 ends of the SARS-CoV-2 RNA genome promote PSCP of nucleocapsid protein (N-protein), whereas the middle of the genome is predicted to consist mostly of solubilizing elements. Using a coarse-grained polymer model, we show that solubilization of N-protein can be achieved if RNA-protein binding interactions are sufficiently strong, sequestering proteins into inert complexes in the dilute phase. PSCP is instead promoted by weak, multivalent interactions. We outline how the spatial patterning of these distinct RNA-protein binding modalities along the genome affect genome cyclization, compaction, and packaging into complexes with single genomes.Septins are membrane-binding cytoskeletal proteins found in all eukaryotes except plants. Combining experiments and agent-based modeling, we show that septin polymerization is non-cooperative and explore the effects of reaction rates on higher-order septin assemblies.Doctor of Philosoph

Computer modelling of block copolymers under external fields

This thesis reports on modelling the morphological of Block Copolymers (BCPs) by using computer simulation. In this work, the Cell Dynamics Simulation (CDS) method is used, which is a good compromise between computational speed and physical accuracy. First, it has been performed a 3-dimensional study of diblock copolymer standing up cylinders in two different types of confinement: topographical and chemical patterns. In the case of square walls of small sizes the system is dominated by the walls, inducing a 2x2 square lattice of cylinders, while in large boxes the system is dominated by hexagonal packing. For intermediate sizes topographical confinement has a stronger influence than chemical pattern confinement and can induce a better system of 3x3 square lattice cylinders. For square confinement compatible with a 4x4 square lattice the tetragonal phase is observed to be a transient system leading towards a twisted hexagonal packing. Simulations have also been performed in a diamond lattice which can naturally accommodate hexagonal packing, and rectangular boxes which can induce better orientation of the hexagonal lattice along the direction parallel to the long side. Next, diblock copolymer cylinder-forming thin films confined between two parallel selective homogeneous walls have been investigated. By changing the value of the surface field and the value of the film thickness several morphologies have been observed. In order to tailor desired structures some of these morphologies are studied under a simple steady shear flow. Shear flow is observed to induce a better hexagonal packing of a monolayer of perforated lamellae and of a monolayer of cylinders perpendicular to the thin film plane. A monolayer of cylinders parallel to the thin film plane with random orientation is found to align perfectly in the shear flow direction. Further increase of the shear rate induces a phase transition: from one perforated lamellae layer to one lamellae layer; from a double layer of perforated lamellae to parallel cylinder layers; and from a monolayer of cylinders perpendicular to the thin film plane to two half parallel cylinder layers. In the end, self-assembly of lamellae-, cylinder-, bicontinuous, and sphere-forming diblock copolymers in spherical confinement is studied. The effects of different confine- ment size and selective surface are examined systematically. The simulations reveal that a rich variety of morphologies, ranging from onion-like structures, perforated lamellae, helices structures, and the coexistence of perforated and lamellae structures, can be formed spontaneously from a randomly generated initial state. The structure diagrams of lamellae-forming diblock copolymers show that the morphologies obtained with a selective surface are similar to those obtained with a negative selective surface, but different to those found with a neutral selective surface. The structural diagrams of bicontinuous-, sphere-, and cylinder-forming diblock copolymers show that the morphologies found for surfaces selective for different blocks are different from each other. In the case of bicontinuous-forming diblock copolymers the morphological behaviour obtained with a neutral surface is similar to those obtained when the surface is selective for the minority block. In the case of sphere-forming diblock copolymers the morphologies obtained with a neutral surface are similar to those found with surface selective for the majority block. Instead, for cylinder-forming diblock copolymers the morphology obtained under a neutral surface is totally different from those obtained when the surface is selective

Interactive visualization of computational fluid dynamics data.

This thesis describes a literature study and a practical research in the area of flow visualization, with special emphasis on the interactive visualization of Computational Fluid Dynamics (CFD) datasets. Given the four main categories of flow visualization methodology; direct, geometric, texture-based and feature-based flow visualization, the research focus of our thesis is on the direct, geometric and feature-based techniques. And the feature-based flow visualization is highlighted in this thesis. After we present an overview of the state-of-the-art of the recent developments in the flow visualization in higher spatial dimensions (2.5D, 3D and 4D), we propose a fast, simple, and interactive glyph placement algorithm for investigating and visualizing boundary flow data based on unstructured, adaptive resolution boundary meshes from CFD dataset. Afterward, we propose a novel, automatic mesh-driven vector field clustering algorithm which couples the properties of the vector field and resolution of underlying mesh into a unified distance measure for producing high-level, intuitive and suggestive visualization of large, unstructured, adaptive resolution boundary CFD meshes based vector fields. Next we present a novel application with multiple-coordinated views for interactive information-assisted visualization of multidimensional marine turbine CFD data. Information visualization techniques are combined with user interaction to exploit our cognitive ability for intuitive extraction of flow features from CFD datasets. Later, we discuss the design and implementation of each visualization technique used in our interactive flow visualization framework, such as glyphs, streamlines, parallel coordinate plots, etc. In this thesis, we focus on the interactive visualization of the real-world CFD datasets, and present a number of new methods or algorithms to address several related challenges in flow visualization. We strongly believe that the user interaction is a crucial part of an effective data analysis and visualization of large and complex datasets such as CFD datasets we use in this thesis. In order to demonstrate the use of the proposed techniques in this thesis, CFD domain experts reviews are also provided

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described