Swinging and tumbling of elastic capsules in shear flow

The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules both with spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximative theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we could reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram.Comment: 20 pages, 7 figure

Implementation and validation of a Herschel-Bulkley PFEM model in Kratos Multiphysics

L'objectiu d'aquest treball de final de màster és la implementació i validació, mitjançant exemples en la literatura, de la llei constitutiva de Herschel-Bulkley de la dinàmica de fluids mitjançant el mètode d'elements finits de partícules (PFEM). La base del treball és la formulació PFEM per a fluids Bingham implementada a la plataforma del codi obert Kratos Multiphysics. El model de Herschel-Bulkley relaciona el tensor de tensions tallant amb el tensor de velocitat de deformació tenint en compte el límit elàstic, que limita l'inici o el final del moviment del fluid; la viscositat del fluid, que és responsable de la resistència del fluid al moviment; i l'índex del fluid, un paràmetre que representa el nivell de no-linealitat del moviment. La llei de Herschel-Bulkley és validada amb problemes de referència de la literatura. Es duu a terme la convergència en l'espai i el temps, l'anàlisi de sensibilitat de les variables del model i les comparacions amb el model estàndard de Bingham. A més, s'aplica l'anomenada regularització de Papanastasiou per a evitar els inconvenients numèrics del model de Herschel-Bulkley. Tots els resultats son graficats al llarg del treball i es comparen amb referències numèriques i experimentals trobades en articles científics. Al llarg dels càlculs numèrics és possible calibrar una sèrie de paràmetres fonamentals per a les simulacions amb el model.El objetivo de este trabajo de final de máster es la implementación y validación, mediante ejemplos en la literatura, de la ley constitutiva de Herschel-Bulkley de la dinámica de fluidos mediante el método de elementos finitos de partículas (PFEM). La base del trabajo es la formulación PFEM para fluidos Bingham implementada en la plataforma de código abierto Kratos Multiphysics. El modelo de Herschel-Bulkley relaciona el tensor de tensiones cortante con el tensor de velocidad de deformación teniendo en cuenta el límite elástico, que limita el inicio o el final del movimiento del fluido; la viscosidad del fluido, que es responsable de la resistencia del fluido al movimiento; y el índice del fluido, un parámetro que representa el nivel de no linealidad del movimiento. La ley de Herschel-Bulkley se valida con problemas de referencia de la literatura. Se lleva a cabo la convergencia en el espacio y el tiempo, el análisis de sensibilidad de las variables del modelo y las comparaciones con el modelo estándar de Bingham. Además, se aplica la llamada regularización de Papanastasiou para evitar los inconvenientes numéricos del modelo de Herschel-Bulkley. Todos los resultados se grafican a lo largo del trabajo y se comparan con referencias numéricas y experimentales encontradas en artículos científicos. A lo largo de los cálculos numéricos es posible calibrar una serie de parámetros fundamentales para las simulaciones con el modelo.The objective of this master's thesis is the implementation and validation, by means of literature examples, of the Herschel-Bulkley constitutive law in fluid dynamics in a particle finite element method (PFEM). The basis of the work is the PFEM formulation for Bingham fluids implemented in the open-source platform Kratos Multiphysics. The Herschel-Bulkley model relates the shear stress tensor to the strain rate tensor taking into account the yield stress, which limits the beginning or the end of the fluid motion; the fluid viscosity, which is responsible for the fluid's resistance to motion; and the fluid index, a parameter representing the level of nonlinearity of the motion. The Herschel-Bulkley law is validated with benchmark problems from the literature. Convergence in space and time, sensitivity analysis of the model variables and comparisons with the standard Bingham model are carried out. In addition, the so-called Papanastasiou regularization is applied to avoid numerical drawbacks arisign from the Herschel-Bulkley model. All results are plotted throughout the paper and compared to both numerical and experimental references found in scientific articles. Throughout the numerical calculations it is possible to calibrate a series of fundamental parameters for simulations with the model

Swinging and tumbling of elastic capsules in shear flow

The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules both with spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximative theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we could reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram.Comment: 20 pages, 7 figure

Multi-scale active shape description in medical imaging

Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed

Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening

This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. Multicomponent persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for chemical and biological problems. Extensive numerical experiments involving more than 4,000 protein-ligand complexes from the PDBBind database and near 100,000 ligands and decoys in the DUD database are performed to test respectively the scoring power and the virtual screening power of the proposed topological approaches. It is demonstrated that the present approaches outperform the modern machine learning based methods in protein-ligand binding affinity predictions and ligand-decoy discrimination