In this work, we present our numerical results of the application of Galerkin-based Isogeometric Analysis (IGA) to incompressible Navier-Stokes-Cahn-Hilliard (NSCH) equations in velocity-pressurephase field-chemical potential formulation. For the approximation of the velocity and pressure fields, LBB compatible non-uniform rational B-spline spaces are used which can be regarded as smooth generalizations of Taylor-Hood pairs of finite element spaces. The one-step θ-scheme is used for the discretization in time. The static and rising bubble, in addition to the nonlinear Rayleigh-Taylor instability flow problems, are considered in two dimensions as model problems in order to investigate the numerical properties of the scheme.

Mechanical forces play an important role in many microbiological phenomena such as embryogenesis, regeneration, cell proliferation and differentiation. Micromanipulation of cells in a controlled environment is a widely used approach for understanding cellular responses with respect to external mechanical forces. While modern micromanipulation and imaging techniques provide useful optical information about the change of overall cell contours under the impact of external loads, the intrinsic mechanisms of energy and signal propagation throughout the cell structure are usually not accessible by direct observation. This work deals with the computational modelling and simulation of intracellular strain state of uniaxially stretched cells captured in a series of images. A nonlinear elastic finite element method on tetrahedral grids was applied for numerical analysis of inhomogeneous stretching of a rat embryonic fibroblast 52 (REF 52) using a simplified two-component model of a eukaryotic cell consisting of a stiffer nucleus surrounded by a softer cytoplasm. The difference between simulated and experimentally observed cell contours is used as a feedback criterion for iterative estimation of canonical material parameters of the two-component model such as stiffness and compressibility. Analysis of comparative simulations with varying material parameters shows that (i) the ratio between the stiffness of cell nucleus and cytoplasm determines intracellular strain distribution and (ii) large deformations result in increased stiffness and decreased compressibility of the cell cytoplasm. The proposed model is able to reproduce the evolution of the cellular shape over a sequence of observed deformations and provides complementary information for a better understanding of mechanical cell response.

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We are interested in a decomposition of motion data into a sparse linear combination of base functions which enable efficient data processing. We combine two prominent frameworks: dynamic time warping (DTW), which offers particularly successful pairwise motion data comparison, and sparse coding (SC), which enables an automatic decomposition of vectorial data into a sparse linear combination of base vectors. We enhance SC via efficient kernelization which extends its application domain to general similarity data such as offered by DTW, and its restriction to non-negative linear representations of signals and base vectors in order to guarantee a meaningful dictionary. We also implemented the proposed method in a classification framework and evaluated its performance on various motion capture benchmark data sets.