arXiv subjects

Simon Praetorius

Publications and source records attributed to Simon Praetorius.

23 records · Page 2Linked to original sources

arXiv2015

A mechanism for cell motility by active polar gels

We analyse a generic motility model, with the motility mechanism arising by contractile stress due to the interaction of myosin and actin. A hydrodynamic active polar gel theory is used to model the cytoplasm of a cell and is combined with a Helfrich-type model to account for membrane properties. The overall model allows to consider motility without the necessity for local adhesion. Besides a detailed numerical approach together with convergence studies for the highly nonlinear free boundary problem, we also compare the induced flow field of the motile cell with that of classical squirmer models and identify the motile cell as a puller or pusher, depending on the strength of the myosin-actin interactions.

q-bio.CB↗

arXiv2015

Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation

We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic description of crystalline materials on diffusive time scales and thus offers the opportunity to study long time behaviour of materials with atomic details. This requires adaptive time stepping and efficient time discretization schemes, for which we use an embedded Rosenbrock scheme. To resolve spatial scales of practical relevance, parallel algorithms are also required, which scale to large numbers of processors. The developed preconditioner provides such a tool. It is based on an approximate factorization of the system matrix and can be implemented efficiently. The preconditioner is analyzed in detail and shown to speed up the computation drastically.

physics.comp-ph↗

arXiv2015

A Navier Stokes Phase Field Crystal Model for Colloidal Suspensions

We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and used to analyse colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

cond-mat.soft↗

arXiv2015

Liquid crystalline growth within a phase-field crystal model

By using a phase-field crystal (PFC) model, the liquid-crystal growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from a isotropic phase is compared with that grown from a columnar/smectic A (CSA) phase. While the shape of a PTC nucleus in the isotropic phase is almost identical to that of a classical PFC model, the shape of a PTC nucleus in CSA is affected by the orientation of stripes in the CSA phase, and irregular hexagonal, elliptical, octagonal, and rectangular shapes are obtained. Concerning the dynamics of the growth process we analyse the topological structure of the nematic-order, which starts from nucleation of $+\frac{1}{2}$ and $-\frac{1}{2}$ disclination pairs at the PTC growth front and evolves into hexagonal cells consisting of $+1$ vortices surrounded by six satellite $-\frac{1}{2}$ disclinations. It is found that the orientational and the positional order do not evolve simultaneously, the orientational order evolves behind the positional order, leading to a large transition zone, which can span over several lattice spacings.

cond-mat.soft↗

arXiv2013

Structure and dynamics of interfaces between two coexisting liquid crystalline phases

The phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid crystalline phases in two spatial dimensions. Depending on the model parameters there is a variety of possible coexistences between two liquid crystalline phases including a plastic triangular crystal (PTC). Here, we calculate numerically the profiles for the mean density and the nematic order tensor across the interface for isotropic-PTC and columnar-PTC respectively smectic A-PTC coexistence. As a general finding, the width of the interface with respect to the nematic order parameter characterizing the orientational order is larger than the width of the mean density interface. In approaching the interface from the PTC side, at first the mean density goes down and then the nematic order parameter follows. The relative shift of the two profiles can be larger than a full lattice constant of the plastic crystal. Finally, we also present numerical results for the dynamic relaxation of an initial order-parameter profile towards its equilibrium interfacial profile. Our predictions for the interfacial profiles can in principle be verified in real-space experiments of colloidal dispersions.

cond-mat.soft↗