CoMe Seminar Series
Sai Chandana Divi , Salik Shaikh, Jordi Vila and Karthik Suresh
Sai Chandana Divi (Master in Computational Mechanics)
Modeling of cells and tissues as active fluid
Within cells, the cytoskeleton organizes into polymer networks with unique properties. At short time-scales, they behave
elastically. However, due to molecular turnover, at longer time-scales they behave like viscous uids in low Reynold limit. In addition to this, they are capable of actively developing tension, thanks to molecular motors using chemical energy. At the tissue scale, epithelial cell formed by monolayers can exhibit, in some regimes, a similar active fluid behavior. Furthermore, as a part of optogenetic technnique, the doped epithelial tissues experience contractility upon illumination. Motivated by this, we considered a monolayer of cells with illumination as an external power input dened as an tension pattern in space and time to engineer contractility patterns to transport material from one part of the tissue to another. Altogether, for the system at low Reynold's limit, governing equations of this compressible active visco-elastic model are developed and solved using linear nite elements. The system is non-dimensionalized and the eect of each independent parameter on the system is analyzed. Finally, this model helps in examining the principles that govern the ability to remodel the material by applying space-time patterns of activity.
Salik Shaikh (Master in Computational Mechanics)
Evaluation of properties of a flexoelectric material using nanoindentation technique
Flexoelectricity is universal in dielectrics and is a size-dependent electromechanical mechanism coupling polarization and strain gradient. Here, we computationally study the nanoindentation technique, and evaluate the properties of the material because of indentation due to three indentors. We shall harness the axisymmetric nature of the indentors. So, we have proposed a formulation for an axisymmetric model. The flexoelectric effects have been accounted for in this this study.
Jordi Vila (Master in Advanced Mathematics and Mathematical Engineering)
Hybridizable Discontinuous Galerkin Method for Incompressible Flows
The increasing interest in high-order discretization techniques for CFD applications is motivated by the high accuracy that these methods provide compared to low-order methods. In this project, the hybridizable discontinuous Galerkin (HDG) method is discussed. HDG represents a novel and competitive alternative to the classical discontinuous Galerkin method by substantially reducing the number of coupled unknowns of the discrete problem. Some numerical examples for the simulation of steady incompressible flows are presented, with special emphasis on the HDG stabilization term in order to ensure the optimal convergence of velocity, pressure and gradient of velocity and the superconvergence of a postprocessed velocity field.
Karthik Suresh (Master in Computational Mechanics)
NURBS-Enhanced Finite Element Hybridizable Discontinuous Galerkin method
with degree adaptivity for steady Stokes flow
High-order methods have the potential to deliver high accuracy with less degrees of freedom when compared with lower order methods. The hybridizable discontinuous Galerkin (HDG) method is a novel discontinuous Galerkin (DG) method with very attractive properties. While retaining the advantages of other DG methods like the inherent stabilization and the local conservation properties, the HDG method reduces the total number of degrees of freedom compared to other DG methods such as the local DG or the compact DG. This work proposes the combination of HDG and NURBS-enhanced finite element method (NEFEM) for the solution of Stokes flow problems using degree adaptivity. The ability of NEFEM to exactly represent the boundary of the domain by means of its NURBS boundary representation is used to ensure that the geometric description is independent on the degree of the polynomials used in the functional approximation. Thus, the degree adaptivity process is only driven by the error of the functional approximation and not by the error of both the functional and the geometric approximation.