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Multiscale Mathematics for Nano-Particle-Endowed Active Membranes and Films

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Technical Report,01 May 2012,30 Apr 2016

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University of South Carolina Columbia

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In this project, we conducted a systematic investigation on active liquid crystal flows and flowing polymer nanocomposites including studies of nonlinear phenomenon in active magnetic microbead rheology, detailed analyses and simulations of active liquid crystal models in thin films, free surface geometries, and the channel geometry, applications of active liquid crystal models to complex biological systems, numerical algorithm development for multiphase fluid flows, network analysis and simulations of nanocomposite systems. We explored spatial-temporal structures using the two-scale kinetic model by mapping out the dynamics in the phase space consisting of the active parameter and the strength of active particle-particle interaction. In addition, we used a continuum active polar liquid crystal model to study the robustness of the structures and their genesis in relation to the inherent instability in the active liquid crystal model in various geometries. Network models are brought in to analyze nanocomposites transport properties and network properties of various complex networks. A series of numerical algorithms for multiphase complex fluid models are developed using a new method that we invented call energy quadratization EQ technique. With the new EQ technique, we designed energy stable schemes for several important model systems of multiphase viscous fluid mixtures, liquid crystal drops, active matter drops, active cells, etc., making the numerical simulation of the underlying fluids and biological objects more reliable.

Subject Categories:

  • Numerical Mathematics
  • Miscellaneous Materials
  • Fluid Mechanics

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