IMA PIP Workshop on Numerical Modeling of Complex Fluids and MHD

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The most common origin and manifestation of anomalous phenomena in complex fluids are different ``elastic'' effects. These can be ascribed to the elasticity of deformable particles, elastic repulsion between charged liquid crystals, polarization of colloids or multi-component phases, elastic effects due to microstructures formation, or bulk elastic effects due to the presence of polymer molecules in viscoelastic complex fluids. Mathematically, such elastic effects can be represented in terms of internal variables. Examples of such internal variables are: the orientational order parameter in liquid crystals, the distribution density function in the dumb-bell model for polymeric materials, the magnetic field in magnetohydrodynamic fluids, and the volume fraction in mixtures of different materials. The different rheological and hydrodynamic properties of these materials can in turn be attributed to the special coupling between the transport of these internal variables and the induced elastic stresses which typically manifest on all scales, and to a large extent determine the specific properties of the system, such as the stability and regularity of particle configurations and the likelihood of specific pattern formations in the system. The understanding of such complex mechanisms which couple different physical scales is crucial in designing accurate mathematical and numerical models and algorithms in order to simulate such systems. This workshop is based on the premise that gaining significant new results and thereby obtaining deeper insight and understanding of materials described by complex fluids (e.g., polymers, emulsions, liquid crystals, magnetorheological fluids, blood suspensions) requires a combined approach consisting of experiment, modeling, analysis, and simulation. The primary objective of the workshop is thus to gather students, junior faculty, and experts to discuss new integrated modeling techniques that properly address the fundamental unresolved issues common to studies of complex fluids: consistency of models with physics, rigorous analysis of the models, numerical and scientific computing issues, and the experimental verification and validation of the predictive capabilities of the mathematical and numerical models. Modeling and simulating the rich pool of designer and smart materials described by complex fluids requires marshaling interdisciplinary research forces to develop and analyze mathematical models and computational tools for such problems. Recently, numerous methodologies and frameworks have been developed in an aim to capture the various time and length scales involved in studies of such complex materials. This workshop will gather key contributors to the development of these new multiscale modeling and simulations techniques, with the aim of introducing these ideas to students and young researchers and also promoting interdisciplinary research on complex fluids applications amongst participants in the future. The workshop will highlight topics from interrelated research areas for both deterministic and stochastic computational approaches, concentrating on: an Energetic Variational approach for multiscale modeling and simulation; computationally and experimentally guided model validation and further development of robust adaptive numerical models and solution methods.