Special Session 151: Encounter and Merging of Mesh-based Methods and Meshless Methods in the Era of Machine Learning

Quasi-entropy: in free energies and closure approximations
Jie Xu
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Peoples Rep of China
Co-Author(s):    Jie Xu
Abstract:
Molecular-theory-based tensor models of liquid crystals typically contain an explicit entropy term deduced from the maximum entropy state. For dynamic models, high-order tensors also appear in the model, for which a classical closure approximation is also given the maximum entropy state. The maximum entropy state is able to maintain the essential properties and structures of the molecular theory in tensor models, but leads to high computational cost. Quasi-entropy is a class of elementary functions to substitute the terms deduced from the maximum entropy state, which can be incorporated both in free energies and in closure approximations. It not only keeps the desired properties and structures of the models, but also reduces the complexity of dealing with implicit functions involving three dimensional integrals to $O(1)$. We present a few representative results in equilibrium states and dynamics.