4 papers · 1 filter
An energy-decreasing algorithm for the finite element approximation of ferronematic equilibrium states
Alexandre Ern, Ruma R. Maity
We develop an energy-decreasing algorithm for the finite element approximation of two-dimensional ferronematic equilibrium states. The problem is formulated as the minimization of…
Deflation-PINNs: Learning Multiple Solutions for PDEs and Landau-de Gennes
Sean Disarò, Ruma Rani Maity, Aras Bacho
Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful…
Numerical analysis for constrained and unconstrained Q-tensor energies for liquid crystals
Heiko Gimperlein, Ruma R. Maity
This paper introduces a comprehensive finite element approximation framework for three-dimensional Landau-de Gennes -tensor energies for nematic liquid crystals, with a particul…
Bayesian Parameter Identification in the Landau-de Gennes Theory for Nematic Liquid Crystals
Heiko Gimperlein, Ruma R. Maity, Apala Majumdar +1
This manuscript establishes a pathway to reconstruct material parameters from measurements within the Landau-de Gennes model for nematic liquid crystals. We present a Bayesian appr…