Roberto F. Ausas

Diego S. Rodrigues, Roberto F. Ausas, Fernando Mut et al.

We propose a robust simulation method for phospholipid membranes. It is based on a mixed three-field formulation that accounts for tangential fluidity (Boussinesq-Scriven law), bending elasticity (Canham-Helfrich model) and inextensibility. The unknowns are the velocity, vector curvature and surface pressure fields, all of which are interpolated with linear continuous finite elements. The method is semi-implicit - it requires the solution of a single linear system per time step. Conditional time stability is observed, with a time step restriction that scales as the square of the mesh size. Mesh quality and refinement are maintained by adaptively remeshing. Another ingredient is a numerical force that emulates the action of an optical tweezer, allowing for virtual interaction with the membrane. Extensive relaxation experiments are reported. Comparisons to exact shapes reveal the orders of convergence for position (5/3), vector curvature (3/2), surface pressure (1) and bending energy (2). Tweezing experiments are also presented. Convergence to the exact dynamics of a cylindrical tether is confirmed. Further tests illustrate the robustness of the method (six tweezers acting simultaneously) and the significance of viscous effects on membrane deformation under external forces.

Stevens Paz, Roberto F. Ausas, Juan P. Carbajal et al.

The coupled problem of hydrodynamics and solute transport for the Najafi-Golestanian three-sphere swimmer is studied, with the Reynolds number set to zero and Péclet numbers (Pe) ranging from 0.06 to 60. The adopted method is the numerical simulation of the problem with a finite element code based upon the FEniCS library. For the swimmer executing the optimal locomotion gait, we report the Sherwood number as a function of Pe in homogeneous fluids and confirm that little gain in solute flux is achieved by swimming unless Pe is significantly larger than 10. We also consider the swimmer as an learning agent moving inside a fluid that has a concentration gradient. The outcomes of Q-learning processes show that learning locomotion (with the displacement as reward) is significantly easier than learning chemotaxis (with the increase of solute flux as reward). The chemotaxis problem, even at low Pe, has a varying environment that renders learning more difficult. Further, the learning difficulty increases severely with the Péclet number. The results demonstrate the challenges that natural and artificial swimmers need to overcome to migrate efficiently when exposed to chemical inhomogeneities.

Elias C. Rodrigues, Roney L. Thompson, Dário A. B. Oliveira et al.

This research employs Universal Differential Equations (UDEs) alongside differentiable physics to model viscoelastic fluids, merging conventional differential equations, neural networks and numerical methods to reconstruct missing terms in constitutive models. This study focuses on analyzing four viscoelastic models: Upper Convected Maxwell (UCM), Johnson-Segalman, Giesekus, and Exponential Phan-Thien-Tanner (ePTT), through the use of synthetic datasets. The methodology was tested across different experimental conditions, including oscillatory and startup flows. While the UDE framework effectively predicts shear and normal stresses for most models, it demonstrates some limitations when applied to the ePTT model. The findings underscore the potential of UDEs in fluid mechanics while identifying critical areas for methodological improvement. Also, a model distillation approach was employed to extract simplified models from complex ones, emphasizing the versatility and robustness of UDEs in rheological modeling.