Active nematic fluids with flow alignment

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2021, Tutor: Jaume Casademunt ViaderWe derive a stream function formulation for the dynamics of 2D active nematics in the absence of topological defects. This formulation extends previous studies by incorporating the flow alignment coupling. We study the linear stability analysis of the spontaneous-flow instability and check it numerically. Then, we obtain numerically the 2D nonlinear stationary states for a particular limit in which active forces dominate over elastic ones, and viscous dissipation dominates over rotational dissipation. Finally, we find significant differences with previous results due to the presence of the flow alignment couplin

Equivariant Networks for Porous Crystalline Materials

Porous crystalline materials have the potential to play a key role in developing solutions for molecular storage, gas separation and carbon adsorption. For these solutions, we need to develop new materials with specific properties. Estimating the properties of such porous materials involves first principle simulation using classical molecular simulations. The computational complexity of these methods can be a barrier to high throughput screening of the potential materials as the space of possible materials is vast. Data-driven methods, specifically machine learning methods based on deep neural networks offer a significant opportunity to significantly scale the simulation of the behavior of these materials. However, to effectively achieve this the Deep Learning models need to utilize the symmetries present in the crystals. Crystals pose specific symmetries that are present in their space group. Existing methods for crystal property prediction either have symmetry constraints that are too restrictive or only incorporate symmetries between unit cells. In addition, these models do not explicitly model the porous structure of the crystal. In this paper, we develop a model which incorporates the symmetries of the unit cell of a crystal in its architecture and explicitly models the porous structure. We evaluate our model by predicting the heat of adsorption of CO$_2$ for different configurations of the Mordenite and ZSM-5 zeolites. Our results confirm that our method performs better than existing methods for crystal property prediction and that the inclusion of pores results in a more efficient model.Comment: Added additional figures as well as additional experiments for MF

Adsorption of Carbon Dioxide in Non-Löwenstein Zeolites

We investigated the effect of the aluminum distribution in the adsorption properties of carbon dioxide in the MFI, MOR, and ITW zeolites. Because of its lack of experimental evidence and theoretical validation, Löwenstein’s rule was not generally imposed, and special attention was paid to the effect of the Al-O-Al linkages. To this end, we first generalized an existing transferable force field for CO2 adsorption in non-Löwenstein zeolites. By means of molecular simulations based on this force field, we showed that the carbon dioxide adsorption efficiency in MFI is determined by the number of Al atoms, rather than by their distribution in the framework. This was attributed to the small size of the CO2 molecules compared to the 3D wide-channel topology of the structure. Conversely, we found that the Al distribution has a higher impact on the heat of adsorption in MOR. Although structures with a very high and very low number of non-Löwenstein bonds presented significant differences, the bonds themselves do not affect the heat of adsorption directly. Instead, we found that an homogeneous distribution of the Al atoms in the sites forming the C-channel is more favorable. Finally, the small-pore distribution of the ITW zeolite led to high values of the heat of adsorption and wide error bars, which made the study feasible just for low aluminum concentrations. In that case, we report a small dependency of the heat of adsorption on the Al distribution.</p

On the stability of the Lagrangian points in the restricted circular 3-body problem

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Àngel Jorba i Monte[en] The 3-body problem is one of the most celebrated problems in mathematics. In this work we aim to find the equilibrium points of one of the three masses, which is considered infinitesimal, and study their stability in two different phase spaces. The question of stability is addressed using both analytical and numerical methods. Whereas the Lyapunov and KAM theories provide us with analytical proofs of the stable or unstable behaviour in the first phase space, analytical methods motivated by the Nekhoroshev theory allow us to compute practical bounds of the time until which the infinitesimal mass remains near the equilibria in the second. Finally, these bounds are applied to the case of a well known system: the Sun-Jupiter-Trojan system