Mathematical Modelling with Multidisciplinary Applications (M3A)
http://hdl.handle.net/20.500.11824/13
2019-01-12T14:34:18ZA least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
http://hdl.handle.net/20.500.11824/909
A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
Petras A.; Ling L.; Piret C.; Ruuth S.J.
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. Recently, a closest point method with explicit time-stepping was proposed that uses finite differences derived from radial basis functions (RBF-FD). Here, we propose a least-squares implicit formulation of the closest point method to impose the constant-along-normal extension of the solution on the surface into the embedding space. Our proposed method is particularly flexible with respect to the choice of the computational grid in the embedding space. In particular, we may compute over a computational tube that contains problematic nodes. This fact enables us to combine the proposed method with the grid based particle method (Leung and Zhao, J. Comput. Phys. 228(8):2993-3024, [2009]) to obtain a numerical method for approximating PDEs on moving surfaces. We present a number of examples to illustrate the numerical convergence properties of our proposed method. Experiments for advection-diffusion equations and Cahn-Hilliard equations that are strongly coupled to the velocity of the surface are also presented.
2018-10-01T00:00:00ZPro-C congruence properties for groups of rooted tree automorphisms
http://hdl.handle.net/20.500.11824/894
Pro-C congruence properties for groups of rooted tree automorphisms
Garrido A.; Uria-Albizuri J.
We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees.
Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-$\mathcal{C}$ completions of the group, where $\mathcal{C}$ is a pseudo-variety of finite groups.
A group acting on a rooted, locally finite tree has the $\mathcal{C}$-congruence subgroup property ($\mathcal{C}$-CSP) if its pro-$\mathcal{C}$ completion coincides with the completion with respect to level stabilizers.
We give a sufficient condition for a weakly regular branch group to have the $\mathcal{C}$-CSP.
In the case where $\mathcal{C}$ is also closed under extensions (for instance the class of all finite $p$-groups for some prime $p$), our sufficient condition is also necessary.
We apply the criterion to show that the Basilica group and the GGS-groups with constant defining vector (odd prime relatives of the Basilica group) have the $p$-CSP.
2018-11-21T00:00:00ZMulti-GGS groups have the congruence subgroup property
http://hdl.handle.net/20.500.11824/885
Multi-GGS groups have the congruence subgroup property
Garrido A.; Uria-Albizuri J.
We generalize the result about the congruence subgroup property for GGS-groups to the family of multi-GGS-groups; that is, all multi-GGS-groups except the one defined by the constant vector have the congruence subgroup property.
Even if the result remains, new ideas are needed in order to generalize the proof.
2018-11-08T00:00:00ZComputational modeling of open-irrigated electrodes for radiofrequency cardiac ablation including blood motion-saline flow interaction
http://hdl.handle.net/20.500.11824/880
Computational modeling of open-irrigated electrodes for radiofrequency cardiac ablation including blood motion-saline flow interaction
González-Suárez A.; Berjano E.; Guerra Ramos J.M.; Gerardo-Giorda L.
Radiofrequency catheter ablation (RFCA) is a routine treatment for cardiac arrhythmias. During RFCA, the electrode-tissue interface temperature should be kept below 80°C to avoid thrombus formation. Open-irrigated electrodes facilitate power delivery while keeping low temperatures around the catheter. No computational model of an open-irrigated elec- trode in endocardial RFCA accounting for both the saline irrigation flow and the blood motion in the cardiac chamber has been proposed yet. We present the first computational model including both effects at once. The model has been validated against existing experi- mental results. Computational results showed that the surface lesion width and blood tem- perature are affected by both the electrode design and the irrigation flow rate. Smaller surface lesion widths and blood temperatures are obtained with higher irrigation flow rate, while the lesion depth is not affected by changing the irrigation flow rate. Larger lesions are obtained with increasing power and the electrode-tissue contact. Also, larger lesions are obtained when electrode is placed horizontally. Overall, the computational findings are in close agreement with previous experimental results providing an excellent tool for future catheter research.
2016-01-01T00:00:00Z