Surface reconstruction of narrow-band guided Gray-Scott model

Field electron microscopy (FEM), high-resolution electron energy loss spectroscopy (HREELS), molecular beams (MB) and temperature-programmed reaction (TPR) have been applied to the study of the kinetics of CO oxidation at low temperature, and to determine the roles of subsurface atomic oxygen (Osub) and surface reconstruction in self-oscillatory phenomena, on Pd(111), Pd(110) and Pt(100) single crystals and on Pd and Pt tip surfaces. It was found that high local concentrations of adsorbed CO during the transition from a Pt(100)-hex reconstructed surface to the unreconstructed 1×1 phase apparently prevents oxygen atoms from occupying hollow sites on the surface, and leads to the appearance of a weakly bound active adsorbed atomic oxygen (Oads) state in an on-top or bridge position. It was also inferred that subsurface oxygen Osub on the Pd(110) surface may play an important role in the formation of new active sites for the weakly bound Oads atoms. Experiments with 18O isotope labeling clearly show that the weakly bound atomic oxygen is the active form of oxygen that reacts with CO to form CO2 at T ∼140–160 K. Sharp tips of Pd and Pt, several hundreds angstroms in diameter, were used to perform in situ investigations of dynamic surface processes. The principal conclusion from those studies was that non–linear reaction kinetics is not restricted to macroscopic planes since: (i) planes as small as ∼200 A in diameter show the same non-linear kinetics as larger flat surfaces; (ii) regular waves appear under conditions leading to reaction rate oscillations; (iii) the propagation of reaction–diffusion waves involves the participation of different crystal nanoplanes via an effective coupling between adjacent planes.

Computer models of the heart have become useful tools in improving understanding of cardiac electrical activation at the cellular level, and in analyzing mechanisms of arrhythmias and antiarrhythmic therapies. In this paper, we propose to use spherical harmonic (SPHARM) surface reconstruction and alignment methods to generate curvilinear meshes for finite element models of ventricular anatomy which incorporate detailed structural information. The endocardial and epicardial surfaces are defined by SPHARM, and the volume between these surfaces is divided into nested shells. Consequently, the resulting mesh comprises hexahedral elements. Using this novel SPHARM-based meshing method, the transmembrane potential propagation is simulated, based on FitzHugh—Nagumo reaction—diffusion equations. The dynamic electrical activation propagations are simulated on realistic cardiac data during a heart cycle. The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation. Our novel curvilinear mesh models have a great potential to be used in an improved simulation of cardiovascular pathologies for testing therapy strategies and planning interventions.