Article records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:12:42 +0000Rotating spiral wave solutions of reaction-diffusion equations
https://resolver.caltech.edu/CaltechAUTHORS:COHsiamjam78b
Authors: {'items': [{'id': 'Cohen-D-S', 'name': {'family': 'Cohen', 'given': 'Donald S.'}}, {'id': 'Neu-J-C', 'name': {'family': 'Neu', 'given': 'John C.'}}, {'id': 'Rosales-R-R', 'name': {'family': 'Rosales', 'given': 'Rodolfo R.'}}]}
Year: 1978
DOI: 10.1137/0135045
We resolve the question of existence of regular rotating spiral waves as a consequence of only the processes of chemical reaction and molecular diffusion. We prove rigorously the existence of these waves as solutions of reaction-diffusion equations, and we exhibit them by means of numerical computations in several concrete cases. Existence is proved via the Schauder fixed point theorem applied to a class of functions with sufficient structure that, in fact, important constructive properties such as asymptotic representations and frequency of rotation are obtained.https://authors.library.caltech.edu/records/7jkqd-7kx75Unification of step bunching phenomena on vicinal surfaces
https://resolver.caltech.edu/CaltechAUTHORS:FOKprb07
Authors: {'items': [{'id': 'Fok-Pak-Wing', 'name': {'family': 'Fok', 'given': 'Pak-Wing'}, 'orcid': '0000-0001-9655-614X'}, {'id': 'Rosales-R-R', 'name': {'family': 'Rosales', 'given': 'Rodolfo R.'}}, {'id': 'Margetis-D', 'name': {'family': 'Margetis', 'given': 'Dionisios'}}]}
Year: 2007
DOI: 10.1103/PhysRevB.76.033408
We unify step bunching (SB) instabilities occurring under various conditions on crystal surfaces below roughening. We show that when attachment-detachment of atoms at step edges is the rate-limiting process, the SB of interacting, concentric circular steps is equivalent to the commonly observed SB of interacting straight steps under deposition, desorption, or drift. We derive a continuum Lagrangian partial differential equation, which is used to study the onset of instabilities for circular steps. These findings place on a common ground SB instabilities from numerical simulations for circular steps and experimental observations of straight steps.https://authors.library.caltech.edu/records/b12js-4w489Facet evolution on supported nanostructures: Effect of finite height
https://resolver.caltech.edu/CaltechAUTHORS:FOKprb08
Authors: {'items': [{'id': 'Fok-Pak-Wing', 'name': {'family': 'Fok', 'given': 'Pak-Wing'}, 'orcid': '0000-0001-9655-614X'}, {'id': 'Rosales-R-R', 'name': {'family': 'Rosales', 'given': 'Rodolfo R.'}}, {'id': 'Margetis-D', 'name': {'family': 'Margetis', 'given': 'Dionisios'}}]}
Year: 2008
DOI: 10.1103/PhysRevB.78.235401
The surface of a nanostructure relaxing on a substrate consists of a finite number of interacting steps and often involves the expansion of facets. Prior theoretical studies of facet evolution have focused on models with an infinite number of steps, which neglect edge effects caused by the presence of the substrate. By considering diffusion of adsorbed atoms (adatoms) on terraces and attachment-detachment of atoms at steps, we show that these edge or finite height effects play an important role in the structure's macroscopic evolution. We assume diffusion-limited kinetics for adatoms and a homoepitaxial substrate. Specifically, using data from step simulations and a continuum theory, we demonstrate a switch in the time behavior of geometric quantities associated with facets: the facet edge position in a straight-step system and the facet radius of an axisymmetric structure. Our analysis and numerical simulations focus on two corresponding model systems where steps repel each other through entropic and elastic dipolar interactions. The first model is a vicinal surface consisting of a finite number of straight steps; for an initially uniform step train, the slope of the surface evolves symmetrically about the centerline, i.e., the middle step when the number of steps is odd. The second model is an axisymmetric structure consisting of a finite number of circular steps; in this case, we include curvature effects which cause steps to collapse under the effect of line tension. In the first case, we show that the position of the facet edge, measured from the centerline, switches from O(t^1/4) behavior to O(t^1/5) (where t is time). In the second case, the facet radius switches from O(t^1/4) to O(t). For the axisymmetric case, we also predict analytically through a continuum shock wave theory how the individual collapse times are modified by the effects of finite height under the assumption that step interactions are weak compared to the step line tension.https://authors.library.caltech.edu/records/ka77b-20w31