Showing papers by "David A. Kessler published in 1992"
TL;DR: In this article, the authors investigated the morphological evolution of strained films during growth and showed that the kinetics ultimately determined the surface morphology of the stretched film, and inferred the morphology from experimental results on a number of strained growth systems.
Abstract: We have investigated the morphological evolution of strained films during growth. Novel Monte Carlo studies, which incorporate linear elasticity, have been performed to simulate film growth with misfit. These studies demonstrate the onset of islanding for sufficiently large misfit. We present an analytic calculation which shows that from the onset of deposition the films are energetically unstable to large-scale islanding. We argue that the kinetics ultimately determines the surface morphology. Dislocations are not necessary for surface lattice relaxation. Support for this picture is inferred from experimental results on a number of strained growth systems.
160 citations
TL;DR: In this paper, a diffusion equation describing phase separation during co-deposition of a binary alloy is derived, and solved in the limit of dominant surface diffusion, which yields results similar to bulk spinodal decomposition, except that long, and possibly all, wavelength are stabilized.
Abstract: A diffusion equation describing phase separation during co‐deposition of a binary alloy is derived, and solved in the limit of dominant surface diffusion. Linear stability analysis yields results similar to bulk spinodal decomposition, except that long, and possibly all, wavelength are stabilized. Decomposition into two phases is investigated by solving the diffusion equation for lamellar and cylindrical symmetry. For the lamellar geometry, typically observed for near‐equal volume fractions, the diffusion equation does not yield wavelength selection criteria. These can be obtained if free energy minimization is assumed. For the cylindrical geometry, solutions for small volume fractions yield domain dimensions proportional to the deposition‐rate dependent surface diffusion length.
63 citations
TL;DR: A simple model of MBE growth which incorporates surface diffusion and deposition in a physically correct manner is presented which does not correspond to that predicted by the continuum model of Villain, Das Sarma, and others.
Abstract: We investigate the statistical properties of the surface of thin films grown by molecular-beam epitaxy (MBE). We present and analyze a simple model of MBE growth which incorporates surface diffusion and deposition in a physically correct manner. The short-time behavior does not correspond to that predicted by the continuum model of Villain, Das Sarma, and others. At long times, the model is governed by Kardar-Parisi-Zhang dynamics.
50 citations
TL;DR: The inner problem of finding the spiral core which smoothly matches onto the asymptotic rotating solution of the FitzHugh-Nagumo model has a solution for all possible outer solutions on scale {epsilon}{sup 2/3}; furthermore, this solution is determined via a simple numerical procedure.
Abstract: We formulate the problem of finding the spiral core which smoothly matches onto the asymptotic rotating solution of the FitzHugh-Nagumo model. We prove that the inner problem (with scale {epsilon}, the ratio of the reaction rates) has a solution for all possible outer solutions on scale {epsilon}{sup 2/3}; furthermore, we explicitly determine this solution via a simple numerical procedure. This completes the rigorous demonstration of the existence of rotating spiral solutions in singly diffusive excitable systems.
20 citations
TL;DR: In the limit of a small (but nonzero) diffusion-constant ratio for a two-component reaction-diffusion model of an excitable medium, the existence of a secondary instability referred to as tip meandering is derived.
Abstract: The rotating spiral pattern seen in a variety of excitable systems is known to undergo a secondary instability referred to as tip meandering. In the limit of a small (but nonzero) diffusion-constant ratio for a two-component reaction-diffusion model of an excitable medium, we derive the existence of this instability; this requires solving the linear problem defined by expanding about the spiral-core steady-state solution found by Bernoff [Physica D 53, 125 (1991)]. We comment on how these results might lead to a full theory of core meandering
10 citations
TL;DR: In this article, a series of numerical simulation studies of simple theoretical models, such as ballistic deposition model and biased solid-on-solid model, are presented to demonstrate the dynamical scaling and phase transitions in a class of surface growth problems in the context of the Kardar-Parisi-Zhang theory.
Abstract: In nonequilibrium surface growth processes, such as molecular beam epitaxy and chemical vapor deposition, kinetic roughening plays a significant role in determining surface morphology. The stochastic dynamics in the processes induce novel scaling in surface roughness with respect to growth time and system sizes. We present here a series of numerical simulation studies of simple theoretical models, such as ballistic deposition model and biased solid-on-solid model, to demonstrate the dynamical scaling and phase transitions in a class of surface growth problems in the context of the Kardar-Parisi-Zhang theory. Different dynamical processes, such as desorption and surface diffusion, are shown to have dramatic effects on the scaling and thus the surface structures.
2 citations
TL;DR: In this paper, the stability of a steadily rotating spiral solution in the outer scaling region of an excitable medium is calculated, suggesting that the transition to meandering is due to a core region instability.
Abstract: The stability of a steadily rotating spiral solution in the outer scaling region of an excitable medium is calculated. The spiral is shown to be stable, suggesting that the transition to meandering is due to a core region instability. The consequences of the coupling of perturbations in the core to the outer region are shown to be consistent with numerical studies.
2 citations
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TL;DR: This is a response to a comment on a possible phase transition of surface growth in a modified ballistic deposition model.
Abstract: This is a response to a comment on a possible phase transition of surface growth in a modified ballistic deposition model. (AIP)
2 citations