Browsing by Author "D. J. Wollkind"

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    Nonlinear stability analyses of pattern formation on solid surfaces during ion-sputtered erosion
    (2005-04-01) A. Pansuwan; C. Rattanakul; Y. Lenbury; D. J. Wollkind; L. Harrison; I. Rajapakse; K. Cooper; Mahidol University; Washington State University Pullman
    The development of spontaneous stationary equilibrium patterns on metallic or semiconductor solid surfaces during ion-sputtered erosion at normal incidence is investigated by means of various weakly nonlinear stability analyses applied to the appropriate governing equation for this phenomenon. In particular, that process can be represented by a damped Kuramoto-Sivashinsky nonlinear partial differential time-evolution equation for the interfacial deviation from a planar surface which includes a deterministic ion-bombardment arrival term and is defined on an unbounded spatial domain. The etching of coherent ripples, rhombic arrays of rectangular mounds or pits, and hexagonal lattices of nanoscale quantum dots or holes during this erosion process is based upon the interplay between roughening caused by ion sputtering and smoothing due to surface diffusion. Then, the theoretical predictions from these analyses are compared with both relevant experimental evidence and numerical simulations as well as placed in the context of some recent pattern formation studies. © 2005 Elsevier Ltd. All rights reserved.
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    Nonlinear stability analyses of vegetative pattern formation in an arid environment
    (2010-07-01) N. Boonkorkuea; Y. Lenbury; F. J. Alvarado; D. J. Wollkind; Mahidol University; PERDO; Tecnologico de Monterrey; Washington State University Pullman
    The development of spontaneous stationary vegetative patterns in an arid isotropic homogeneous environment is investigated by means of various weakly nonlinear stability analyses applied to the appropriate governing equation for this phenomenon. In particular, that process can be represented by a fourth-order partial differential time-evolution logistic equation for the total plant biomass per unit area divided by the carrying capacity of its territory and defined on an unbounded flat spatial domain. Those patterns that consist of parallel stripes, labyrinth-like mazes, rhombic arrays of rectangular patches, and hexagonal distributions of spots or gaps are generated by the balance between the effects of short-range facilitation and long-range competition. Then those theoretical predictions are compared with both relevant observational evidence and existing numerical simulations as well as placed in the context of the results from some recent nonlinear pattern formation studies. © 2010 Taylor & Francis.
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    Weakly nonlinear analysis of a model of signal transduction pathway involving membrane based recptors
    (2009-12-15) C. Rattanakul; Y. Lenbury; D. J. Wollkind; V. Chatsudthipong; Mahidol University; South Carolina Commission on Higher Education; Washington State University Pullman
    We present the result of our construction and analysis of a model for a signal transduction pathway which involves membrane based receptors, mediated by G-protein. The process may be represented by two reaction-diffusion equations involving a stimulating hormone or first messenger and an inhibitor, both of which may diffuse over the cell membrane and bilayers. A weakly nonlinear stability analysis is then carried out yielding information concerning quantitative relation between the system parameters and stable spatial patterns which is expected to shed more light on the function and dysfunction of the pathway that can potentially be linked to different pathological conditions. © 2009 Elsevier Ltd.