Quasi-Stationary Distributions for Models of Heterogeneous Catalysis

We construct the quasi-stationary (QS) distribution for two models of heterogeneous catalysis having two absorbing states: the ZGB model for the oxidation of CO, and a version with noninstantaneous reactions. Using a mean-field-like approximation, we study the quasi-stationary surface coverages, moment ratios and the lifetime of the QS state. We also derive an improved, consistent one-site mean-field theory for the ZGB model.Comment: 18 pages, 13 figure

Fractal rain distributions and chaotic advection

Localized rain events have been found to follow power-law distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws can be generated by treating raindrops as passive tracers advected by the velocity field of a two-dimensional system of point vortices [R. Dickman, PRL 90, 108701 (2003)]. Here I review observational and theoretical aspects of fractal rain distributions and chaotic advection, and present new results on tracer distributions in the vortex model.Comment: 16 pages; 8 figures (high resolution versions of figures 1-3 available on request

Numerical analysis of the master equation

Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme that remains stable with much larger time increments than can be used in standard methods. When only the stationary distribution is required, a direct iteration method is even more rapid; this method may be extended to construct the quasi-stationary distribution of a process with an absorbing state. Applications to birth-and-death processes reveal gains in efficiency of two or more orders of magnitude.Comment: 7 pages 3 figure

Master Questions, Student Questions, and Genuine Questions: A Performative Analysis of Questions in Chan Encounter Dialogues

I want to know whether Chan masters and students depicted in classical Chan transmission literature can be interpreted as asking open (or what I will call “genuine”) questions. My task is significant because asking genuine questions appears to be a decisive factor in ascertaining whether these figures represent models for dialogue—the kind of dialogue championed in democratic society and valued by promoters of interreligious exchange. My study also contributes to a more comprehensive understanding of early Chan not only by detailing contrasts between contemporary interests and classical Chan, but more importantly by paying greater attention to the role language and rhetoric play in classical Chan. What roles do questions play in Chan encounter dialogues, and are any of the questions genuine? Is there anything about the conventions of the genre that keeps readers from interpreting some questions in this way? To address these topics, I will proceed as follows. First, on a global level and for critical-historical context, I survey Chan transmission literature of the Song dynasty in which encounter dialogues appear, and their role in developments of Chan/Zen traditions. Second, I zoom in on structural elements of encounter dialogues in particular as a genre. Third, aligning with the trajectory of performative analyses of Chan literature called for by Sharf and Faure, I turn to develop and criticize a performative model of questions from resources in recent analytic and continental philosophy of language and I apply that model to some questions in encounter dialogue literature