Local statistics for random domino tilings of the Aztec diamond

We prove an asymptotic formula for the probability that, if one chooses a domino tiling of a large Aztec diamond at random according to the uniform distribution on such tilings, the tiling will contain a domino covering a given pair of adjacent lattice squares. This formula quantifies the effect of the diamond's boundary conditions on the behavior of typical tilings; in addition, it yields a new proof of the arctic circle theorem of Jockusch, Propp, and Shor. Our approach is to use the saddle point method to estimate certain weighted sums of squares of Krawtchouk polynomials (whose relevance to domino tilings is demonstrated elsewhere), and to combine these estimates with some exponential sum bounds to deduce our final result. This approach generalizes straightforwardly to the case in which the probability distribution on the set of tilings incorporates bias favoring horizontal over vertical tiles or vice versa. We also prove a fairly general large deviation estimate for domino tilings of simply-connected planar regions that implies that some of our results on Aztec diamonds apply to many other similar regions as well.Comment: 42 pages, 7 figure

Penggunaan Kartu Domino Kimia pada Materi Koloid terhadap Motivasi dan Hasil Belajar di SMA

This research was aimed to determine the differences of motivation and learning result between students who were taught domino chemistry card with students who were taught without domino chemistry card and determine domino chemistry card\u27s effect on chemistry learning with domino chemistry against learning result in coloid subject matter eleven grade of SMA Negeri 1 Sekadau Hilir. The form of research that used was quasy-experimental with research design was Nonequivalent Control Group Design. Thirty one students of eleven grade IPA 1 and thirty two students of eleven grade IPA 2 participated in this research. Data analysis using U-Mann Whitney test showed that there were differences motivation and learning result between students who were taught use domino chemistry card with students who were taught without domino chemistry card. Based on calculation of effect size that was 0,79 (medium), domino chemistry card gave 28,52% effect on increased student learning result

Sequential escapes: onset of slow domino regime via a saddle connection

We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable "quiescent" equilibrium to a more stable "active" equilibrium. The presence of coupling introduces dependence between the escape processes: for diffusive coupling there is a strongly coupled limit (fast domino regime) where the escapes are strongly synchronised while for intermediate coupling (slow domino regime) without partially escaped stable states, there is still a delayed effect. These regimes can be associated with bifurcations of equilibria in the low-noise limit. In this paper we consider a localized form of non-diffusive (i.e pulse-like) coupling and find similar changes in the distribution of escape times with coupling strength. However we find transition to a slow domino regime that is not associated with any bifurcations of equilibria. We show that this transition can be understood as a codimension-one saddle connection bifurcation for the low-noise limit. At transition, the most likely escape path from one attractor hits the escape saddle from the basin of another partially escaped attractor. After this bifurcation we find increasing coefficient of variation of the subsequent escape times

Fire as a primary event of accident domino sequences: The case of BLEVE

The domino sequences found in major accidents have been analyzed for a large set of cases (330); the first event triggering the domino effect was an explosion or a fire, both with approximately the same contribution; the same proportion has been found when all domino effect steps were considered. Although fire effects usually reach a distance much shorter than those of an explosion, as fire is the most frequent major accident it is often found as the first step of domino sequences. This is especially true in the case of BLEVEs. Both in fixed plants and in the transportation of hazardous materials, in the event of a fire, if flames affect a vessel and the fireproofing layer has been damaged, a BLEW can occur at any moment 127 BLEW accidents involving domino effect have been analyzed. It has been found that fire is significantly more frequent than explosion, both in triggering the domino effect sequence and in intermediate steps. The time to failure can range from 1 min or even less up to several hours, an aspect that should be very important for the management of the emergency. A set of conclusions are inferred from this survey. (C) 2015 Elsevier Ltd. All rights reserved.Postprint (author's final draft

Economics of spatial coexistence of genetically modified and conventional crops: Oilseed rape in Central France

Europe is currently struggling to implement coherent coexistence regulations on genetically modified (GM) and non-GM crops in all EU Member States. We conduct simulations with the software ArcView® on a GIS dataset of a hypothetical case of GM herbicide tolerant oilseed rape cultivation in Central France. Our findings show that rigid coexistence rules, such as large distance requirements, may impose a severe burden on GM crop production in Europe. These rules are not proportional to the farmers’ basic incentives for coexistence and hence not consistent with the objectives of the European Commission. More alarming, we show that in densely planted areas a domino-effect may occur. This effect raises coexistence costs and even adds to the non-proportionality of rigid coexistence regulations. Instead, we show that flexible measures would be preferable since they are proportional to the incentives for coexistence and, hence, less counterproductive for European agriculture.regulation, GIS modelling, domino-effect, Crop Production/Industries,

The Inverse Domino Effect: Are Economic Reforms Contagious?

This paper examines whether a country’s economic reforms are affected by reforms adopted by other countries. A simple model of economic reforms is developed to motivate the econometric work. Unsurprisingly, the model predicts that reforms are more likely when factors of production are internationally mobile and reforms are pursued in other economies. More interesting is the finding that reforms are not driven by greater trade openness. Using the change in the Index of Economic Freedom as the measure of market-liberalising reforms, we examine two issues. First, we examine whether economic reforms are ‘habit-forming’, and secondly, we identify the most important channels through which reforms are transmitted from country to country. For a panel of 144 countries and the years 1995-2006, we find little evidence that reforms are habit- forming, if anything there is a status quo bias. However, we do find evidence of the importance of reforms in other countries. Consistent with our model, international trade is not a vehicle for the diffusion of economic reforms, rather the most important mechanism is geographical or cultural proximity.Economic reforms; economic freedom; resource flow models; spatial interdependence