scholarly journals Near-critical 2D percolation with heavy-tailed impurities, forest fires and frozen percolation

2021 ◽  
Author(s):  
Jacob van den Berg ◽  
Pierre Nolin
Keyword(s):  
Forest Fires ◽  
Characteristic Length ◽  
Critical Time ◽  
Critical Value ◽  
Critical Percolation ◽  
Infinite Cluster ◽  
Physics Literature ◽  
Heavy Tailed ◽  
Frozen Percolation ◽  
The Impact

AbstractWe introduce a new percolation model on planar lattices. First, impurities (“holes”) are removed independently from the lattice. On the remaining part, we then consider site percolation with some parameter p close to the critical value $$p_c$$ p c . The mentioned impurities are not only microscopic, but allowed to be mesoscopic (“heavy-tailed”, in some sense). For technical reasons (the proofs of our results use quite precise bounds on critical exponents in Bernoulli percolation), our study focuses on the triangular lattice. We determine explicitly the range of parameters in the distribution of impurities for which the connectivity properties of percolation remain of the same order as without impurities, for distances below a certain characteristic length. This generalizes a celebrated result by Kesten for classical near-critical percolation (which can be viewed as critical percolation with single-site impurities). New challenges arise from the potentially large impurities. This generalization, which is also of independent interest, turns out to be crucial to study models of forest fires (or epidemics). In these models, all vertices are initially vacant, and then become occupied at rate 1. If an occupied vertex is hit by lightning, which occurs at a very small rate $$\zeta $$ ζ , its entire occupied cluster burns immediately, so that all its vertices become vacant. Our results for percolation with impurities are instrumental in analyzing the behavior of these forest fire models near and beyond the critical time (i.e. the time after which, in a forest without fires, an infinite cluster of trees emerges). In particular, we prove (so far, for the case when burnt trees do not recover) the existence of a sequence of “exceptional scales” (functions of $$\zeta $$ ζ ). For forests on boxes with such side lengths, the impact of fires does not vanish in the limit as $$\zeta \searrow 0$$ ζ ↘ 0 . This surprising behavior, related to the non-monotonicity of these processes, was not predicted in the physics literature.

Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

2012 ◽  
Vol 13 (2) ◽  
pp. 228-240 ◽  
Author(s):  
G. Bamberg ◽  
A. Neuhierl
Keyword(s):  
Heavy Tails ◽  
Geometric Mean ◽  
Asymptotic Optimality ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Risky Asset ◽  
Optimal Investment Strategy ◽  
Optimality Properties ◽  
Heavy Tailed ◽  
The Impact

Abstract The strategy to maximize the long-term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two-asset economy with one risky asset and a risk-free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy-tailed log returns than for light-tailed log returns.

Item Pool Development for the School-Aged Life Impact Burn Recovery Evaluation (SA- LIBRE5-12) Profile Computerized Adaptive Test (CAT): An Observer-Reported Outcome Assessment Measuring the Impact of Burn Injuries in School-Aged Children

2021 ◽  
Author(s):  
Silvanys L Rodríguez-Mercedes ◽  
Khushbu F Patel ◽  
Camerin A Rencken ◽  
Gabrielle G Grant ◽  
Kate Surette ◽  
...  
Keyword(s):  
Conceptual Framework ◽  
Critical Time ◽  
Cognitive Interviews ◽  
Item Pool ◽  
Computerized Adaptive Test ◽  
School Aged Children ◽  
Adaptive Test ◽  
Life Impact ◽  
The Impact ◽  
Item Pools

Abstract Introduction The transition from early childhood to teen years (5-12) is a critical time of development, which can be made particularly challenging by a burn injury. Assessing post-burn recovery during these years is important for improving pediatric survivors’ development and health outcomes. Few validated burn-specific measures exist for this age group. The purpose of this study was to generate item pools that will be used to create a future computerized adaptive test (CAT) assessing post-burn recovery in school-aged children. Methods Item pool development was guided by the previously developed School-Aged Life Impact Burn Recovery Evaluation (SA-LIBRE5-12) Conceptual Framework. The item pool development process involved a systematic literature review, extraction of candidate items from existing legacy measures, iterative item review during expert consensus meetings, and parent cognitive interviews. Results The iterative item review with experts consisted of six rounds. A total of 10 parent cognitive interviews were conducted. The three broad themes of concern were items that needed 1) clarification, needed context or were vague, 2) age dependence and relevance, and 3) word choice. The cognitive interviews indicated that survey instructions, recall period, item stem, and response choices were interpretable by respondents. Final item pool based on parental feedback consist of 57, 81, and 60 items in Physical, Psychological, and Family and Social Functioning respectively. Conclusion Developed item pools (n=198) in three domains are consistent with the existing conceptual framework. The next step involves field-testing the item pool and calibration using item response theory to develop and validate the SA-LIBRE5-12 CAT Profile.

Global warming and forest fires in Canada

1993 ◽  
Vol 69 (3) ◽  
pp. 290-293 ◽  
Author(s):  
Brian J. Stocks
Keyword(s):  
Global Warming ◽  
Forest Fire ◽  
Forest Fires ◽  
Fire Management ◽  
Warming Trend ◽  
Research Activities ◽  
Forest Fire Management ◽  
The Future ◽  
Innovative Thinking ◽  
The Impact

The looming possibility of global warming raises legitimate concerns for the future of the forest resource in Canada. While evidence of a global warming trend is not conclusive at this time, governments would be wise to anticipate, and begin planning for, such an eventuality. The forest fire business is likely to be affected both early and dramatically by any trend toward warmer and drier conditions in Canada, and fire managers should be aware that the future will likely require new and innovative thinking in forest fire management. This paper summarizes research activities currently underway to assess the impact of global warming on forest fires, and speculates on future fire management problems and strategies.

Optimal Number and Location of Watchtowers for Immediate Detection of Forest Fires in a Small Island

2017 ◽  
Vol 8 (4) ◽  
pp. 1-19 ◽  
Author(s):  
Stavros Sakellariou ◽  
Fani Samara ◽  
Stergios Tampekis ◽  
Olga Christopoulou ◽  
Athanassios Sfougaris
Keyword(s):  
Early Detection ◽  
Spatial Structure ◽  
Forest Fires ◽  
Critical Time ◽  
Spatial Optimization ◽  
Optimal Number ◽  
Small Island ◽  
Environmental Consequences ◽  
Fire Ignitions ◽  
Visible Area

A crucial factor for prevention and immediate confrontation of destructive fires and their socioeconomic and environmental consequences constitutes the early detection and spatial localization of fire ignitions, so that the firefighting forces to be activated and act within the critical time of response. Thus, principal objective of the paper constitutes the spatial optimization of the most effective locations of watchtowers developing a constructive network for the immediate and early detection of forest fires. This optimization involves the exploration of the fewest locations for watchtowers with the maximum visible area and reduced degree of overlapping. The results highlighted 4 groups of watchtowers (20 observers in total) determining the optimum locations. The total visibility amounted to 70% of the island, while the visibility percentages per land cover are variable, since they are depended on the spatial structure of them. Definitely, the final selection of the final number and the spatial structure of the watchtowers purely constitute decisions of political nature and will.

The Impact of Geometric Variation on Compressor Two-Dimensional Incidence Range

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Martin N. Goodhand ◽  
Robert J. Miller ◽  
Hang W. Lung
Keyword(s):  
Design Process ◽  
Design Space ◽  
Leading Edge ◽  
Critical Value ◽  
Two Dimensional ◽  
Suction Surface ◽  
Design Intent ◽  
Manufacture Process ◽  
The Impact ◽  
Geometric Variation

An important question for a designer is how, in the design process, to deal with the small geometric variations which result from either the manufacture process or in-service deterioration. For some blade designs geometric variations will have little or no effect on the performance of a row of blades, while in others their effects can be significant. This paper shows that blade designs which are most sensitive are those which are susceptible to a distinct switch in the fluid mechanisms responsible for limiting blade performance. To demonstrate this principle, the sensitivity of compressor 2D incidence range to manufacture variations is considered. Only one switch in mechanisms was observed, the onset of flow separation at the leading edge. This switch is only sensitive to geometric variations around the leading edge, 0–3% of the suction surface. The consequence for these manufacture variations was a 10% reduction in the blade's positive incidence range. For this switch, the boundary in the design space is best defined in terms of the blade pressure distribution. Blade designs where the acceleration exceeds a critical value just downstream of the leading edge are shown to be robust to geometric variation. Two historic designs, supercritical blades and blades with sharp leading edges, though superior in design intent, are shown to sit outside this robust region and thus, in practice, perform worse. The improved understanding of the robust, region of the design space is then used to design a blade capable of a robust, 5% increase in operating incidence range.

The impact of urban and forest fires on the airborne fungal spore aerobiology

Aerobiologia ◽  
2018 ◽  
Vol 34 (4) ◽  
pp. 585-592 ◽  
Author(s):  
Irene Camacho ◽  
André Góis ◽  
Roberto Camacho ◽  
Vítor Nóbrega ◽  
Fernandez
Keyword(s):  
Forest Fires ◽  
Fungal Spore ◽  
Airborne Fungal Spore ◽  
The Impact

Role of forest fires in Holocene stand-scale dynamics in the unmanaged taiga forest of northwestern Russia

The Holocene ◽  
2014 ◽  
Vol 24 (11) ◽  
pp. 1503-1514 ◽  
Author(s):  
Niina Kuosmanen ◽  
Keyan Fang ◽  
Richard HW Bradshaw ◽  
Jennifer L Clear ◽  
Heikki Seppä
Keyword(s):  
Forest Fires ◽  
Siberian Larch ◽  
Wavelet Coherence ◽  
Individual Tree ◽  
Study Region ◽  
Taiga Forest ◽  
The Impact ◽  
Wavelet Coherence Analysis ◽  
Northwestern Russia

Fossil pollen, conifer stomata, and charcoal records for the last 10,000 years were studied from three small hollow sites (Larix Hollow, Mosquito Hollow, and Olga Hollow) located at the modern western range limit of Siberian larch ( Larix sibirica) in northwestern Russia to investigate the role of forest fires in stand-scale dynamics of taiga vegetation. Wavelet coherence analysis was utilized to reveal the significance of fire on the vegetation composition at different timescales by assessing the phase and strength of the relationship between forest fires and most common boreal tree taxa in a time–frequency window. Pollen and stomata data show that all of the modern-day common tree taxa, including Norway spruce ( Picea abies) and Siberian larch, have been present in the study region since the early Holocene. The absence of charcoal layers at Mosquito Hollow suggests that this site has acted as a fire-free refugium with continuous dominance of spruce throughout the Holocene. Meanwhile, the Larix Hollow record indicates frequent local fire events and as a consequence, a more variable tree species composition. The wavelet coherence results show that the impact of forest fires on vegetation varies from short-term (<200-year periods) changes in individual tree taxa to long-term (400–800 years) changes in forest composition, such as the expansion of spruce population after local high-intensity fires around 7500–7000 cal. yr BP and the increase in abundance of birch and alder during periods of high fire frequency. Our results suggest that Holocene fire histories can be markedly different within a small geographical area, demonstrating the importance of site-specific factors in the local fire regime in the unmanaged taiga forest.

scholarly journals Hotspots of boundary accumulation: dynamics and statistics of micro-swimmers in flowing films

2016 ◽  
Vol 13 (115) ◽  
pp. 20150936 ◽  
Author(s):  
Arnold J. T. M. Mathijssen ◽  
Amin Doostmohammadi ◽  
Julia M. Yeomans ◽  
Tyler N. Shendruk
Keyword(s):  
Solid Wall ◽  
Critical Value ◽  
Hydrodynamic Interactions ◽  
Critical Flow ◽  
Natural Environments ◽  
Flow Strength ◽  
Surfaces And Interfaces ◽  
Biological Flows ◽  
The Impact ◽  
Systematic Framework

Biological flows over surfaces and interfaces can result in accumulation hotspots or depleted voids of microorganisms in natural environments. Apprehending the mechanisms that lead to such distributions is essential for understanding biofilm initiation. Using a systematic framework, we resolve the dynamics and statistics of swimming microbes within flowing films, considering the impact of confinement through steric and hydrodynamic interactions, flow and motility, along with Brownian and run–tumble fluctuations. Micro-swimmers can be peeled off the solid wall above a critical flow strength. However, the interplay of flow and fluctuations causes organisms to migrate back towards the wall above a secondary critical value. Hence, faster flows may not always be the most efficacious strategy to discourage biofilm initiation. Moreover, we find run–tumble dynamics commonly used by flagellated microbes to be an intrinsically more successful strategy to escape from boundaries than equivalent levels of enhanced Brownian noise in ciliated organisms.

scholarly journals Nonlinear feedback in a six-dimensional Lorenz Model: impact of an additional heating term

2015 ◽  
Vol 2 (2) ◽  
pp. 475-512
Author(s):  
B.-W. Shen
Keyword(s):  
Rayleigh Number ◽  
Numerical Solutions ◽  
Critical Rayleigh Number ◽  
Critical Value ◽  
Small Scale ◽  
Solution Stability ◽  
Nonlinear Feedback ◽  
Lorenz Model ◽  
Additional Heating ◽  
The Impact

Abstract. In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the steamfunction is referred to as a secondary streamfunction mode, while the two additional modes, that appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number (rc) is determined to be 41.1. The critical value is larger than that in the 3DLM (rc ~ 24.74), but slightly smaller than the one in the 5DLM (rc ~ 42.9). A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1) negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2) the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3) overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization), consistent with the following statement by Lorenz (1972): If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado. The implications of this and previous work, as well as future work, are also discussed.

scholarly journals Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Junji Jia ◽  
Ke Huang
Keyword(s):  
Gravitational Lensing ◽  
Deflection Angle ◽  
Strong Field ◽  
Distance Effect ◽  
Critical Value ◽  
Field Limit ◽  
Perturbative Method ◽  
The Deflection Angle ◽  
The Impact ◽  
Strong Field Limit

AbstractA perturbative method to compute the deflection angle of both timelike and null rays in arbitrary static and spherically symmetric spacetimes in the strong field limit is proposed. The result takes a quasi-series form of $$(1-b_c/b)$$ ( 1 - b c / b ) where b is the impact parameter and $$b_c$$ b c is its critical value, with coefficients of the series explicitly given. This result also naturally takes into account the finite distance effect of both the source and detector, and allows to solve the apparent angles of the relativistic images in a more precise way. From this, the BH angular shadow size is expressed as a simple formula containing metric functions and particle/photon sphere radius. The magnification of the relativistic images were shown to diverge at different values of the source-detector angular coordinate difference, depending on the relation between the source and detector distance from the lens. To verify all these results, we then applied them to the Hayward BH spacetime, concentrating on the effects of its charge parameter l and the asymptotic velocity v of the signal. The BH shadow size were found to decrease slightly as l increases to its critical value, and increase as v decreases from light speed. For the deflection angle and the magnification of the images however, both the increase of l and decrease of v will increase their values.

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