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Using GIS data in a m:nACk cellular automata to perform an avalanche
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Index
• • • • • • Avalanche problem Cellular automata m:n-ACk Avalanche model Results Conclusions
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Avalanche
Two main types of snow avalanche: • Loose-snow avalanche originates at a point and propagates downhill by successively dislodging increasing numbers of poorly cohering snow grains, typically gaining width as movement continues down slope. • Slab avalanche, occurs when a distinct cohesive snow layer breaks away as a unit and slides because it is poorly Cellular automata – the snow or ground Avalanche – anchored to m:n-Ack – Avalanche model – Results
– Conclusions
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Avalanche fatalities in IKAR Countries
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 4
Cellular automata
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 5
Game of life
• The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is the best-known example of a cellular automaton. • Glider gun and
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m:n-ACk
A multi n dimensional cellular automaton is a cellular automaton generalization composed by m layers with n dimensions each one. The representation is: • m:n-ACk Where • m: is the automaton number of layers. • n: is the different layers dimension. • Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results k: is the number of main layers (1 by
– Conclusions
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m:n-ACk
• Defined over the mathematical topology concept. • 1:n-AC 1 is the common cellular automata if the topology used is the discrete topology defined over N or Z. • The implementation, as is usual, can be a matrix.
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State of the automata
• Em[x1,..,xn], layer m state in x1,..,xn position
– Em is a function describing cell state in position x1,..,xn of layer m.
• EG[x1,..,xn], automata status in x1,..,xn position.
– EG returns automata global state in position georeferenced by coordinates x1,..,xn. Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results
– Conclusions
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Evolution Function m
• Function defined for the layer m to modify its state through the state of others layers using combination function Ψ, and vicinity and nucleus functions.
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 10
Avalanche Model data
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Avalanche Model
• 6+N:2-AC4+N on Z2
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 12
Vicinity and nucleus function
• Vicinity function: vn(x1,x1) = {(x11,x2-1), (x1-1,x2), (x1-1,x2+1), (x1,x2-1), (x1,x2), (x1,x2+1), (x1+1,x2-1), (x1+1,x2), (x1+1,x2+1)} • Nucleus function: nc(x1,x1)= {(x1,x1)}
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 13
Evolution functions
• E2[i]: Thickness of the snow. The function that rules this layer is “Modify information(p)” • E4[i]: Density, compactness of the snow, in our case is 0.5 (Mears 1976). • E6[i]: State of the snow. The function is defined in the next diagrams. • EN[i]: Obstacles. The function that
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SDL formalism
• Object-oriented, formal language defined by The International Telecommunications Union as recommendation Z.100. • Intended for the specification of complex, event-driven, real-time, and interactive applications involving many concurrent activities that communicate using discrete signals.
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 15
Moore neighbourhood
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 16
Λ:state of the snow
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 17
Empty process
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Results
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 19
Results
Avalanche – Cellular automata – m:n-Ack – Avalanche model – Results – Conclusions GISRUK 2007 20
Conclusions
• An application to represent in virtual reality format the avalanche phenomena using GIS data thought the m:n-CAk cellular automaton is presented. • The comparison of the output data with studied phenomena shows promising results. • The structure in layers simplify the calculus of the evolution functions, allowing an easier implementation of the model, and a clear specification. • Avalanche –represents all m:n-Ack – Avalanche model – Results Layers Cellular automata – the model variables,
– Conclusions
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Thanks!
Pau Fonseca i Casas pau@fib.upc.edu
Technical University of Catalonia Barcelona School of Informatics Computing laboratory Barcelona Jordi Girona 1-3 (+34)93401773
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Static process
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Dynamic process
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Evolution function
• The increment in the force is used in the next expression to determine if the snow continues its movement to other cell, or stops its movement, if the force is equal to zero.
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Evolution function
• Where • IFi,t=Impulse force, depends on the quantity and quality of the snow, and the slope. • SFFi,t= Sliding friction force between the avalanche and the underlying snow or ground. • IFFi,t= Internal dynamic shear resistance due to collisions and momentum exchange between particles and blocks of snow, (internal friction force). • ASFFi,t= Turbulent friction within the snow/air suspension, (air suspension friction force). • AFFi,t=Shear between the avalanche and the surrounding air, (air friction force). • FFFi,t= Fluid-dynamic drag at the front of the avalanche
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5
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5
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5
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1 vs 3
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