An avalanche is modelled as a critical branching process ( ) with offspring variance
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems
Many Parts, One Behaviour, Ch Self-organised criticality and avalanches
Problem
An avalanche is modelled as a critical branching process (σ=1) with offspring variance v=1.5. The probability that the avalanche survives to at least generation T falls, for large T, as xT≈2/(vT).
((a)) Find the number of generations T at which the survival probability first falls to 0.01.
((b)) State, using the form of xT, the exponent of the probability density P(T) of avalanche durations.