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In-Depth Information
Many complex macroscopic phenomena, which own the same locality property of
CA
, seem difficult to be modelled in the classical
CA
frame, because they consist
often of processes involving different frameworks of space and time and need
transition rules, far from a typical transition function of a finite automaton.
This paper suggests some mechanisms (when they are practicable) which permit to
define the macroscopic phenomenon in terms of a
CA
formalism [4]. Different
applications [5], [6] were developed according to some of these specifications. A
particular complex example is here exhibited: landslides characterized by very rapid
debris flows with strong soil erosion, generating an avalanche effect.
The second section considers some
CA
criteria for modelling complex macroscopic
phenomena together with a practical approach for modelling flows, the third section
presents the model SCIDDICA (release S3hex) for very rapid debris flows with
strong soil erosion, the fourth section shows a result of the simulations of the
landslides occurred in Sarno (1998, Italy); some conclusions are reported at the end.
2 Some
CA
Criteria for Modelling Macroscopic Phenomena
The criteria here reported are empirical and may be applied only to particular classes
of macroscopic phenomena, involving surface flows. The proposed recipes don't
guarantee by themselves success in the simulation. In fact, when the model is
validated on real cases of a certain typology, the model applications in similar
conditions are reliable.
The physical laws expressed for complex phenomena involve systems of
differential equations; they are difficult to be managed, even considering numerical
methods, which are often revealed inapplicable.
The approximations, that are here proposed, are rough, however they want to
translate in a context of locality with discrete time and space the conservation laws of
physics and the features of minimisation, typical of physical equations, concerning the
energy variations.
2.1 Model Specifications for Time and Space
Simulations of real macroscopic events need to define a correspondence of the system
and its evolution with the model and the corresponding simulations. At least, the
dimension of the cell and the time correspondence to a
CA
step must be fixed. They
are defined as global parameters, because their values are global to all the
CA
; of
course other global parameters could be necessary.
In order to fix these two essential global parameters, further points must be
considered, when the phenomenon is complex and can involve time and/or space
heterogeneity in the sense specified later on.
The state of the cell must account for all the characteristics, relevant to the
evolution of the system and relative to the space portion corresponding to the cell.
Each characteristic could be individuated as a substate; the permitted values of the
substate must form a finite set. The set of possible states of the cell is given by the
Cartesian product of the sets of substates. In case that one of the characteristics (e.g. a
