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**Complex
Network Modeling in Maritime Search and Rescue Operation**

Complex Network is is class of complex system models which describes
the dynamical set of objects. Their structure varies with time and
they can be defined in probabilistic terms. Now we can find this
class of complex system in various fields. Perhaps the most popular
network that appears when the term 'complex network' comes is social
network which may be online as well as offline. There are few others
like citation networks, telecommunication networks and so on. But yes
there are other systems which are similarly complex in it's structure
and dynamics. One such scenario is the collective behavior of
floating drifters at sea.

Drifting floaters are one of the major subjects of Search and Rescue
( SAR ) operations. One
option is a rescue of lost vessels’ crew
members. Drifting and visibility are important
factors for such kind
of rescue operations. Another option is a search for lifeboats,
washed off
containers or even World War II mines. Such drift ing
objects are
hazardous for shipping.

Now by floating drifters we mean a group of object that is floating
in the sea with a visible distance . In context of SAR we can
consider the plane wreckage floating in the sea as floating drifters
after the plane is crashed into the sea.

Let's consider there are V no of floating drifters in the sea. Each
drifter can be visible within a given range. Let us consider the line
of sight between two floating drifters as an edge E. Now this network
evolves with time as position of each drifter is changing with the
motion of waves and winds. So orientation of entire graph is getting
changed with time. With the periodic motion of wave, a drifter can go
out of sight and thus loosing an edge or it may comes back in sight
and thus creates an edge. The set (V, E) forms a Complex Network that
evolves in time. Initially the structure of Complex Network may be
rather regular,
but at later time the network structure is in
destruction due to irregular wind, wave and current loads.

In the above picture we can see how the network of floating drifters have evolved over time. At time t1 it was very regular in nature and as time elapses the orientation of the network changes due to the effect of waves, winds and current. See at time t3 it becomes a graph of 2 components and in a later time they can be joined again by a link if a drifters come into the visible sight.

Now the sea surface can also be modeled with the superposition of finite
number of harmonic waves. The disturbance of waves is determined by a
two-dimensional disturbance energy spectrum S(ω,θ), where
ω — the angular
frequency of the wave and θ —
the angle between the direction of the running wave and wind direction.

There are various
models of the spectra of disturbance expressed in terms of the energy density function of the
angular frequency and direction of
propagation . An example of such
a spectrum is a spectrum of Pierson-Moskowitz. The continuous spectrum of disturbance can be approximated by a finite number of harmonics. In order to provide a quick generation of harmonic heights and velocities, the two-dimensional Fast Fourier Transform (FFT) can be used. With the help of all these mathematical tools the planer displacement and velocities of floating drifters and water particles can be obtained. These attributes help us to understand the dynamics of the floating drifters.

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**Application: In Search and Rescue Plans**

Considering all the factors including direction of wind, wave, gravity the probable trajectory of the floating drifters can be approximated which helps in rescue operation. Because for example when a plane crashes in mid air and all its wreckage falls into the sea from that high altitude then the wreckage will be spread across miles over the sea. So the helicopter needs to follow the direction of the main wave initially and after that it needs to predict to some extent about the probable location of other parts of the plane considering all the natural parameters like wind, sea wave, current etc.

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