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Fig. 2. Most common modeling techniques for all combinations of continuous/
discrete and deterministic/stochastic models. The techniques for physical and phe-
nomenological models are identical, but in the former case the models are based on
physical principles. Common examples of application of each technique are given in
the shaded areas.
accounted for as an individual entity. Examples include MD simula-
tions, 50 where the position and velocity of each atom are explicitly
tracked and atoms are treated as individual, discrete entities. In a contin-
uous model, a mean field average is followed in space and time. Examples
of such field quantities are concentration, temperature, and charge
density.
In continuous models, we distinguish two types of quantities. On the
one hand, quantities whose value in a homogeneous system does not
depend on the averaging volume are called “intensive”. Examples include
concentration or temperature. If 1 L of water at 20
C is divided into two
half-liter glasses, the water in each of the two glasses will still have a tem-
perature of 20
°
C, even though the volume is halved. The temperature of
the water is independent of the volume of water, hence making temper-
ature an intensive property. On the other hand, quantities whose value in
a homogeneous system depends on the volume are called “extensive”.
These are quantities such as mass, heat, or charge. Neither of the two
half-liters of water has the same mass as the original liter. Intensive and
°
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