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Types of Simulations
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We divide physics simulations into three broad categories:

  1. Continuous
    Simulations of physical phenomena that develop in a continuous manner in time and space, such as heat flowing through a metal or planets orbiting the sun.

  2. Event
    Simulations of phenomena that occur within a discrete units in time and space such as particle collisions. The aim could be to examine mean behavior over a large number of events or to capture the occasional rare event.

  3. Static
    Modeling of a system in which there is no time component. For example, an optics demonstration in which the position of a lens could be moved by the user to see its affect on the image.
Simulations of the continuous phenomena could mean the use of analytically derived formulas that provide the time dependence of, say, the position of a planet in an orbit simulator. Or, more frequently, it will involve the numerical solution of a differential equation to solve for the time dependence of the variables of interest.

Events at the atomic level vary from event to event due to the probabilistic nature of quantum mechanics.

For example, the study of elastic particle scattering (i.e. two particles collide but don't break up) will involve a differential cross-section formula that provides the probability that a particle will scatter into a given solid angle element. This will be constrained by kinematics, that is, the conservation of energy and momentum.

In the simulation, random number generation will be used to vary the particle scattering events weighted by the cross-section probability and kinematics. Thus, simulating many events basically carries out a Monte Carlo integration of a differential cross-section times a kinematic phase space term.

Event simulations can also be of use for physics at the macroscopic level, as well, since there can be variations in initial conditions and other probablistic influences on the system.

For example, one cannot predict exactly where a large piece of debris in a decaying orbit will eventually enter the atmosphere or where a surviving piece might land. There are unpredictable variations in the atmospheric density due to solar heating. The interaction with a non-uniform shaped piece of material, which is also probably rotating, can't be modeled exactly.

So one would simulate many possible scenarios or events to determine an area on the earth within which there is high probability the debris will hit.

In this sense, the continuous and event types of simulation overlap. That is, one might run an asteroid orbit simulation multiple times with different initial conditions to examine whether it might eventually intercept the earth.

However, the emphasis of the continuous type simulation is on how the phenomena develops over time during a single "run" rather than the average behavior over many runs.

Latest update: Dec.10.200

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