page_title: Computer simulation
section_title: Computer simulation in science
hierarchical_section_title: Computer simulation / Computer simulation in science
caption_attribution_description: This is a shot from a three dimensional computer simulation of the process of en:osmosis. The blue en:mesh is impermeable to the larger balls, whereas all of the balls are (in the animated version) bouncing about according to the rules of physical simulation of the kinetics of an ideal gas. Averaged over long period of time, each ball has has the same kinetic energy as each of the other balls, even though at any given moment the velocities are distributed according to the appropriate en:Boltzmann functions. Likewise, each species (in this case color) of balls (as a group) exerts time averaged force (due to the bouncing) upon the walls of the box, which corresponds to the partial en:pressure contribution associated with that group. These properties emerge even though the collision function used in the simulation is trivial, to wit: void Mass::collide (Mass *X) { vector v_cm; v_cm = (velocity*mass+X-&gt;velocity*X-&gt;mass)/(mass+X-&gt;mass); velocity = v_cm*2 - velocity; X-&gt;velocity = v_cm*2 - X-&gt;velocity; m_bCollision = true; X-&gt;m_bCollision = true; } Accordingly, one can make theoretical assumtions about the behaviour of such mixtures according to the application of Dalton's law of partial pressures, and so on, and thereby gain some insights into how certain physical processes really work.
context_page_description: Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of or the outcome of a real-world or physical system. Since they allow to check the reliability of chosen mathematical models, computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics, astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.
  Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large-scale programs that run for hours or days on network-based groups of computers. The scale of events being simulated by computer simulations has far exceeded anything possible using traditional paper-and-pencil mathematical modeling.
context_section_description: Generic examples of types of computer simulations in science, which are derived from an underlying mathematical description:
  a numerical simulation of differential equations that cannot be solved analytically, theories that involve continuous systems such as phenomena in physical cosmology, fluid dynamics (e.g., climate models, roadway noise models, roadway air dispersion models), continuum mechanics and chemical kinetics fall into this category.
  a stochastic simulation, typically used for discrete systems where events occur probabilistically and which cannot be described directly with differential equations (this is a discrete simulation in the above sense). Phenomena in this category include genetic drift, biochemical or gene regulatory networks with small numbers of molecules. (see also: Monte Carlo method).
  multiparticle simulation of the response of nanomaterials at multiple scales to an applied force for the purpose of modeling their thermoelastic and thermodynamic properties. Techniques used for such simulations are Molecular dynamics, Molecular mechanics, Monte Carlo method, and Multiscale Green's function.
  Specific examples of computer simulations follow:
  statistical simulations based upon an agglomeration of a large number of input profiles, such as the forecasting of equilibrium temperature of receiving waters, allowing the gamut of meteorological data to be input for a specific locale. This technique was developed for thermal pollution forecasting.
  agent based simulation has been used effectively in ecology, where it is often called "individual based modeling" and is used in situations for which individual variability in the agents cannot be neglected, such as population dynamics of salmon and trout (most purely mathematical models assume all trout behave identically).
  time stepped dynamic model. In hydrology there are several such hydrology transport models such as the SWMM and DSSAM Models developed by the U.S. Environmental Protection Agency for river water quality forecasting.
  computer simulations have also been used to formally model theories of human cognition and performance, e.g., ACT-R.
  computer simulation using molecular modeling for drug discovery.
  computer simulation to model viral infection in mammalian cells.
  computer simulation for studying the selective sensitivity of bonds by mechanochemistry during grinding of organic molecules.
  Computational fluid dynamics simulations are used to simulate the behaviour of flowing air, water and other fluids. One-, two- and three-dimensional models are used. A one-dimensional model might simulate the effects of water hammer in a pipe. A two-dimensional model might be used to simulate the drag forces on the cross-section of an aeroplane wing. A three-dimensional simulation might estimate the heating and cooling requirements of a large building.
  An understanding of statistical thermodynamic molecular theory is fundamental to the appreciation of molecular solutions. Development of the Potential Distribution Theorem (PDT) allows this complex subject to be simplified to down-to-earth presentations of molecular theory.
  Notable, and sometimes controversial, computer simulations used in science include: Donella Meadows' World3 used in the Limits to Growth, James Lovelock's Daisyworld and Thomas Ray's Tierra.
  In social sciences, computer simulation is an integral component of the five angles of analysis fostered by the data percolation methodology, which also includes qualitative and quantitative methods, reviews of the literature (including scholarly), and interviews with experts, and which forms an extension of data triangulation. Of course, similar to any other scientific method, replication is an important part of computational modeling
caption: Computer simulation of the process of osmosis
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