=========================== http://en.wikipedia.org/wiki/EXPTIME Other examples of EXPTIME-complete problems include the problem of evaluating a position in generalized chess,[5] checkers,[6] or Go (with Japanese ko rules).[7] These games have a chance of being EXPTIME-complete http://www.eternityii.com/ http://en.wikipedia.org/wiki/Eternity_II_puzzle ======================================= http://uk.youtube.com/watch?v=v6shurn2W0w&NR=1 - space sim. use galaxy pic maybe http://hardware.slashdot.org/comments.pl?sid=304863&cid=20703909 - big O for raytracing http://games.slashdot.org/comments.pl?sid=422720&cid=22096546 - more big O =============================== that were too complex for an analytical solution -- so they had to be evaluated numerically "analytical vs numerical" Closed-form expression / Analytic solution vs Analytical expression (slightly wider catgeory http://everything2.com/e2node/statistical%2520mechanics =========================== Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow: fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and reportedly modeling fission weapon detonation. Some of its principles are even used in traffic engineering, where traffic is treated as a continuous fluid. Fluid dynamics offers a systematic structure that underlies these practical disciplines and that embraces empirical and semi-empirical laws, derived from flow measurement, used to solve practical problems. The solution of a fluid dynamics problem typically involves calculation of various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time. ======================= http://en.wikipedia.org/wiki/Computational_fluid_dynamics Computational fluid dynamics (CFD) is one of the branches of fluid mechanics that uses numerical methods and algorithms The fundamental basis of any CFD problem are the Navier-Stokes equations (Euler are simpler) (but seems to be solvable through Lattice Boltzmann methods) ------------ Continuum Mechanics vs. Molecular Mechanics http://en.wikipedia.org/wiki/Navier-Stokes_equations http://en.wikipedia.org/wiki/Molecular_dynamics They may be used to model weather, ocean currents, water flow in a pipe, flow around an airfoil (wing), and motion of stars inside a galaxy. As such, these equations in both full and simplified forms, are used in the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of the effects of pollution, etc. Coupled with Maxwell's equations they can be used to model and study magnetohydrodynamics. http://en.wikipedia.org/wiki/Molecular_dynamics#Molecular_dynamics_algorithms ============================= ====================================== People who DO know the topic CAN explain it in accessible ways, and DO NOT utter blatant falsities. Some examples of this is: "This problem, like many others, is NP-complete. Sigh, everything good in life is NP-complete" (meaning, many important problems that we need and would love to solve are, unfortunately, NP-complete. It is ABSOLUTELY TRUE that NP-completeness crops up more than we'd like... and sometimes in unexpected places) "P ?= NP issue is analogous to why ordinary people can't compose like Mozart, but can still appreciate his work for the genius that it is." (listening and appreciating music is like being a verifier, you can check that a solution to a hard problem is correct, but you can't produce the solutions yourself. An ordinary person could brute force it by continuously composing until something came out that was magnificient... but then that could take a very very long time). THESE comments are constructive... AND correct.