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Flying ice cube
In molecular dynamics (MD) simulations, the flying ice cube effect is a numerical integration artifact in which the energy of high-frequency fundamental modes is drained into low-frequency modes, particularly into zero-frequency motions such as overall translation and rotation of the system. The artifact derives its name from a particularly noticeable manifestation that arises in simulations of particles in vacuum, where the system being simulated acquires high linear momentum and experiences extremely damped internal motions, freezing the system into a single conformation reminiscent of an ice cube or other rigid body flying through space. The artifact is entirely a consequence of molecular dynamics algorithms and is wholly unphysical, since it violates the principle of equipartition of energy. This is one of several unphysical artifacts that can be observed in molecular dynamics simulations, often arising from the need to balance numerical accuracy with computational efficiency sufficient to achieve adequate sampling of dynamics. The artifact can also occur in generalizations of classical MD simulations, as with Drude oscillators.
==Origin==
The flying ice cube artifact arises from repeated rescalings of the velocities of the particles in the simulation system. The artifact will not occur if the center-of-mass velocity of the system is kept separate and apart from those velocities being rescaled. Velocity rescaling is a means of imposing a thermostat on the system, forcing it to maintain a roughly constant temperature. These rescalings are traditionally done, as in the Berendsen thermostat, by multiplying the system's velocities by a factor α, which equals the ratio of the desired mean kinetic energy divided by the instantaneous amount of kinetic energy. This scheme fails, however, because the instantaneous kinetic energy is located in the ''denominator'' of the ratio α; fluctuations in the kinetic energy make positive second-order contributions to α, making its average value greater than one even when the instaneous kinetic energy has the proper mean. This causes the constant energy terms — such as those of overall translation and rotation — to grow continuously. Since these energies are constantly increasing, the same rescaling decreases the internal energies, diminishing the internal vibrations. This may be shown mathematically as well; the fluctuating internal kinetic energy has its highs and lows, but its highs are decreased more by velocity rescaling than its lows are increased, leading to a net decrease on average with every rescaling.
When the rotation and translation of the system center of mass are not periodically removed, a particularly noticeable form of the artifact occurs in which nearly all of the system's kinetic energy accrues to these two forms of motion, resulting in a system with essentially no energy associated with internal motions which therefore appears to move as a rigid body. This problem can arise in explicit solvent under unusual circumstances, particularly when the Berendsen barostat is used or when the simulation parameters do not respect conservation of energy, but the artifact occurs most visibly in simulations in vacuum.〔
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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