molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...

(MD) simulations, the flying ice cube effect is an artifact in which the energy of high-

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is ...

fundamental mode A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies ...

s is drained into low-frequency modes, particularly into zero-frequency motions such as overall

translation Translation is the communication of the Meaning (linguistic), meaning of a #Source and target languages, source-language text by means of an Dynamic and formal equivalence, equivalent #Source and target languages, target-language text. The ...

and

rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...

of the system. The artifact derives its name from a particularly noticeable manifestation that arises in simulations of particles in

vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often di ...

, where the system being simulated acquires high linear

momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass ...

and experiences extremely damped internal motions, freezing the system into a single conformation reminiscent of an

ice cube An ice cube is a small piece of ice, which is typically rectangular as viewed from above and trapezoidal as viewed from the side. Ice cubes are products of mechanical refrigeration and are usually produced to cool beverages. They may be p ...

or other

rigid body In physics, a rigid body (also known as a rigid object) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external fo ...

flying through space. The artifact is entirely a consequence of molecular dynamics

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

s and is wholly unphysical, since it violates the principle of equipartition of energy.

Origin and avoidance

The flying ice cube artifact arises from repeated rescalings of the velocities of the particles in the simulation system. Velocity rescaling is a means of imposing a

thermostat A thermostat is a regulating device component which senses the temperature of a physical system and performs actions so that the system's temperature is maintained near a desired setpoint. Thermostats are used in any device or system tha ...

on the system by multiplying the velocities of a system's particles by a factor after an integration timestep is completed, as is done by the Berendsen thermostat and the Bussi–Donadio–Parrinello thermostat. These schemes fail when the rescaling is done to a kinetic energy distribution of an ensemble that is not invariant under microcanonical molecular dynamics; thus, the Berendsen thermostat (which rescales to the isokinetic ensemble) exhibits the artifact, while the Bussi–Donadio–Parrinello thermostat (which rescales to the canonical ensemble) does not exhibit the artifact. Rescaling to an ensemble that is not invariant under microcanonical molecular dynamics results in a violation of the balance condition that is a requirement of Monte Carlo simulations (molecular dynamics simulations with velocity rescaling thermostats can be thought of as Monte Carlo simulations with molecular dynamics moves and velocity rescaling moves), which is the artifact's underlying reason. When the flying ice cube problem was first found, the Bussi–Donadio–Parrinello thermostat had not yet been developed, and it was desired to continue using the Berendsen thermostat due to the efficiency with which velocity rescaling thermostats relax systems to desired temperatures. Thus, suggestions were given to avoid the flying ice cube effect under the Berendsen thermostat, such as periodically removing the center-of-mass motions and using a longer temperature coupling time. However, more recently it has been recommended that the better practice is to discontinue use of the Berendsen thermostat entirely in favor of the Bussi–Donadio–Parrinello thermostat, as it has been shown that the latter thermostat does not exhibit the flying ice cube effect.

References

{{reflist Molecular dynamics Numerical artefacts