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In the physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is calculated using the following equation: v RMS = 3 R T M {\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}
The qualification of "rms" (root mean square) arises because it is the nuclear cross-section, proportional to the square of the radius, which is determining for electron scattering. This definition of charge radius is often applied to composite hadrons such as a proton, neutron, pion, or kaon, that are made up of more than one quark.
If is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then [1] [2] =. If v th {\displaystyle v_{\text{th}}} is defined as the mean of the magnitude of the velocity in any one dimension (i.e. any single direction), then v th = 2 k B T π m . {\displaystyle v_{\text{th}}={\sqrt {\frac {2k_{\text{B ...
According to the equipartition of energy this means that there is a thermal energy of 3 / 2 kT per atom. This corresponds very well with experimental data. The thermal energy can be used to calculate the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass.
When a dynamical system fluctuates about some well-defined average position, the RMSD from the average over time can be referred to as the RMSF or root mean square fluctuation. The size of this fluctuation can be measured, for example using Mössbauer spectroscopy or nuclear magnetic resonance , and can provide important physical information.
In bioinformatics, the root mean square deviation of atomic positions is the measure of the average distance between the atoms of superimposed proteins. In structure based drug design , the RMSD is a measure of the difference between a crystal conformation of the ligand conformation and a docking prediction.
In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a result of one or more successive collisions with other particles.
Physically, the turbulence kinetic energy is characterized by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model.