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There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Deposition due to Brownian motion obeys both Fick's first and second laws. The resulting deposition flux is defined as J = n D π t {\textstyle J=n{\sqrt {\frac {D}{\pi t}}}} , where J is deposition flux, n is the initial number density , D is the diffusion constant and t is time.
The Feret diameter D F, which corresponds to the distance between two parallel tangents on opposite sides of the particle's projected image. The Martin diameter D M, defined as the chord length of the outline of the particle, which bisects the area of particle projection. In other terms, it is the length of the line dividing the projection in ...
(If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.) Momentum space is the set of all momentum vectors p a physical system can have; the momentum vector of a particle corresponds to its motion, with dimension of mass ⋅ length ⋅ time −1 .
A particle speed probability distribution indicates which speeds are more likely: a randomly chosen particle will have a speed selected randomly from the distribution, and is more likely to be within one range of speeds than another. The kinetic theory of gases applies to the classical ideal gas, which is an idealization of real gases.
The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
It is the most common measure of the spatial extent of random motion, and can be thought of as measuring the portion of the system "explored" by the random walker. In the realm of biophysics and environmental engineering , the Mean Squared Displacement is measured over time to determine if a particle is spreading slowly due to diffusion , or if ...
The four-force is defined as the rate of change in the four-momentum of a particle with respect to the particle's proper time.Hence,: =. For a particle of constant invariant mass >, the four-momentum is given by the relation =, where = (,) is the four-velocity.