Maxwell, distribution

Flowever, W (u) should also be given by the equilibrium Maxwell distribution... 

The velocity distribution of the electrons in a plasma is generally a complicated function whose exact shape is detennined by many factors. It is often assumed for reasons of convenience in calculations tliat such velocity distributions are Maxwellian and tliat tlie electrons are in tliennodynamical equilibrium. The Maxwell distribution is given by... 

Figure C2.13.2. Electron energy distributions/(U) for a mean electron energy of 4.2 eV, Maxwell distribution (M), Dmyvesteyn distribution (D) and a calculated distribution (Ar) for an Ar plasma [12].

We might then assume a Maxwell distribution of momenta so that the overall phase space distribution is that of a Maxwell-Tsallis statistics. 

Velocities are randomly chosen from a Maxwell distribution at a given temperature. 

It is appropriate to consider first the question of what kind of accuracy is expected from a simulation. In molecular dynamics (MD) very small perturbations to initial conditions grow exponentially in time until they completely overwhelm the trajectory itself. Hence, it is inappropriate to expect that accurate trajectories be computed for more than a short time interval. Rather it is expected only that the trajectories have the correct statistical properties, which is sensible if, for example, the initial velocities are randomly generated from a Maxwell distribution. 

This factor is reminiscent of the radial distribution function for electron probability in an atom and the Maxwell distribution of molecular velocities in a gas, both of which pass through a maximum for similar reasons. 

Maxwell distribution A relation describing the way in which molecular speeds or energies are shared among gas molecules, 121... 

We studied the effect of the mechanical stretching field on the conformations of the macromolecules in the melt. It is known that for a freely jointed chain the Maxwell distribution of end-to-end distances holds50). 

Maxwell Distribution.—From the behavior of the 5-function, we may expect that a gas starting from some initial distribution func-... 

Maxwell distribution, 18 Maxwell equations in Coulomb gauge, 645... 

S FIGURE 4.27 The Maxwell distribution t again, but now the curves correspond to the speeds of a single substance inf molar fyg mass 50 g-mol 1) at different... 

A plot of the Maxwell distribution for the same gas at several different temperatures shows that the average speed increases as the temperature is raised (Fig 4.27). We knew that already (Section 4.9) but the curves also show that the spread of speeds widens as the temperature increases. At low temperatures, most molecules of a gas have speeds close to the average speed. At high temperatures, a high proportion have speeds widely different from their average speed. Because the kinetic energy of a molecule in a gas is proportional to the square of its speed, the distribution of molecular kinetic energies follows the same trends. 

J I I Describe the effect of molar mass and temperature on the Maxwell distribution of molecular speeds (Section 4.11). 

Consider the Maxwell distribution of speeds found in Fig. 4.27. (a) From the graph, find the location that represents the most probable speed of the molecules at each temperature. 

The root mean square speed rrrm of gas molecules was derived in Section 4.10. Using the Maxwell distribution of speeds, we can also calculate the mean speed and most probable (mp) speed of a collection of molecules. The equations used to calculate these two quantities are i/mean = (8RT/-nM),a and... 

Maxwell distribution of molecular speeds The formula for calculating the percentage of molecules that move at any given speed in a gas at a specified temperature. 

Maxwell, J. C., 164 Maxwell distribution of speeds, 164, 560 mean bond enthalpy, 254 mean relative speed, 559 mechanical equilibrium, 290 mechanics, 1... 

In order to reduce the complexity of the problem, several approximation schemes have been developed. In the BGK model, the collision integral is replaced by a simple local term ensuring that the well-known Maxwell distribution is reached at thermal equilibrium [16]. The linearization method assumes that the phase space distribution is given by a small perturbation h on top of a (local) Maxwell distribu-tion/o (see, e.g., [17, 18]) ... 

H.M. Talbot, R.N. Head, R.P. Harris and J.R. Maxwell, Distribution and stability of steryl chlorin esters in copepod faecal pellets from diatom grazing. Org. Geochem. 30 (1999) 1163-1174. 

MSN.2. I. Prigogine and E. Xhrouet, On the perturbation of Maxwell distribution function by chemical reactons in gases, Physica 15, 913-932 (1949). 

The velocity distribution in a neutron gas at equilibrium is subject to the laws of the kinetic theory of gases. The neutron velocities at equilibrium obey the Maxwell distribution... 

Doppler broadening arises from the random thermal motion of the atoms relative to the observer. The velocity V, of an atom in the line of sight will vary according to the Maxwell distribution, the atoms moving in all directions relative to the observer. The frequency will be displaced by... 

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