Atom velocities

One method, simple to implement and reliable, is to periodically reselect atomic velocities at random from the Maxwell-Boltzmaim distribution [79]. This is rather like an occasional random coupling with a thennal bath. The resampling may be done to individual atoms, or to the entire system some giudance on the reselection frequency may be found in [79]. 

This expression shows diat if die detuning Acuj is negative (i.e. red detuned from resonance), dieii die cooling force will oppose die motion and be proportional to die atomic velocity. The one-diniensional motion of die atom, subject to an opposing force proportional to its velocity, is described by a damped haniionic oscillator. The Doppler damping or friction coefficient is die proportionality factor. 

Equation (Cl.4.35) yields two remarkable predictions first, tliat tire sub-Doppler friction coefficient can be a big number compared to since at far detuning Aj /T is a big number and second, tliat a p is independent of tire applied field intensity. This last result contrasts sharjDly witli tire Doppler friction coefficient which is proportional to field intensity up to saturation (see equation (C1.4.24). However, even tliough a p looks impressive, tire range of atomic velocities over which is can operate are restricted by tire condition tliat T lcv. The ratio of tire capture velocities for Doppler versus sub-Doppler cooling is tlierefore only uipi/uj 2 Figure Cl. 4.6 illustrates... 

A molecular dynamics simulation nsnally starts with a molecular structure refined by geometry optimization, but wnthont atomic velocities. To completely describe the dynamics of a classical system con lain in g X atom s, yon m nsl define 6N variables. These correspond to ilX geometric coordinates (x, y, and /) and iSX variables for the velocities of each atom in the x, y, and /. directions. 

The initial velocities are often adjusted so that the total momentum of the system is zer Such a system then samples from the constant NVEP ensemble. To set the total line momentum of the system to zero, the sum of the components of the atomic momen along the x, y and z axes is calculated. This gives the total momentum of the system each direction, which, when divided by the total mass, is subtracted from the atom velocities to give an overall momentum of zero. 

The Maxwell-Boltzmann velocity distribution function resembles the Gaussian distribution function because molecular and atomic velocities are randomly distributed about their mean. For a hypothetical particle constrained to move on the A -axis, or for the A -component of velocities of a real collection of particles moving freely in 3-space, the peak in the velocity distribution is at the mean, Vj. = 0. This leads to an apparent contradiction. As we know from the kinetic theor y of gases, at T > 0 all molecules are in motion. How can all particles be moving when the most probable velocity is = 0 ... 

Choose an initial set of atom velocities. These are usually chosen to obey a Boltzmann distribution for some temperature, then normalized so that the net momentum for the entire system is zero (it is not a flowing system). 

Equilibration corrects the velocities of atoms. Velocities resulting from heating do not simulate the type of motion found in a real molecular system. Instead, these velocities depend on a random distribution of values corresponding to a given temperature and on the forces in a partially minimized structure. 

Initializing the initial kinetic energy and temperature of the system it is necessary to start the motion at some level, eg, assume a Boltzmann (random) distribution of atomic velocities, at 300 K. 

Unlike the initial coordinates, which can be obtained experimentally, the only relevant information available about atomic velocities is the system s temperature T, which determines the velocity distribution. In the absence of a better guideline, initial velocities (v , Vy, Vy) are usually randomly assigned from the standard Maxwellian velocity distribution at a temperature T,... 

Atomic velocity distribution, 130,131 Atomic volume, 94, 98 alkali metals, 94 halogens, 97 inert gases, 91 third-row elements, 101 Atomic weight, 33 table, inside back cover Atoms, 21 conservation of, 40 electrical nature of, 236 measuring dimensions of, 245 Avogadro, Amadeo hypothesis, 25, 52 hypothesis and kinetic theory, 58 law, 25 number, 33 Azo dyes, 344... 

Collisions between the Na atoms and molecules will redistribute the atomic velocities and fill the velocity hole created by radiation pressure. These collisions, however, are relatively infrequent. Therefore, ample time exists for a long laser pulse to push the atoms out of resonance before collisions can rethermalize the vapor. This loss in excitation efficiency can be overcome with... 

In the case of a space separation of the laser beams (i.e. if the atomic velocity is perpendicular to the direction of the laser beams), the interferometer is in a Mach-Zehnder configuration. Then, the interferometer is also sensitive to rotations, as in the Sagnac geometry (Sagnac, 1913) for light interferometers. For a Sagnac loop enclosing area A, a rotation Q, produces a phase shift ... 

Fig. 14. 3D representation of the H-atom velocity flux contour, d a/dvd(cos6). The contours are constructed directly from a total of 33 slices of the Doppler-selected TOF measurements. 

Fig. 21. The product D-atom velocity-flux contour map, d

Initial velocities needed to kickstart the simulation is taken as a random distribution. Temperature is calculated from atomic velocities using the ideal-gas relationship... 

Figure 5.4. Calculated gas velocity field near a close-coupled atomizer velocity vectors (right) and stream lines (left) (Atomization gas Ar, Ma = 1 at nozzle exit.). (Reprinted with permission from Ref. 325.)...

Effects of isotopic mass on molecular and atomic velocities and diffiisivity... 

The addition of constraints to the equations of motion have also been used to produce thermostats at surfaces which control the flux of heat in and out of the substrate. For example, Riley et al. have proposed a velocity reset procedure which regulates atomic motion by coupling the current velocity of each atom with a velocity chosen from a Maxwellian distribution . In a similar scheme, Agrawal et al. have added a friction term to atomic velocities which depends in part on the difference between the current temperature of the surface region and that desired for the substrate . This approach was... 

The temperature specified for the dynamics calculation defines the atomic velocity stribution. In the current studies, the temperature was allowed to ramp downward from 300 K to 20 K over a 10 ps period (5000 dynamics steps). This allowed the coal structures initially to overcome potential energy barriers between different conformations, and later to approach a minimum energy state. 

Bed moisture content Solution type and feed rate Bed temperature Fluidization velocity Aspect ratio Nozzle position and atomization Velocity Air distributor design Jet grinding... 

Motion of atoms in molecules can be quite well described in terms of classical mechanics, due to the relatively high mass of atomic nuclei. Given a set of starting coordinates and atomic velocities, it is possible to solve Newton s equations of motion to describe the time evolution of the atoms across the potential energy surface. In principle, such molecular dynamics (MD) simulations can give very detailed insight into chemical reactivity and some examples will be given below. 

Therefore, if the incident atomic velocity vz is normal to the surface, the best -position to place the surface on which the atoms are to be deposited is at a distance ... 

With an appropriate choice of B the compensation is effective for all atomic velocities. As the velocity of the thermal beam of hydrogen atoms at 300 K is not well known, the magnetic field will be used to measure precisely the velocity distribution, and so the second order Doppler shift. 

Nevertheless, his hypothesis, even in its present form, allows for some quantitative comparisons between experimental results and theoretical predictions. First of all, experiments were implemented to determine the strength and direction of the effective field Eef / with respect to the direction of the atom velocity. For this purpose the system with longitudinal (that is. parallel or antiparallel to the atom velocity vector) electric field was installed. If the electrodes, creating the field are shortened and grounded, then, with change of distance L, distinct 2P-interference pattern is observed, produced by the field Pe// With presence of an external electric field coinciding with the velocity direction, the amplitude of beets is increased, and the character of the interference curve testifies coincidence of the phases of beets caused by the external field and the field Pe// ... 

In case of opposite direction of the field the amplitude of beets is decreased and the mismatch of phases occurs. The processing of data obtained shows, that the direction of the field Eef / coincides with the direction of the atom velocity, as it follows from the Kadomtsev s theory and its intensity (for the used geometry of slits) is equal to 4.6 V/cm. Such a value is also in satisfactory agreement with Kadomtsev s prediction. 

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