Transferring momentum

The probability of a transition —>/resulting from any external perturbation which impulsively transfers momentum q to the internal momenta of the electrons of the target system is... 

On the other hand, when a liquid is sheared between two planes, and there is bonding with the planes, the bonds transfer momentum from the faster plane to the slower one. This is the liquid-like mode. In this case, the viscosity coefficient decreases with increasing temperature. 

The pumping action is due to a high-speed rotating surface that transfers momentum to the gas molecules (see Fig. 1.16). 

Prom the theoretical point of view, calculation of the corrections of order a (Za) contains nothing fundamentally new in comparison with the corrections of order a Za). The scale for these corrections is provided by the factor 4a (Za) /(7r n ) m, as one may easily see from the respective discussion above in Sect. 2.3. Corrections depend only on the values of the form factors and their derivatives at zero transferred momentum and the only challenge is to calculate respective radiative corrections with sufficient accuracy. 

Calculation of the corrections of order a Za) is similar to calculation of the contributions of order a Za). Respective corrections depend only on the values of the three-loop form factors or their derivatives at vanishing transferred momentum. The three-loop contribution to the slope of the Dirac form factor (Fig. 3.5) was calculated anal3dically [32]... 

Collisions between molecules occur in the gas phase. These collisions can transfer momentum and energy between the collision partners, or lead to net transport of mass from one part of the system to another. 

The probability per unit that the system will transfer momentum, hk, and energy, ha, to the probe regardless of the initial state is consequently... 

In this formula v denotes the velocity of the incident particle, which has the charge z q is the transferred momentum m and e are the electron... 

While some reconciliation models only have material balance relationships, more meaningful reconciliation results are obtained with models that include material balances, heat balances, equilibrium constraints (both in the separation and reaction domains), rate relationships (heat transfer, mass transfer, momentum transfer, and kinetics), as well as equipment-specific relationships. In other words, one should include more than just material balance constraints when reconciling a model. Heat balance, kinetics, transport relationships—if needed for the... 

Brownian motion random motion of small particles, such as dust or smoke particles, suspended in a gas or liquid it is caused by collisions of the particle with gas or solvent molecules that transfer momentum to the particle and cause it to move... 

An electron that impinges and reflects on the crystal at a glancing angle 6, transfers momentum to the crystal, on impact and on rebound, to the amount of 2mvsin0, only if it matches the quantized momentum states of the crystal, i.e. 

Figure 3.15 Sputtering shown as an ion impinging on a surface, transferring momentum to the substrate, and substrate material being ejected.

Here fj(k) is the field amplitude of the light scattered by particle j with its center of mass at the position ry, Nis the number of particles in the scattering volume, K = K/ — K is the transferred momentum, and k = K. For elastic scattering K, = K/ = 2tuis/2q, where is the incident light wavelength in vacuum. Thus,... 

The mass elements of a flowing fluid transfer momentum. This is understood to be the product of the mass and velocity. A mass element dM, which flows at a velocity of transports a momentum w dM = w gdV. The total momentum / transported in a fluid of volume V(/,) is therefore... 

The setting up of the constitutive relation for a binary system is a relatively easy task because, as pointed out earlier, there is only one independent diffusion flux, only one independent composition gradient (driving force) and, therefore, only one independent constant of proportionality (diffusion coefficient). The situation gets quite a bit more complicated when we turn our attention to systems containing more than two components. The simplest multicomponent mixture is one containing three components, a ternary mixture. In a three component mixture the molecules of species 1 collide, not only with the molecules of species 2, but also with the molecules of species 3. The result is that species 1 transfers momentum to species 2 in 1-2 collisions and to species 3 in 1-3 collisions as well. We already know how much momentum is transferred in the 1-2 collisions and all we have to do to complete the force-momentum balance is to add on a term for the transfer of momentum in the 1-3 collisions. Thus,... 

It is anticipated that for dilute gases the mean free path is a signiflcant parameter that governs the mechanism of transfer, deflned as the mean distance traveled by a molecule between two successive collisions [87]. The basic physical interpretation of the transfer phenomenon is thus that a molecule traveling a free path of a certain distance is in effect transferring momentum, energy and mass over that distance. 

All vibrations are active in INS and, in principle, measurable. This stems from the mass of the neutron ca 1 unified atomic mass imit). When scattered the neutron transfers momentum to the atom and INS measurements are not limited to observation at the Brillouin zone centre, as are photon techniques. The measured INS intensities are, inter alia, proportional to the concentration of the elements in the sample. 

Fig. 2.2 A diagram of the momentum vectors in a scattering event shown in real space, above, and their relationship to the scattering triangle, shown below. The incident, i, and final, f, neutron momenta, k and the transferred momentum Q, are shown in the figure.

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