Inelastic dissipation

In Fig. 3, the energy lost due to inelastic collisions and viscous gas are compared. For a mixture flow, compared with inelastic dissipation, the viscous dissipation is relatively small, especially in the region near the boundary wall. Hence it may be acceptable to neglect the effect of the drag force in establishing the boundary conditions. When the granular temperature decreases, the viscous dissipation becomes more important until it is, indeed, greater than the inelastic collision dissipation. 

Consideration of small homogeneous closed cycles of deformation which involve inelastic loading leads, as before, to a dissipation inequality... 

The mode of energy dissipation by electrons in materials is either through inelastic or elastic collisions with the nuclei of the medium [28,51]. The angle of incidence of... 

Thus far the discussion has centered on elastic tunneling, but consideration of inelastic processes may offer additional analytical opportunities. An energy scale of the relevant phenomena is presented in Table 2. Inelastic tunneling was first observed in metal-oxide-metal junctions. It was immediately developed as a technique for photon-free vibrational spectroscopy (lETS) where the tunneling electrons dissipate energy by coupling to vibra-... 

Figure 1 illustrates different modes of electron transfer between electrolyte states and carriers in the bands at the semiconductor surface. If the overlap between the electrolyte levels and the semiconductor bands is insufficient to allow direct, isoenergetic electron transfer, then an inelastic, energy-dissipating process mustnbe used to explain experimentally observed electron transfer. Duke has argued that a complete theory for electron transfer includes terms that allow direct, inelastic processes. The probability of such processes, however, has not been treated quantitatively. 

When the gas-solid flow in a multiphase system is dominated by the interparticle collisions, the stresses and other dynamic properties of the solid phase can be postulated to be analogous to those of gas molecules. Thus, the kinetic theory of gases is adopted in the modeling of dense gas-solid flows. In this model, it is assumed that collision among particles is the only mechanism for the transport of mass, momentum, and energy of the particles. The energy dissipation due to inelastic collisions is included in the model despite the elastic collision condition dictated by the theory. 

The term fa) is the volume-averaged dissipation function for the energy dissipated by the viscous force, which is irreversible dissipation of mechanical work into thermal energy or heat. For the solid-particle phase, the kinetic energy loss by attrition or inelastic collision may be included in this term. 

After an energetic ion strikes a surface, it will decelerate as its kinetic energy is dissipated via elastic (nuclear collision) and inelastic processes. A small fraction of the ions may reflect from the surface the majority are implanted beneath the surface. The average distance an ion travels before it is stopped within a solid increases with collision energy. Figure 12 shows the mean depth of penetration achieved by He+ incident on a silicon surface. Molecular dynamics simulations reveal that within the first picosecond after a keV ion impacts a solid, a local hot spot develops at the... 

If there are no dissipative effects, that is, friction, viscosity, inelasticity, electrical resistance, and so on, during a quasi-static process, the process is termed reversible. Only an infinitesimal change is required to reverse the process, a concept that leads to the name reversible. Most industrial processes exhibit heat transfer over finite temperature differenees, mixing of dissimilar substances, sudden changes in phase, mass transport under finite concentration differences, free expansion, pipe friction, and other mechanical, chemical, and thermal nonidealities, and consequently are deemed irreversible. An irreversible process always involves a degradation of the potential of the process to do work, that is, will not produce the maximum amount of work that would be possible via a reversible process (if such a process could occur). 

Dissipation of energy due to inelastic collisions can be expressed in the form ... 

Phase contrast in AM AFM can be observed primarily due to inelastic contributions and some elastic ones (topography, contact-noncontact transitions, and variation of elasticity if dissipative channels are present). Attractive (low amplitude, L branch) and repulsive (high amplitude, H branch) regimes are shown below (Fig. 1.15 and 1.16). 

The interaction between electrons and the bridge molecular vibrations plays an important role in E-M-E junctions, and its effect on the change of current caused by energy dissipation from eN interactions is relevant experimentally [8, 65, 66], Inelastic transport affects device characteristics and Joule heating, which ultimately... 

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