Mean energy density

As can be seen from the power and momentum balance, Eqs. (46) and (47), a temporal evolution of the mean energy density u, t) and/or of the particle current density j t) is initiated if the instantaneous compensation of the respective gain from the field and the corresponding total loss in collisions is disturbed for any reason. Generally, by collisional dissipation, the electron component tries to reduce these disturbances and to again establish the compensated state in both... 

The representations of the total power loss in collisions P (/) and of the mean energy density Eqs. (48) and (16) clearly indicate that the rapidity of the dissipation of the kinetic energy per volume unit t) dU contained in the... 

The behavior of the individual terms in the momentum balance (right) is similar to that in the power balance. Now the normalized momentum loss in elastic collisions r (z)/I oo) oscillates around the oscillating momentum gain /(z)// (oo), and the somewhat lesser deviations between these quantities are compensated for to a large extent by the normalized source term d/dz) [(2/3m )u z)]/P oQ) of the momentum balance (dotted-dashed curve) containing the spatial derivative of the mean energy density , (z). 

On-load voltage per cell IV) Operating temperature CC) Mean energy density Attractive features... 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

The phenomenon of acoustic cavitation results in an enormous concentration of energy. If one considers the energy density in an acoustic field that produces cavitation and that in the coUapsed cavitation bubble, there is an amplification factor of over eleven orders of magnitude. The enormous local temperatures and pressures so created result in phenomena such as sonochemistry and sonoluminescence and provide a unique means for fundamental studies of chemistry and physics under extreme conditions. A diverse set of apphcations of ultrasound to enhancing chemical reactivity has been explored, with important apphcations in mixed-phase synthesis, materials chemistry, and biomedical uses. 

One consequence of the Z dependence is that the higher energy density per volume may be used to advantage by emulsification of the dispersed phase into a reduced amount of the continuous phase, followed by dilution. A reduced amount of the continuous phase means an increased value of Z, because the energy input is dissipated into a smaller volume. An exception to this rule is found if the continuous phase contains soHd particles. In such a case forces acting through the Hquid medium are not efficient for obvious reasons, and mechanical means such as a roUer mill should be used. 

The mixture cohesive energy density, coh-m> was not to be obtained from some mixture equation of state but rather from the pure-component cohesive energy densities via appropriate mixing rules. Scatchard and Hildebrand chose a quadratic expression in volume fractions (rather than the usual mole fractions) for coh-m arid used the traditional geometric mean mixing rule for the cross constant ... 

Intensity at a Point of Superposition (1.17) The measurable physical parameter of an optical wave is its energy density or intensity. If two fields are superimposed, the measured intensity is given by the sum of the individual intensities plus aterm which describes the long term correlation of the field amplifudes. Long ferm means time scales which are large compared to the inverse of the mean frequency uj/2Tt (about 10 s) the time scale is set by the time resolution of the detector. This is why the held product term is expressed in the form of an ergodic mean ). An interferometer produces superimposed helds, the correlation of which carries the desired information about the astronomical source. We will discuss exactly how this happens in the following sections. 

According to current turbulence measurements in stirred tanks, there is a very considerable difference between the maximum energy density and the mean energy dissipation. Various authors (see e.g. [24] -[26] conclude that the... 

The mean-field expression for the free-energy density of the polymer solution is therefore [ 13,14]... 

Now the probability density that the collision will result in an energy loss q is given by <7 /X, and the resultant mean energy loss in one collision is given by... 

Sucrose has the greater energy density, meaning that for 1 g of compound, more energy is released when sucrose is oxidized than when tristearin is oxidized. 

Energy density is 0.46eVcm-3. Mean energy is 1.6GeV. 

Few years later, Fuentealba and Cedillo [23] has shown that the variation of the Kohn-Sham FF with respect to the external perturbation depends on the knowledge on the highest occupied molecular orbital (HOMO) density and a mean energy difference of all of the occupied and unoccupied orbital. The quantity, mean energy difference, has been approximately interpreted as hardness. Under this approximation, it has been stated that the greater the hardness, the smaller the variation of the FF, under the external perturbation. This statement then signifies that the system will become less reactive as the hardness of the system increases due to the external perturbation. 

In variable-density flow, additional estimated terms are needed for the mean energy equation (Jenny et al. 2001). 

For variable-density flow, Muradoglu etal. (2001) identify a third independent consistency condition involving the mean energy equation. 

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