Recovered energy densities

P is an empirical parameter that was determined to 0.0042 by a least-squares fit to the exactly known exchange energies of the rare gas atoms He through Rn. In addition to the sum rules, this functional was designed to recover the exchange energy density asymptotically far from a finite system. 

Knowing the contribution of fluctuations to the entropy and specific heat we may recover their contribution to the free energy and energy densities... 

Let us assume a many-electron atom enclosed within an infinitely hard spherical cavity of radius R and develop the method and calculations so that we may recover the free-atom case when . This procedure also allows to look at the evolution of its ground state energy as the cage volume shrinks as has been done elsewhere [25,53]. The TFDW energy-density functional for an atom enclosed within a spherical cavity of radius R is written as... 

When Zotefoam HDPE materials of density 98 kg m" were subjected to a single major compressive impact (419), after recovery at 50 °C for 1 hour, the performance, defined as the energy density absorbed before the compressive stress reached 2.5 MPa was back to 75% of the initial value. Further severe impacts caused a further deterioration of the performance of the recovered foam. Peak compressive strains of 80 to 90% caused some permanent buckling of the cell walls of HDPE foams. The recovery is much slower than the 0.1 second impact time, so is not a conventional linear viscoelastic response. It must be driven by the compressed air in internal cells in the gas, with some contribution from viscoelasticity of the polymer. Recovery of dimensions had slowed to a very low rate after 10 seconds at 20 °C or after 10 seconds at 50 °C. 

Until now, the classical DLVO results have been recovered. Let us suppose that another interaction, whose free energy density is —aP dPP z)ldz ( is also present. An integration by parts leads to... 

In contrast to the gradient expansion of the exchange hole of Perdew [135], the BR functional does not reduce to LSDA in the uniform density limit. To recover this limit approximately, Becke and Roussel multiplied the term t — t ) in Eq. (141) by an adjustment factor of 0.8. At the same time, the BR exchange energy density has the correct — p(r)/2r asymptotic behavior in the r — oo limit. 

Here cp is the potential generated by the charge distribution q itself and not an external potential as before. This explains the factor of 1/2 as compared to Eq. (2.148). Exploiting the field equation (2.146) and integrating by parts the energy density Ug of a static electric field (cf. Eq. (2.108)) is immediately recovered,... 

The interest in w-butanol as a biofuel has increased in recent years owing to its superior fuel qualities compared to ethanol. These include a higher octane number, lower heat of vaporization, higher energy density (energy/volume), and lower vapor pressure. However, in the traditional ABE (acetone-butanol-ethanol) fermentation process, the concentration of n-butanol coming from the fermenter is lower than that achieved in ethanol fermentation. In addition, acetone and ethanol are also produced. Recent studies to improve yield and increase w-butanol concentration have explored fed-batch systems with stripping, adsorption, liquid-liquid extraction, distillation, and/or pervaporation to recover products. 

An analysis of the ability of plant structures to resist the effects of explosions can usually be limited to an examination of their capacity to resist the free field or reflected and focused overpressure. In estimating the peak overpressure on a structure, the pressure-distance relationships developed for TNT can be utilized for the detonation of solid substances. For solid substances whose energy density differs from that of TNT, factors to be used in calculating equivalent weights of TNT should be recovered from the literature. For substances known to have explosive potential but whose explosive properties have not been investigated and tabulated, it is reasonable, as a first estimate, to assume that their explosive properties are equivalent to those of TNT. 

Increased energy density - more energy is recovered from the plastic by these methods than by simple combustion. 

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