Thermal lattice

Where n is the charge-carrier concentration and e the elementary charge. The electrons do not move undisturbed, but are scattered by collision with other carriers and thermal lattice vibrations, so-called phonons, and structural defects. Upon lowering the temperature, collision probability and thermal lattice vibrations are reduced, and the mobility of the electron increases, while n is constant. This leads to a large increase of conductivity with decreasing temperature. 

At this last stage of the degradation process, the whole energy absorbed by the nonmetals is recovered in the following five forms (1) structural imperfections, (2) thermal lattice energy, (3) photon energy, (4) excited electronic states, and (5) electrons of positive energy. Let us also point out that electrons and photons may eventually escape from the solid. 

Several theories were developed to explain the remarkably short halogen Ti values. While it was clear that a time-dependent FFG was present at the relevant nuclear site, early consensus regarding the origin was not found. As mentioned earlier, Y-M proposed that the time-dependent FFG was generated by the distorted ions (due to M-X covalent bonding) coupling to thermal lattice... 

Perdok WG, Christoffersen J, Arends J (1987) The thermal lattice expansion of calcium hydroxylapatite. J CiysM Growth 80 149-154... 

Meghadadi Isfahan AH, Soleimani A (2012) Thermal lattice Boltzmann simulation of rarefied gas flows nanochannels for wide range of Knudsen number. Adv Mater Res 403-408 5313-5317... 

Lopez P, Bayazitoglu (2013) Y An extended thermal lattice Boltzmaim model for transition flow, Int J of Heat Mass Transfer, 65 374-380... 

This paper sets forth a general method to demonstrate the quantitative consistency (or inconsistency) of results of thermal reactor lattice experiments. The method is ot particular importance in selecting standard benchmark experiments for comparison testing of lattice analysis codes and neutron cross sections. Benchmark thermal lattice experiments are currently selected by consensus, which usually means the e]Q>eriment is geometrically simple, well-documented, reasonably complete, and qualitatively consistent. The quantitative tests reported here were, applied to 19 frequently used thermal benchmark lattice experiments, and only two of these lattices proved to be quantitatively consistent and generally useful as benchmarks., ... 

The three quantitative consistency tests were applied to 19 thermal lattice e riments that are used as benchmarks. The lattice cglieulations required were performed by the RAHABR lattice anatysis module of the JOSHUA System using ENDF/B-IV cross sections. ... 

Subcritical thermal lattice experiments show systematic inconsistencies the most notable being the consistently high experimental material buckling, ... 

Because so few thermai benchmark e q>eriments can be shown to be quantitatively consistent, new thermal lattice experiments are required to supply benchmarks to test lattice analysis codes and neutron cross sections. 

AalAT dynamic (thermal) lattice expansion activation energy... 

In table 5 the lattice parameters, a, of the cubic p-RH2+jr phases are presented as a function of x at several temperatures. The static and thermal lattice expansions have been added when available. We note the well-known general contraction (negative Aa/Ax-values) of the dihydride lattice with increasing x, which is an expression of the strong ionic character of its interaction with the excess H atoms on O sites an example is given in fig. 9 for the case of YH2+ (, where the break in the a(x)-curve at x=0.10 H/Y indicates the limit of the pure p-phase. 

Mostly used is the thermal Lattice-Boltzmann method (TLBM) which is a hybrid approach combining two solution procedures. The flow field is again calculated with the LBM, whereas the temperature field is simulated using a finite-difference approach [20]. A good review about the issue of thermal fields combined with LBM is given by LaUemand and Luo [21]. In the present contribution, the method proposed by Filippova and Hanel [20] was implemented for simulating coupled fluid and temperature fields. 

Yuan, P., Schaefer, L. A. (2005). Thermal lattice Boltzmann two-phase flow model and its application to heat transfer problems—Part 1. Theoretical foundation. Journal of Eluids Engineering, 128, 142-150. 

Debye s theory of the specific heats of solids depends on the existence of a high number of standing, high frequency, elastic waves that are associated with thermal lattice vibrations. Central to his approach is the proposal that in a solid the phonon spectral density (p) increases continuously, and with a direct dependence on the square of the frequency (cutoff frequency (Q, at about 10 Hz) above which the phonon density vanishes for a solid continuum containing N atoms in a sample of volume V, the proportionality constant is 6 V/v, where V is the velocity of propagation. At a typical nuclear... 

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