Density evolution

De Santis A., Sampoli M., Morales P, Signorelli G. Density evolution of Rayleigh and Raman depolarized scattering in fluid N2. Mol. Phys. 35, 1125-40 (1978). 

In this case our aim is to determine the relaxation time 0 that is the timescale of the probability density evolution from the initial W(x, 0) to the final value W(x, oo) for any x / x0. On the other hand we may consider the probability... 

Currently the time dependent DFT methods are becoming popular among the workers in the area of molecular modelling of TMCs. A comprehensive review of this area is recently given by renown workers in this field [116]. From this review one can clearly see [117] that the equations used for the density evolution in time are formally equivalent to those known in the time dependent Hartree-Fock (TDHF) theory [118-120] or in its equivalent - the random phase approximation (RPA) both well known for more than three quarters of a century (more recent references can be found in [36,121,122]). This allows to use the analysis performed for one of these equivalent theories to understand the features of others. 

In order to start the multiscale modeling, internal state variables were adopted to reflect void/crack nucleation, void growth, and void coalescence from the casting microstructural features (porosity and particles) under different temperatures, strain rates, and deformation paths [115, 116, 221, 283]. Furthermore, internal state variables were used to reflect the dislocation density evolution that affects the work hardening rate and, thus, stress state under different temperatures and strain rates [25, 283-285]. In order to determine the pertinent effects of the microstructural features to be admitted into the internal state variable theory, several different length scale analyses were performed. Once the pertinent microstructural features were determined and included in the macroscale internal state variable model, notch tests [216, 286] and control arm tests were performed to validate the model s precision. After the validation process, optimization studies were performed to reduce the weight of the control arm [287-289]. 

A model for the cure of silicone sealants has been developed. Crosslink density evolution has been studied. The model leads to a better understanding of behavior differences between fast curing acetic type silicone sealants and Alkoxy type silicone sealants with a slower cure. The model explains problems such as tacky surfaces. The data obtained in this study help in designing formulations well-tailored to specific application requirements. 

Fig. 5,14. Spatio-temporal breathing patterns of the DBRT electron density evolution, phase portrait, and voltage evolution for (a) e = 7.0 periodic breathing, (b) e = 9.1 chaotic breathing (r = —35, Uo = —84.2895, K = 0). Time t and space x are measured in units of the tunneling time Ta and the diffusion length la, respectively. Typical values at 4K are Ta = 3.3 ps and la = 100 nm [47].

The parameter 5- = k /k shows the detachment ability that compensates for electron losses dne to attachment. If 5- 1, the attachment inflnence is negligible and kinetic equation (4-21) becomes eqnivalent to one for non-electronegative gases. The kinetic equation inclndes the effective rate coefficients of ionization, kf = kj + g, and recombination, k f = kf + gk. Eqnation (4-21) describes electron density evolution to the steady-state magnitnde of the recombination-controlled regime ... 

Table 7.1. Variation of the relative density. Evolution of the morphological parameters as a function of the annealing temperature...

Fig. 4.15 Density evolutions of green body pressed uniaxialy. Reproduced with permission from [108]. Copyright 2013, Elsevier...

This equation represents a mathematical expression of existing hierarchy of the time scale of partial processes of single-component systems with little density evolution. 

Releases of liquefied toxic or flammable gases often take place in aerosol form, consisting of vapor and liquid droplets of the released species, together with entrained humid air. This has been demonstrated in several laboratory and field-scale experiments (e.g., Koopman et al., 1986, Moodie and Ewan, 1990 Nolan et al., 1990 Schmidli et al., 1990 Nielsen et al., 1997). Aerosol phenomena may have a significant influence on the temperature and density evolution of the source term and on the subsequent heavy gas dispersion. In particular, the deposition of substance liquid droplets may, under certain conditions, cause a substantial decrease of concentration. 

The thermodynamical nonequilibrium effects in a two-phase cloud have two essential consequences (1) the thermodynamical behavior of the mixture is different, in particular the temperature and density evolution, and (2) the deposition of contaminant liquid may cause... 

Figure 9.49 Grain size-density evolution during final stage sintering for different values of the ratio of the coarsening rate to the densification rate F, assuming coarsening by surface diffusion and densification by grain boundary diffusion. (From ref 73.)...

Fig. 10. Plots presenting the energy density evolution for polyacetal over a range of stress...

Figure 17.4 Schematic representation of a phase diagram illustrating the density evolution from the liquid to the gas without crossing the T-C line which corresponds to the liquid-gas equilibrium line, C being the critical point and T being the triple point. P,. and T,. are the critical pressure and temperature, respectively. Reproduced from Ref [291 with permission from The Royal Society of Chemistry.

Figure 5 Surface hydroxyl group density evolution Ti-OH is the number of titanium atoms that are bonded with the OH groups from water dissociation. Ti tot) is the total number of surface Ti atoms. The ratio of Ti-OH/Ti(tot) is monitored as a function of simulation time. More water molecules will dissociate on a more reactive TiOj surface, which leads to a larger ratio of Ti-OH/ri(tot). Figure taken from Huang et al (2014).

Figure 7.12. Power density evolution with operation time for (a) conventional anodes, (b) SDC coated Ni-SDC anode (Ding et ah, 2008a).

Figure 4 Density evolution with x ab initio calculated ( ), compared with X-ray measurements (A) [2]...

How can the low stress creep strain rate regime be explained Additional tests and microscopic observations are required, alongside a predictive model. The dislocation density evolution will undoubtedly have to be taken into account in such simulations ... 

Bq = external magnetic flux density Bq = detection field = magnetic flux density, evolution interval Bp = magnetic flux density, preparation interval Gj(r) = dipolar autocorrelation function = in-... 

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