Mean kinetic temperature fluctuations

MD method, the system studied has constant energy. Its temperature can be defined via the mean kinetic energy. Other thermodynamic properties can be calculated from the numerical derivatives of the energy or by using their relations to certain fluctuations of the system. The specific heat, for instance, can be obtained from the derivative of the energy with respect to the temperature or from the temperature fluctuations. It will be clear that for these derived quantities the uncertainties are larger than for the trajectory itself. 

An equation for the granular temperature can then be achieved by subtracting the mechanical energy equation from the above equation for the sum of the fluctuating and mean kinetic energy forms. 

Let us consider a shear flow that is steady and homogeneous in the x X2 plane with the only nonzero mean velocity m 1( 3). The kinetic energy of the turbulence is given by jUjU j = j(u u -I- M2 2 + 3 3)- A measure of the effect of the turbulence on temperature fluctuations is the mean-square fluctuation 9 The dynamic equations governing and 9 in this situation reduce to... 

Case 1. u 0 > 0, Rf <0. Positive values of u occur with positive values of 0. The actual mean profile is 0(.X3) = T(xj) — as shown in Figure 16.3. Consider a parcel of air that experiences an upward displacement with > 0. Its temperature will change adiabatically if the fluctuation is rapid. At the new level, the temperature fluctuation O is the difference between the parcel s temperature 0 xi) and that of the surroundings 0(X3 + / ). The parcel s actual temperature T decreases in accordance with the adiabatic relation, but its temperature 0, 0 = T — Tg, relative to an adiabatic profile, remains constant. Thus, in this case. O > 0. The production of turbulent kinetic energy is increased in (16.60). Since the actual mean temperature profile must be as shown in Figure 16.3 (Case 1) we know that this situation occurs under /[Pg.860]

Floudas and coworkers [88] investigated the static and kinetic aspects of the order-disorder transition in SI2 and SIB miktoarm stars using SAXS and rheology. At temperatures above the order-disorder transition (ODT) the mean field theory describes the experimental results quite well. Near the ODT, SAXS profiles gave evidence for the existence of fluctuations. Both samples separated into cylindrical microdomains below the ODT. The ODT was determined on shear oriented samples and found, by SAXS, to be 379 K in both cases. This was confirmed by rheology. The discontinuities in SAXS peak intensity and in the storage modulus near the ODT were more pronounced for the miktoarm stars than for the diblocks. The %N values, where % is the interaction parameter and N the... 

For example, the presence of a mean temperature gradient (a gradient of the mean molecular kinetic energy) normal to the surface means that each interchange of gas molecules would also transfer a net quantity of heat, even though the average convective flux of heat associated with u is zero because u n = 0 on the surface S we have chosen. It is this additional transport that is due to fluctuations in the molecular velocity about the continuum... 

---