Environmental Engineering Reference
In-Depth Information
account for a large percentage of the total modes [33]. As a result,
although the heat bath can maintain a constant temperature, the
major contribution comes from LEM, which cannot be utilized in
heat transport. Therefore, there exists a large TJ when there is only
one layer of NH heat bath. With the number of heat bath layer
increasing, TJ will be reduced as shown in Fig. 1.6a. This is because
oftheexponentialdecayfeatureofLEMoverdistance.Withmultiple
layers of heat bath which are away from the localized region, other
modes can be excited and dominate in heat transport. Therefore,
the localized effect on the thermal transport is suppressed. The
reductioninTJleadstolargeincreaseinheatfluxfromNL
=
1toNL
=
2(Fig.1.6c).Furtherincreaseofheatbathlayerscannoteventually
eliminate TJ. The small retained TJ is due to the thermal interface
resistance betweenheat bath and rest of the parts.
With Langevin heat bath, the accumulation effect of LEM can be
removed automatically, resulting in a small TJ even with one layer
of heat bath (Fig. 1.6b). In addition, when NL increases, heat flux
converges to a constant value much faster than the case with NH
heat bath. The reason is that with Langevin heat bath, each mode
can be excited randomly at every time step due to the stochastic
characteristic of Langevin heat bath, which can effectively suppress
the accumulation ofLEM over time.
The large TJ induced by LEM can be further understood by
looking at the autocorrelation function of atom's velocity. Figure 1.7
plots the normalized autocorrelation function of velocity for atoms
in the middle of NWs with the same parameters used in Fig.
1.6a,b. With one layer of NH heat bath, since it mainly utilizes
LEM to maintain the constant temperature, there exists obviously
nonvanishing correlation in the long-time region. This artificial
correlation is the direct evidence of the existence and accumulation
effect of LEM mentioned above, which leads to the large TJ. With
multiple layers of NH, the artificial correlation vanishes because all
the modes can contribute to the thermal transport, thus a much
smallerTJ.Moreover,duetothestochasticcharacteristicofLangevin
heat bath, the artificial correlation does not exist, regardless of the
numberof heat bath layers applied.
Next we check the temperature jump in other popularly used
deterministicheatbath,suchastheBerendsenheatbath[38].Itisa
