$($a$)$ Using the temperature profile data obtained from MD simulations in class, perform an averaging of the temperature profile gradients and calculate a time$-$averaged thermal conductivity value for the LJ liquid example discussed in class.

$($b$)[$Conceptual$]$ Thermal conduction typically happens according to two sources: electron transport and mechanical vibrations $($phonon transport$).$ Explain the difference between these two mechanism and discuss for which type of materials can each mechanism be the dominant factor. Considering the MD simulations for calculating the thermal conductivity discussed in class, which thermal conduction mechanism $($or both$)$ are modeled by such MD simulations?$$

$($c$)$ Your goal for this part is to develop a code that helps you visualize the temperature gradient profile explained in the MD simulations in class. Using the resulting file from the 'dump command' and the profile file from the fix ave$/$chunk command, re$-$create the dump file so that the last column for each particle represents the temperature of the bin $($region in the z direction$)$ that the particle belongs to$.$ Then, load the resulting file into Ovito and show the corresponding temperature gradient profile using the 'Color coding' option under the modification tab, based on the temperatures assigned to the particles.$$

Is assigning a temperature to individual particles physically meaningful or is it only ok for visualization purposes?

$$

$-$submit your full report as a word or pdf document.$$

$--$values obtained from class$--$

$10\mathrm{.}025308\mathrm{.}751\mathrm{.}88106$

$20\mathrm{.}075329\mathrm{.}521\mathrm{.}80705$

$30\mathrm{.}125355\mathrm{.}561\mathrm{.}60597$

$40\mathrm{.}175370\mathrm{.}51\mathrm{.}58009$

$50\mathrm{.}225398\mathrm{.}111\mathrm{.}47476$

$60\mathrm{.}275399\mathrm{.}661\mathrm{.}36888$

$70\mathrm{.}325417\mathrm{.}581\mathrm{.}34123$

$80\mathrm{.}375435\mathrm{.}761\mathrm{.}23217$

$90\mathrm{.}425453\mathrm{.}271\mathrm{.}17503$

$100\mathrm{.}475460\mathrm{.}561\mathrm{.}15041$

$110\mathrm{.}525478\mathrm{.}411\mathrm{.}08077$

$120\mathrm{.}575462\mathrm{.}031\mathrm{.}12252$

$130\mathrm{.}625450\mathrm{.}211\mathrm{.}18823$

$140\mathrm{.}675440\mathrm{.}971\mathrm{.}24106$

$150\mathrm{.}725417\mathrm{.}741\mathrm{.}33065$

$160\mathrm{.}775400\mathrm{.}761\mathrm{.}38157$

$170\mathrm{.}825383\mathrm{.}481\mathrm{.}46382$

$180\mathrm{.}875364\mathrm{.}641\mathrm{.}54513$

$190\mathrm{.}925343\mathrm{.}381\mathrm{.}65519$

$200\mathrm{.}975329\mathrm{.}111\mathrm{.}77054$