along the local directions $\bm{s}_{i}$ should follow Maxwell’s distribution with a theoretical standard deviation (SD) of $\sqrt{k_{B}T/(m_{0}L_{i})}$. Two different simulations are considered in this part: (i) an edge dislocation line with fixed endpoints which is discretized into 1000 dislocation segments with segment length 20$b$; (ii) a similar edge dislocation line with non-equidistant nodes and $L_{i}$ changing from 20$b$ to 200$b$. The time step $\Delta t_{j}$ is chosen constant and equals 50fs. For larger time steps, the mean kinetic energy and velocity distribution can be used to determine whether the selection is suitable or not. A series of temperatures (300K, 600K, 900K and 1200K) are simulated to check the correctness of the Langevin force implementation. Material parameters are taken from [@Hiratani2002_JEMT] in order to compare with these simulations, in which Langevin force were applied on dislocation segments rather than nodes. The shear modulus and Poisson ratio are $\mu$=54.6 GPa and $\nu$=0.324, respectively; the magnitude of Burgers vector $b$=0.256nm and mass density is $\rho$=8900kg/m$^{3}$. The drag coefficient is assumed proportional to temperature and listed in Table \[table:1\].

Kinetic temperatures and velocity distributions for different Langevin temperatures are shown in Figs. \[fig:kinetic\_temperature\] and \[fig:velocity\_distribution\], respectively for a dislocation with equi-distant nodes. The principle 