influence on simulated temperature and thermal equilibration time decreases with increased dislocation length, which is the opposite of the result obtained when Langevin forces are applied on dislocation segments [@Hiratani2002_JEMT].

   Length($b$)   simulated temperature(K)   TSD(m/s)   simulated SD(m/s)   $t_{equ}$(ps)
  ------------- -------------------------- ---------- ------------------- ---------------
       100                 1188               47.1           47.0            $\sim$8.7
       200                 1190               33.3           32.3            $\sim$8.1
       400                 1190               23.5           23.7            $\sim$5.8
       800                 1185               16.6           15.4            $\sim$4.4

\[table:3\]

Simulation results {#sec:4}
==================

Spatio-temporal roughening of a dislocation line under influence of thermal forces {#sec:4.1}
----------------------------------------------------------------------------------

We simulate an edge dislocation of length $2 \times 10^4 b$ pinned at its endpoints. The line direction is identified with the $x$ direction of a Cartesian coordinate system, the glide plane is the $xy$ plane. The system is assumed to be of infinite extension in $z$ direction and periodic boundary conditions are imposed on a simulation cell of extension $2 \times 10^4 b$ in $x$ and $2 \times 10^4 b$ in $y$ direction. The dislocation is discretized into 1000 nodes with an inital spacing of $20b$.

In our investigation of the spatio-temporal behavior of the dislocation under the influence of thermal forces, we first consider a dislocation that has been evolving for sufficient time to establish thermal equilibrium. In 