pinning regime, rough estimates of the pinning force in a numerically very efficient manner.

Discrete Stochastic Dislocation Dynamics {#sec:3}
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Description of model {#sec:3.1}
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In the present model which focuses on core effects, a non singular theory [@Cai2006_JMPS; @Arsenlis2007_MSMSE] is considered. After discretization of the dislocation into nodes connected by segments, the equation of motion of dislocation node $i$ is escribed by the following equation: $$\label{equ:1}
m_{0}L_{i} \bm{a}_{i}=-BL_{i} \bm{v}_{i} + \bm{F}_{i}^{\rm disloc} + \bm{F}_{i,T} + \bm{F}_{i}^{\rm a} + \bm{F}_{i}^{\rm q}.$$ Here $m_{0}\approx\rho b^{2}/2$ is the effective dislocation mass per unit length, , $\rho$ and $b$ are the material mass density and magnitude of Burgers vector, respectively; $L_{i}$ is an effective length associated with node $i$ due to dislocation segments connecting to it; $B$ is the drag coefficient per unit length; $ \bm{f}_{i}^{\rm disloc} $ includes the self force $\bm{f}_{i}^{\rm self}$, core force $\bm{f}_{i}^{\rm core} $ and the force from dislocation segment-segment interactions; $\bm{f}_{i,T}$ is a Langevin force which accounts for thermal fluctuations; $\bm{f}_{i}^{\rm a}$ is the force due to the externally applied stress and $\bm{f}_{i}^{\rm q}$ is the force due to a spatial force field that may be used to model the influence of atomic disorder.

The Langevin force 