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A set of interacting vortices in $2D$ in the presence of a substrate withsquare symmetry and at filling ratio $1$ can display a low temperature solidphase where only one of the reciprocal lattice vectors of the substrate ispresent\cite{toby1,fasano}. This partially pinned vortex lattice melts to amodulated liquid via a continuous transition \cite{toby1}. Brownian dynamicssimulation is carried out to study the behavior of driven partially pinnedsolid at different temperatures. The average vortex velocity for forces abovethe depinning threshold shows a non-monotonic behavior with temperature, with aminimum in the average velocity close to the melting point. This is reminiscentof the peak effect seen in vortex systems with random disorder. This effect inthe current system can be qualitatively explained by an effective increase inthe barriers encountered by the particles as $T_c$ is approached. Approximatecalculation of the energy barriers as a function of temperature, from thesimulation supports this claim.

physica a statistical mechanics and its applications

Brownian dynamics study of driven partially pinned solid in the presence  of square array of pinning centers: Enhanced pinning close to the melting  transition