Drag force on a line defect moving through an otherwise undisturbed field: Disclination line in a nematic liquid crystal

The drag force (per unit length) acting on a steadily moving disclination line is calculated. The problem is formulated in two equivalent ways: One involving a linear partial differential equation but with ambiguous boundary conditions, and another involving a nonlinear equation but with uniquely defined boundary conditions. The second formulation is solved numerically; the results of the numerical simulation are then used to fix the boundary conditions for the first formulation, which is solved analytically. A finite value is obtained for the drag force, without a need to introduce the integration cutoff at the sample size.