We present sCOLA -- an extension of the N-body COmoving Lagrangian Acceleration (COLA) method to the spatial domain. Similar to the original temporal-domain COLA, sCOLA is an N-body method for solving for large-scale structure in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory. Incorporating the sCOLA method in an N-body code allows one to gain computational speed by capturing the gravitational potential from the far field using perturbative techniques, while letting the N-body code solve only for the near field. The far and near fields are completely decoupled, effectively localizing gravity for the N-body side of the code. Thus, running an N-body code for a small simulation volume using sCOLA can reproduce the results of a standard N-body run for the same small volume embedded inside a much larger simulation. We demonstrate that sCOLA can be safely combined with the original temporal-domain COLA. sCOLA can be used as a method for performing zoom-in simulations. It also allows N-body codes to be made embarrassingly parallel, thus allowing for efficiently tiling a volume of interest using grid computing. Moreover, sCOLA can be useful for cheaply generating large ensembles of accurate mock halo catalogs required to study galaxy clustering. Surveys that will benefit the most are ones with large aspect ratios, such as pencil-beam surveys, where sCOLA can easily capture the effects of large-scale transverse modes without the need to substantially increase the simulated volume. As an illustration of the method, we present proof-of-concept zoom-in simulations using a freely available sCOLA-based N-body code.

We study the properties of the local transverse deviations of magnetic field lines at a fixed moment in time. Those deviations "evolve" smoothly in a plane normal to the field-line direction as one moves that plane along the field line. Since the evolution can be described by a planar flow in the normal plane, we derive most of our results in the context of a toy model for planar fluid flow. We then generalize our results to include the effects of field-line curvature. We show that the type of flow is determined by the two non-zero eigenvalues of the gradient of the normalized magnetic field. The eigenvalue difference quantifies the local rate of squeezing or coiling of neighboring field lines, which we relate to standard notions of fluid vorticity and shear. The resulting squeezing rate can be used in the detection of null points, hyperbolic flux tubes and current sheets. Once integrated along field lines, that rate gives a squeeze factor, which is an approximation to the squashing factor, which is usually employed in locating quasi-separatrix layers (QSLs), which are possible sites for magnetic reconnection. Unlike the squeeze factor, the squashing factor can miss QSLs for which field lines are squeezed and then unsqueezed. In that regard, the squeeze factor is a better proxy for locating QSLs than the squashing factor. In another application of our analysis, we construct an approximation to the local rate of twist of neighboring field lines, which we refer to as the coiling rate. That rate can be integrated along a field line to give a coiling number, $\mathrm{N_c}$. We show that unlike the standard local twist number, $\mathrm{N_c}$ gives an unbiased approximation to the number of twists neighboring field lines make around one another. $\mathrm{N_c}$ can be useful for the study of flux rope instabilities, such as the kink instability, and can be used in the detection of flux ropes.