To numerically solve the two-dimensional advection equation, we propose a family of fourth- and higher-order semi-Lagrangian finite volume (SLFV) methods that feature (1) fourth-, sixth-, and eighth-order convergence rates, (2) applicability to both regular and irregular domains with arbitrarily complex topology and geometry, (3) ease of handling both zero and nonzero source terms, and (4) the same algorithmic steps for both periodic and incoming penetration conditions. Test results confirm the analysis and demonstrate the accuracy, flexibility, robustness, and excellent conditioning of the proposed SLFV method.

The interaction mechanism between a single microscopic object like a cell, a particle, a molecule, or an atom and its interacting electromagnetic field is fundamental in single-object manipulation such as optical trap and magnetic trap. Function-on-demand, single-object manipulation relies on a high degree of freedom control of electromagnetic field at localized scales, which remains challenging. Here we propose a manipulation concept: programmable single-object manipulation, based on programming the electromagnetic field in a multi-bit electrode system. This concept is materialized on a Programmable Electric Tweezer (PET) with four individually addressed electrodes, marking a transition from function-fixed single-object manipulation to function-programmable single-object manipulation. By programming the localized electric field, our PET can provide various manipulation functions for achieving precise trapping, movement and rotation of multiscale single microscopic objects, including single proteins, nucleic acids, microparticles and bacteria. Implementing these functions, we are able not only to manipulate the object of interest on demand but also quantitatively measure the charge to mass ratio of a single microparticle via the Paul trap and the electrical properties of an individual bacterial cell by the rotation analysis. Finally, with superposed single-particle trapping and rotation, we demonstrate the spontaneous relaxation of DNA supercoiling and observe an unexpected pause phenomenon in the relaxation process, highlighting the versatility and the potential of PET in uncovering stochastic biophysical phenomena at the single-molecule level.