Two fluid space-time discontinuous Galerkin finite element method. Part I: numerical algorithm

A novel numerical method for two fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local {\it hp}-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC

An optically actuated surface scanning probe

We demonstrate the use of an extended, optically trapped probe that is capable of imaging surface topography with nanometre precision, whilst applying ultra-low, femto-Newton sized forces. This degree of precision and sensitivity is acquired through three distinct strategies. First, the probe itself is shaped in such a way as to soften the trap along the sensing axis and stiffen it in transverse directions. Next, these characteristics are enhanced by selectively position clamping independent motions of the probe. Finally, force clamping is used to refine the surface contact response. Detailed analyses are presented for each of these mechanisms. To test our sensor, we scan it laterally over a calibration sample consisting of a series of graduated steps, and demonstrate a height resolution of ∼ 11 nm. Using equipartition theory, we estimate that an average force of only ∼ 140 fN is exerted on the sample during the scan, making this technique ideal for the investigation of delicate biological samples

Individual differences in human path integration abilities correlate with gray matter volume in retrosplenial cortex, hippocampus, and medial prefrontal cortex

Humans differ in their individual navigational abilities. These individual differences may exist in part because successful navigation relies on several disparate abilities, which rely on different brain structures. One such navigational capability is path integration, the updating of position and orientation, in which navigators track distances, directions, and locations in space during movement. Although structural differences related to landmark-based navigation have been examined, gray matter volume related to path integration ability has not yet been tested. Here, we examined individual differences in two path integration paradigms: (1) a location tracking task and (2) a task tracking translational and rotational self-motion. Using voxel-based morphometry, we related differences in performance in these path integration tasks to variation in brain morphology in 26 healthy young adults. Performance in the location tracking task positively correlated with individual differences in gray matter volume in three areas critical for path integration: the hippocampus, the retrosplenial cortex, and the medial prefrontal cortex. These regions are consistent with the path integration system known from computational and animal models and provide novel evidence that morphological variability in retrosplenial and medial prefrontal cortices underlies individual differences in human path integration ability. The results for tracking rotational self-motion-but not translation or location-demonstrated that cerebellum gray matter volume correlated with individual performance. Our findings also suggest that these three aspects of path integration are largely independent. Together, the results of this study provide a link between individual abilities and the functional correlates, computational models, and animal models of path integration