Figure 1: (Left) Rayleigh-Taylor instability, 4 phases. (Center) liquids of varying viscosity, 5 phases. (Right) burning oil in water, 4 phases. AbstractThe particle level set method has proven successful for the simulation of two separate regions (such as water and air, or fuel and products). In this paper, we propose a novel approach to extend this method to the simulation of as many regions as desired. The various regions can be liquids (or gases) of any type with differing viscosities, densities, viscoelastic properties, etc. We also propose techniques for simulating interactions between materials, whether it be simple surface tension forces or more complex chemical reactions with one material converting to another or two materials combining to form a third. We use a separate particle level set method for each region, and propose a novel projection algorithm that decodes the resulting vector of level set values providing a "dictionary" that translates between them and the standard single-valued level set representation. An additional difficulty occurs since discretization stencils (for interpolation, tracing semi-Lagrangian rays, etc.) cross region boundaries naively combining non-smooth or even discontinuous data. This has recently been addressed via ghost values, e.g. for fire or bubbles. We instead propose a new paradigm that allows one to incorporate physical jump conditions in data "on the fly," which is significantly more efficient for multiple regions especially at triple points or near boundaries with solids.

We present a model of cytoplasmically driven microtubule-based pronuclear motion in the single-celled Caenorhabditis elegans embryo. In this model, a centrosome pair at the male pronucleus initiates stochastic microtubule (MT) growth. These MTs encounter motor proteins, distributed throughout the cytoplasm, that attach and exert a pulling force. The consequent MT-length-dependent pulling forces drag the pronucleus through the cytoplasm. On physical grounds, we assume that the motor proteins also exert equal and opposite forces on the surrounding viscous cytoplasm, here modeled as an incompressible Newtonian fluid constrained within an ellipsoidal eggshell. This naturally leads to streaming flows along the MTs. Our computational method is based on an immersed boundary formulation that allows for the simultaneous treatment of fluid flow and the dynamics of structures immersed within. Our simulations demonstrate that the balance of MT pulling forces and viscous nuclear drag is sufficient to move the pronucleus, while simultaneously generating minus-end directed flows along MTs that are similar to the observed movement of yolk granules toward the center of asters. Our simulations show pronuclear migration, and moreover, a robust pronuclear centration and rotation very similar to that observed in vivo. We find also that the confinement provided by the eggshell significantly affects the internal dynamics of the cytoplasm, increasing by an order of magnitude the forces necessary to translocate and center the pronucleus. cellular mechanics | fluid-structure interactions | motor proteinmicrotubule interactions | nuclear positioning P roper nuclear positioning is crucial to the successful progression of early development in animal cells and depends on active and passive mechanisms. In many types of cells, nuclear positioning has been shown to depend on the microtubule (MT) cytoskeleton, and several mechanisms for such MT-based motion have been proposed (1). One type of MT-based motion occurs in WT Caenorhabditis elegans where the male pronucleus is tightly associated with two centrosomes that act as MTorganizing centers (MTOCs) to nucleate MTs. In sand dollar embryo, it was observed that a male pronucleus will move in the direction of its longest MTs until it is centered within the region allowing MT growth (2). This led to the proposal of cytoplasmically based length-dependent forces, with the molecular basis being minusend directed motor proteins such as dynein distributed and anchored in the cytoplasm (2). Despite the appeal of such a model, one is left to identify the cytoplasmic substrate able to anchor the motor proteins and thus counteract the drag on the MTOC and its associated structures and lead to nuclear motion. Recently, Kimura and Kimura showed that endosomes, lysosomes, and yolk granules may act as such substrates in C. elegans (3).Although pronuclear motion under a length-dependent MTbased force model was studied in ref. 4, the effect of forces on the cytoplasm was not considered and forces in the model we...

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Figure 1: (Left) Many rigid balls with varying densities plunge into a pool of water. (Center) Water splashes out of an elastic cloth bag. (Right) A balloon shoots upwards, releasing a jet of smoke. AbstractWe propose a novel solid/fluid coupling method that treats the coupled system in a fully implicit manner making it stable for arbitrary time steps, large density ratios, etc. In contrast to previous work in computer graphics, we derive our method using a simple back-ofthe-envelope approach which lumps the solid and fluid momenta together, and which we show exactly conserves the momentum of the coupled system. Notably, our method uses the standard Cartesian fluid discretization and does not require (moving) conforming tetrahedral meshes or ALE frameworks. Furthermore, we use a standard Lagrangian framework for the solid, thus supporting arbitrary solid constitutive models, both implicit and explicit time integration, etc. The method is quite general, working for smoke, water, and multiphase fluids as well as both rigid and deformable solids, and both volumes and thin shells. Rigid shells and cloth are handled automatically without special treatment, and we support fully one-sided discretizations without leaking. Our equations are fully symmetric, allowing for the use of fast solvers, which is a natural result of properly conserving momentum. Finally, for simple explicit time integration of rigid bodies, we show that our equations reduce to a form similar to previous work via a single block Gaussian elimination operation, but that this approach scales poorly, i.e. as though in four spatial dimensions rather than three.