Tamar Shinar

Hybrid simulation of deformable solids

Although mesh-based methods are efficient for simulating simple hyperelasticity, maintaining and adapting a mesh-based representation is less appealing in more complex scenarios, e.g. collision, plasticity and fracture. Thus, meshless or point-based methods have enjoyed recent popularity due to their added flexibility in dealing with these situations. Our approach begins with an initial mesh that is either conforming (as generated by ones favorite meshing algorithm) or non-conforming (e.g. a BCC background lattice). We then propose a framework for embedding arbitrary sample points into this initial mesh allowing for the straightforward handling of collisions, plasticity and fracture without the need for complex remeshing. A straightforward consequence of this new framework is the ability to naturally handle T-junctions alleviating the requirement for a manifold initial mesh. The arbitrarily added embedded points are endowed with full simulation capability allowing them to collide, interact with each other, and interact with the parent geometry in the fashion of a particle-centric simulation system. We demonstrate how this formulation facilitates tasks such as arbitrary refinement or resampling for collision processing, the handling of multiple and possibly conflicting constraints (e.g. when cloth is nonphysically pinched between two objects), the straightforward treatment of fracture, and sub-element resolution of elasticity and plasticity.

Two-way coupling of fluids to rigid and deformable solids and shells

We 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-of-the-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 form similar to previous work via a single block Gaussian elimination operation, but that this approach scales poorly, i.e. as though four spatial dimensions rather than three.

Two-way coupling of rigid and deformable bodies

We propose a framework for the full two-way coupling of rigid and deformable bodies, which is achieved with both a unified time integration scheme as well as individual two-way coupled algorithms at each point of that scheme. As our algorithm is two-way coupled in every fashion, we do not require ad hoc methods for dealing with stability issues or interleaving parts of the simulation. We maintain the ability to treat the key desirable aspects of rigid bodies (e.g. contact, collision, stacking, and friction) and deformable bodies (e.g. arbitrary constitutive models, thin shells, and self-collisions). In addition, our simulation framework supports more advanced features such as proportional derivative controlled articulation between rigid bodies. This not only allows for the robust simulation of a number of new phenomena, but also directly lends itself to the design of deformable creatures with proportional derivative controlled articulated rigid skeletons that interact in a life-like way with their environment.

Wrinkled flames and cellular patterns

We model flames and fire using the Navier-Stokes equations combined with the level set method and jump conditions to model the reaction front. Previous works modeled the flame using a combination of propagation in the normal direction and a curvature term which leads to a level set equation that is parabolic in nature and thus overly dissipative and smooth. Asymptotic theory shows that one can obtain more interesting velocities and fully hyperbolic (as opposed to parabolic) equations for the level set evolution. In particular, researchers in the field of detonation shock dynamics (DSD) have derived a set of equations which exhibit characteristic cellular patterns. We show how to make use of the DSD framework in the context of computer graphics simulations of flames and fire to obtain interesting features such as flame wrinkling and cellular patterns.

A model of cytoplasmically driven microtubule-based motion in the single-celled Caenorhabditis elegans embryo

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.

On Boundary Condition Capturing for Multiphase Interfaces

This review paper begins with an overview of the boundary condition capturing approach to solving problems with interfaces. Although the authors’ original motivation was to extend the ghost fluid method from compressible to incompressible flow, the elliptic nature of incompressible flow quickly quenched the idea that ghost cells could be defined and used in the usual manner. Instead the boundary conditions had to be implicitly captured by the matrix formulation itself, leading to the novel approach. We first review the work on the variable coefficient Poisson equation, noting that the simplicity of the method allowed for an elegant convergence proof. Simplicity and robustness also allowed for a quick extension to three-dimensional two-phase incompressible flows including the effects of viscosity and surface tension, which is discussed subsequently. The method has enjoyed popularity in both computational physics and computer graphics, and we show some comparisons with the traditional delta function approach for the visual simulation of bubbles. Finally, we discuss extensions to problems where the velocity is discontinuous as well, as is the case for premixed flames, and show an example of multiple interacting liquids that includes all of the aforementioned phenomena.

Dynamics simulations for engineering macromolecular interactions

The predictable engineering of well-behaved transcriptional circuits is a central goal of synthetic biology. The artificial attachment of promoters to transcription factor genes usually results in noisy or chaotic behaviors, and such systems are unlikely to be useful in practical applications. Natural transcriptional regulation relies extensively on protein-protein interactions to insure tightly controlled behavior, but such tight control has been elusive in engineered systems. To help engineer protein-protein interactions, we have developed a molecular dynamics simulation framework that simplifies features of proteins moving by constrained Brownian motion, with the goal of performing long simulations. The behavior of a simulated protein system is determined by summation of forces that include a Brownian force, a drag force, excluded volume constraints, relative position constraints, and binding constraints that relate to experimentally determined on-rates and off-rates for chosen protein elements in a system. Proteins are abstracted as spheres. Binding surfaces are defined radially within a protein. Peptide linkers are abstracted as small protein-like spheres with rigid connections. To address whether our framework could generate useful predictions, we simulated the behavior of an engineered fusion protein consisting of two 20,000 Da proteins attached by flexible glycine/serine-type linkers. The two protein elements remained closely associated, as if constrained by a random walk in three dimensions of the peptide linker, as opposed to showing a distribution of distances expected if movement were dominated by Brownian motion of the protein domains only. We also simulated the behavior of fluorescent proteins tethered by a linker of varying length, compared the predicted Förster resonance energy transfer with previous experimental observations, and obtained a good correspondence. Finally, we simulated the binding behavior of a fusion of two ligands that could simultaneously bind to distinct cell-surface receptors, and explored the landscape of linker lengths and stiffnesses that could enhance receptor binding of one ligand when the other ligand has already bound to its receptor, thus, addressing potential mechanisms for improving targeted signal transduction proteins. These specific results have implications for the design of targeted fusion proteins and artificial transcription factors involving fusion of natural domains. More broadly, the simulation framework described here could be extended to include more detailed system features such as non-spherical protein shapes and electrostatics, without requiring detailed, computationally expensive specifications. This framework should be useful in predicting behavior of engineered protein systems including binding and dissociation reactions.

Example-based plastic deformation of rigid bodies

Physics-based animation is often used to animate scenes containing destruction of near-rigid, man-made materials. For these applications, the most important visual features are plastic deformation and fracture. Methods based on continuum mechanics model these materials as elastoplastic, and must perform expensive elasticity computations even though elastic deformations are imperceptibly small for rigid materials. We introduce an example-based plasticity model based on linear blend skinning that allows artists to author simulation objects using familiar tools. Dynamics are computed using an unmodified rigid body simulator, making our method computationally efficient and easy to integrate into existing pipelines. We introduce a flexible technique for mapping impulses computed by the rigid body solver to local, example-based deformations. For completeness, our method also supports prescoring based fracture. We demonstrate the practicality of our method by animating a variety of destructive scenes.

Ductile fracture for clustered shape matching

In this paper, we incorporate ductile fracture into the clustered shape matching simulation framework for deformable bodies, thus filling a gap in the shape matching literature. Our plasticity and fracture models are inspired by the finite element literature on deformable bodies, but are adapted to the clustered shape matching framework. The resulting approach is fast, versatile, and simple to implement.

DIMENSIONAL REDUCTION OF A MULTISCALE CONTINUUM MODEL OF MICROTUBULE GLIDING ASSAYS

Microtubule gliding assays, in which molecular motors anchored to a plate drive the gliding motion of filaments in a quasi--two-dimensional fluid layer, have been shown to organize into a variety of large-scale patterns. We derive a fully three-dimensional multiscale coarse-grained model of a gliding assay including the evolution of densities of rigid filaments, bound motors, and free motors, coupled to fluid equations. Our model combines continuum theories of polymeric liquids with the force spreading approach of the immersed boundary method. We use dimensional and asymptotic analysis to derive a reduced two-dimensional model and show that, to leading order, the filaments evolve in a plane, similar to what is experimentally observed. We simulate our model numerically with a GPU-based implementation and observe the same qualitative behavior as in experimental work.