We analyze a new mathematical and numerical framework, the " Voronoi Implicit Interface Method" (" VIIM" ), first introduced in Saye and Sethian (2011) [R.I. Saye, J.A. Sethian, The Voronoi Implicit Interface Method for computing multiphase physics, PNAS 108 (49) (2011) 19498-19503] for tracking multiple interacting and evolving regions (" phases" ) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.). From a mathematical point of view, the method provides a theoretical framework for moving interface problems that involve multiple junctions, defining the motion as the formal limit of a sequence of related problems. Discretizing this theoretical framework provides a numerical methodolology which automatically handles multiple junctions, triple points and quadruple points in two dimensions, as well as triple lines, etc. in higher dimensions. Topological changes in the system occur naturally, with no surgery required. In this paper, we present the method in detail, and demonstrate several new extensions of the method to different physical phenomena, including curvature flow with surface energy densities defined on a per-phase basis, as well as multiphase fluid flow in which density, viscosity and surface tension can be defined on a per-phase basis.We test this method in a variety of ways. We perform rigorous analysis and demonstrate convergence in both two and three dimensions for a variety of evolving interface problems, including verification of von Neumann-Mullins' law in two dimensions (and its analog in three dimensions), as well as normal driven flow and curvature flow with and without constraints, demonstrating topological change and the effects of different boundary conditions. We couple the method to a second order projection method solver for incompressible fluid flow, and study the effects of membrane permeability and impermeability, large shearing torsional forces, and the effects of varying density, viscosity and surface tension on a per-phase basis. Finally, we demonstrate convergence in both space and time of a topological change in a multiphase foam. © 2012 Elsevier Inc..

We present a set of multi-scale interlinked algorithms to model the dynamics of evolving foams. These algorithms couple the key effects of macroscopic bubble rearrangement, thin film drainage, and membrane rupture. For each of the mechanisms, we construct consistent and accurate algorithms, and couple them together to work across the wide range of space and time scales that occur in foam dynamics. These algorithms include second order finite difference projection methods for computing incompressible fluid flow on the macroscale, second order finite element methods to solve thin film drainage equations in the lamellae and Plateau borders, multiphase Voronoi Implicit Interface Methods to track interconnected membrane boundaries and capture topological changes, and Lagrangian particle methods for conservative liquid redistribution during rearrangement and rupture. We derive a full set of numerical approximations that are coupled via interface jump conditions and flux boundary conditions, and show convergence for the individual mechanisms. We demonstrate our approach by computing a variety of foam dynamics, including coupled evolution of three-dimensional bubble clusters attached to an anchored membrane and collapse of a foam cluster.

The level-set approach of Osher & Sethian to tracking interfaces is successfully adapted to the simulation of a premixed turbulent open V-flame including the effects of exothermicity and baroclinicity. In accord with experimental observations this algorithm, along with a flame anchoring scheme, predicts flame cusping for a case in which a strong vortex pair interacts with the flame front. The computed velocity and scalar statistics obtained for the turbulent V-flame compare reasonably well with experimental results by Cheng & Shepherd, and demonstrate the importance of flame-generated vorticity in the determination of flame dynamics and product velocity characteristics. © 1995, Cambridge University Press. All rights reserved.

X-ray tomography is widely used for three-dimensional structure determination in many areas of science, from the millimeter to the nanometer scale. The resolution and quality of the 3D reconstruction is limited by the availability of alignment parameters that correct for the mechanical shifts of the sample or sample stage for the images that constitute a scan. In this paper we describe an algorithm for marker-free, fully automated and accurately aligned and reconstructed X-ray tomography data. Our approach solves the tomographic reconstruction jointly with projection data alignment based on a rigid-body deformation model. We demonstrate the robustness of our method on both synthetic phantom and experimental data and show that our method is highly efficient in recovering relatively large alignment errors without prior knowledge of a low resolution approximation of the 3D structure or a reasonable estimate of alignment parameters.

One potential solution to reduce the concentration of carbon dioxide in the atmosphere is the geologic storage of captured CO2 in underground rock formations, also known as carbon sequestration. There is ongoing research to guarantee that this process is both efficient and safe. We describe tools that provide measurements of media porosity, and permeability estimates, including visualization of pore structures. Existing standard algorithms make limited use of geometric information in calculating permeability of complex microstructures. This quantity is important for the analysis of biomineralization, a subsurface process that can affect physical properties of porous media. This paper introduces geometric and topological descriptors that enhance the estimation of material permeability. Our analysis framework includes the processing of experimental data, segmentation, and feature extraction and making novel use of multiscale topological analysis to quantify maximum flow through porous networks. We illustrate our results using synchrotron-based X-ray computed microtomography of glass beads during biomineralization. We also benchmark the proposed algorithms using simulated data sets modeling jammed packed bead beds of a monodispersive material.