Extraction and Visualization of Swirl and Tumble Motion from Engine Simulation Data

Figure 1: Unsteady visualization of vortices from in-cylinder tumble motion in a gas engine and its relationship to the boundary. During the valve cycle (left to right), the piston head that shapes the bottom of the geometry moves down (not shown). The volume rendering shows vortices using a two-dimensional transfer function of λ2 and normalized helicity (legend). The main tumble vortex is extracted and visible as off-center and with an undesired diagonal orientation. The flow structure on the boundary is visualized using boundary topology. A direct correspondence between the volume and boundary visualizations can be observed. In the third image, the intersection of the main vortex with the boundary results in critical points on the front and back walls. Optimizing the combustion process within an engine block is central to the performance of many motorized vehicles. Associated with this process are two important patterns of flow: swirl and tumble motion, which optimize the mixing of fluid within each of an engine’s cylinders. Good visualizations are necessary to analyze the simulation data of these in-cylinder flows. We present a range of methods including integral, feature-based, and imagebased schemes with the goal of extracting and visualizing these tw

Monte Carlo simulations of fluid vesicles with in plane orientational ordering

We present a method for simulating fluid vesicles with in-plane orientational ordering. The method involves computation of local curvature tensor and parallel transport of the orientational field on a randomly triangulated surface. It is shown that the model reproduces the known equilibrium conformation of fluid membranes and work well for a large range of bending rigidities. Introduction of nematic ordering leads to stiffening of the membrane. Nematic ordering can also result in anisotropic rigidity on the surface leading to formation of membrane tubes.Comment: 11 Pages, 12 Figures, To appear in Phys. Rev.

Optic nerve head three-dimensional shape analysis

We present a method for optic nerve head (ONH) 3-D shape analysis from retinal optical coherence tomography (OCT). The possibility to noninvasively acquire in vivo high-resolution 3-D volumes of the ONH using spectral domain OCT drives the need to develop tools that quantify the shape of this structure and extract information for clinical applications. The presented method automatically generates a 3-D ONH model and then allows the computation of several 3-D parameters describing the ONH. The method starts with a high-resolution OCT volume scan as input. From this scan, the model-defining inner limiting membrane (ILM) as inner surface and the retinal pigment epithelium as outer surface are segmented, and the Bruch's membrane opening (BMO) as the model origin is detected. Based on the generated ONH model by triangulated 3-D surface reconstruction, different parameters (areas, volumes, annular surface ring, minimum distances) of different ONH regions can then be computed. Additionally, the bending energy (roughness) in the BMO region on the ILM surface and 3-D BMO-MRW surface area are computed. We show that our method is reliable and robust across a large variety of ONH topologies (specific to this structure) and present a first clinical application

CuBe: parametric modeling of 3D foveal shape using cubic Bézier

Optical coherence tomography (OCT) allows three-dimensional (3D) imaging of the retina, and is commonly used for assessing pathological changes of fovea and macula in many diseases. Many neuroinflammatory conditions are known to cause modifications to the fovea shape. In this paper, we propose a method for parametric modeling of the foveal shape. Our method exploits invariant features of the macula from OCT data and applies a cubic Bézier polynomial along with a least square optimization to produce a best fit parametric model of the fovea. Additionally, we provide several parameters of the foveal shape based on the proposed 3D parametric modeling. Our quantitative and visual results show that the proposed model is not only able to reconstruct important features from the foveal shape, but also produces less error compared to the state-of-the-art methods. Finally, we apply the model in a comparison of healthy control eyes and eyes from patients with neuroinflammatory central nervous system disorders and optic neuritis, and show that several derived model parameters show significant differences between the two groups

Flows and Decompositions of Games: Harmonic and Potential Games

In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the equilibria of a game, but plays a fundamental role in their efficiency properties, thus decoupling the location of equilibria and their payoff-related properties. Exploiting the properties of the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the properties of potential and harmonic games to "nearby" games. We exemplify this point by showing that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of its projection onto the set of potential games

Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

Uniform convergence of discrete curvatures from nets of curvature lines

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.Comment: 21 pages, 8 figure