Modelling calving front dynamics using a level-set method: application to Jakobshavn Isbræ, West Greenland, links model results in MATLAB format

Calving is a major mechanism of ice discharge of the Antarctic and Greenland ice sheets, and a change in calving front position affects the entire stress regime of marine terminating glaciers. The representation of calving front dynamics in a 2-D or 3-D ice sheet model remains non-trivial. Here, we present the theoretical and technical framework for a level-set method, an implicit boundary tracking scheme, which we implement into the Ice Sheet System Model (ISSM). This scheme allows us to study the dynamic response of a drainage basin to user-defined calving rates. We apply the method to Jakobshavn Isbræ, a major marine terminating outlet glacier of the West Greenland Ice Sheet. The model robustly reproduces the high sensitivity of the glacier to calving, and we find that enhanced calving triggers significant acceleration of the ice stream. Upstream acceleration is sustained through a combination of mechanisms. However, both lateral stress and ice influx stabilize the ice stream. This study provides new insights into the ongoing changes occurring at Jakobshavn Isbræ and emphasizes that the incorporation of moving boundaries and dynamic lateral effects, not captured in flow-line models, is key for realistic model projections of sea level rise on centennial timescales.

Optimal Multiresolution 3D Level-Set Method for Liver Segmentation incorporating Local Curvature Constraints

Advanced liver surgery requires a precise pre-operative planning, where liver segmentation and remnant liver volume are key elements to avoid post-operative liver failure. In that context, level-set algorithms have achieved better results than others, especially with altered liver parenchyma or in cases with previous surgery. In order to improve functional liver parenchyma volume measurements, in this work we propose two strategies to enhance previous level-set algorithms: an optimal multi-resolution strategy with fine details correction and adaptive curvature, as well as an additional semiautomatic step imposing local curvature constraints. Results show more accurate segmentations, especially in elongated structures, detecting internal lesions and avoiding leakages to close structures

Level Set Segmentation with Shape and Appearance Models Using Affine Moment Descriptors

We propose a level set based variational approach that incorporates shape priors into edge-based and region-based models. The evolution of the active contour depends on local and global information. It has been implemented using an efficient narrow band technique. For each boundary pixel we calculate its dynamic according to its gray level, the neighborhood and geometric properties established by training shapes. We also propose a criterion for shape aligning based on affine transformation using an image normalization procedure. Finally, we illustrate the benefits of the our approach on the liver segmentation from CT images.

A level set approach for the analysis of flow and compaction during resin infusion in composite materials

Fluid flow and fabric compaction during vacuum assisted resin infusion (VARI) of composite materials was simulated using a level set-based approach. Fluid infusion through the fiber preform was modeled using Darcy’s equations for the fluid flow through a porous media. The stress partition between the fluid and the fiber bed was included by means of Terzaghi’s effective stress theory. Tracking the fluid front during infusion was introduced by means of the level set method. The resulting partial differential equations for the fluid infusion and the evolution of flow front were discretized and solved approximately using the finite differences method with a uniform grid discretization of the spatial domain. The model results were validated against uniaxial VARI experiments through an [0]8 E-glass plain woven preform. The physical parameters of the model were also independently measured. The model results (in terms of the fabric thickness, pressure and fluid front evolution during filling) were in good agreement with the numerical simulations, showing the potential of the level set method to simulate resin infusion

A fast marching level set method for monotonically advancing fronts.

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. This paper describes a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for Hamilton-Jacobi equations, and fast adaptive narrow band level set methods. The technique is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory.

Image processing via level set curvature flow.

We present a controlled image smoothing and enhancement method based on a curvature flow interpretation of the geometric heat equation. Compared to existing techniques, the model has several distinct advantages. (i) It contains just one enhancement parameter. (ii) The scheme naturally inherits a stopping criterion from the image; continued application of the scheme produces no further change. (iii) The method is one of the fastest possible schemes based on a curvature-controlled approach.

Incorporating level set methods in Geographical Information Systems (GIS) for land-surface process modelling

Land-surface processes include a broad class of models that operate at a landscape scale. Current modelling approaches tend to be specialised towards one type of process, yet it is the interaction of processes that is increasing seen as important to obtain a more integrated approach to land management. This paper presents a technique and a tool that may be applied generically to landscape processes. The technique tracks moving interfaces across landscapes for processes such as water flow, biochemical diffusion, and plant dispersal. Its theoretical development applies a Lagrangian approach to motion over a Eulerian grid space by tracking quantities across a landscape as an evolving front. An algorithm for this technique, called level set method, is implemented in a geographical information system (GIS). It fits with a field data model in GIS and is implemented as operators in map algebra. The paper describes an implementation of the level set methods in a map algebra programming language, called MapScript, and gives example program scripts for applications in ecology and hydrology.

Simultaneous optimisation of structural topology and material grading using level set method

Peer reviewed

Modelling of water removal during a paper vacuum dewatering process using a Level-Set method

Water removal in paper manufacturing is an energy-intensive process. The dewatering process generally consists of four stages of which the first three stages include mechanical water removal through gravity filtration, vacuum dewatering and wet pressing. In the fourth stage, water is removed thermally, which is the most expensive stage in terms of energy use. In order to analyse water removal during a vacuum dewatering process, a numerical model was created by using a Level-Set method. Various different 2D structures of the paper model were created in MATLAB code with randomly positioned circular fibres with identical orientation. The model considers the influence of the forming fabric which supports the paper sheet during the dewatering process, by using volume forces to represent flow resistance in the momentum equation. The models were used to estimate the dry content of the porous structure for various dwell times. The relation between dry content and dwell time was compared to laboratory data for paper sheets with basis weights of 20 and 50 g/m2 exposed to vacuum levels between 20 kPa and 60 kPa. The comparison showed reasonable results for dewatering and air flow rates. The random positioning of the fibres influences the dewatering rate slightly. In order to achieve more accurate comparisons, the random orientation of the fibres needs to be considered, as well as the deformation and displacement of the fibres during the dewatering process.

Uma nova abordagem do método Level Set baseada em conhecimento a e priori da forma

The analysis of fluid behavior in multiphase flow is very relevant to guarantee system safety. The use of equipment to describe such behavior is subjected to factors such as the high level of investments and of specialized labor. The application of image processing techniques to flow analysis can be a good alternative, however, very little research has been developed. In this subject, this study aims at developing a new approach to image segmentation based on Level Set method that connects the active contours and prior knowledge. In order to do that, a model shape of the targeted object is trained and defined through a model of point distribution and later this model is inserted as one of the extension velocity functions for the curve evolution at zero level of level set method. The proposed approach creates a framework that consists in three terms of energy and an extension velocity function λLg(θ)+vAg(θ)+muP(0)+θf. The first three terms of the equation are the same ones introduced in (LI CHENYANG XU; FOX, 2005) and the last part of the equation θf is based on the representation of object shape proposed in this work. Two method variations are used: one restricted (Restrict Level Set - RLS) and the other with no restriction (Free Level Set - FLS). The first one is used in image segmentation that contains targets with little variation in shape and pose. The second will be used to correctly identify the shape of the bubbles in the liquid gas two phase flows. The efficiency and robustness of the approach RLS and FLS are presented in the images of the liquid gas two phase flows and in the image dataset HTZ (FERRARI et al., 2009). The results confirm the good performance of the proposed algorithm (RLS and FLS) and indicate that the approach may be used as an efficient method to validate and/or calibrate the various existing equipment used as meters for two phase flow properties, as well as in other image segmentation problems.

Deposition and biokinetics of inhaled nanoparticles

Particle biokinetics is important in hazard identification and characterization of inhaled particles. Such studies intend to convert external to internal exposure or biologically effective dose, and may help to set limits in that way. Here we focus on the biokinetics of inhaled nanometer sized particles in comparison to micrometer sized ones.The presented approach ranges from inhaled particle deposition probability and retention in the respiratory tract to biokinetics and clearance of particles out of the respiratory tract. Particle transport into the blood circulation (translocation), towards secondary target organs and tissues (accumulation), and out of the body (clearance) is considered. The macroscopically assessed amount of particles in the respiratory tract and secondary target organs provides dose estimates for toxicological studies on the level of the whole organism. Complementary, microscopic analyses at the individual particle level provide detailed information about which cells and subcellular components are the target of inhaled particles. These studies contribute to shed light on mechanisms and modes of action eventually leading to adverse health effects by inhaled nanoparticles.We review current methods for macroscopic and microscopic analyses of particle deposition, retention and clearance. Existing macroscopic knowledge on particle biokinetics and microscopic views on particle organ interactions are discussed comparing nanometer and micrometer sized particles. We emphasize the importance for quantitative analyses and the use of particle doses derived from real world exposures.

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

Densities with Spherical Level Sets in the Gauss-exponential Domain

2000 Mathematics Subject Classification: 60F05, 60B10.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

Mercúrio total em cabelo de crianças de uma população costeira, Cananéia, São Paulo, Brasil

Os níveis de mercúrio (Hg) total em cabelos estão diretamente relacionados à alimentação, particularmente ao consumo de peixes por populações costeiras com grande representação caiçara. No presente estudo foram avaliados os níveis de mercúrio total em cabelos de crianças com idade entre 4 e 12 anos, pertencente a três escolas públicas da cidade de Cananéia, São Paulo, Brasil. Os resultados obtidos (mediana e intervalo) para mercúrio total foram de: 0,04mg.kg-1 (0,01-0,77mg.kg-1), 0,39mg.kg-1 (< 0,01-3,33mg.kg-1) e 0,39mg.kg-1 (< 0,01-2,81mg.kg-1) considerando as escolas ES1, ES2 e ES3, respectivamente. Em geral, os valores encontrados estiveram bem abaixo do valor preconizado pela Organização Mundial da Saúde para uma população adulta não exposta ao mercúrio (2,0mg.kg-1). Os baixos valores observados e a inexistência de valores de referência para mercúrio total em cabelos de crianças brasileiras possibilitam a consideração desses valores como possível referência nacional em cabelos de populações costeiras, uma vez que foram obtidos em região de baixo impacto ambiental.