Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds

This paper develops the theory of geodesic regression and least-squares estimation on Riemannian manifolds. Geodesic regression is a method for finding the relationship between a real-valued independent variable and a manifold-valued dependent random variable, where this relationship is modeled as a geodesic curve on the manifold. Least-squares estimation is formulated intrinsically as a minimization of the sum-of-squared geodesic distances of the data to the estimated model. Geodesic regression is a direct generalization of linear regression to the manifold setting, and it provides a simple parameterization of the estimated relationship as an initial point and velocity, analogous to the intercept and slope. A nonparametric permutation test for determining the significance of the trend is also given. For the case of symmetric spaces, two main theoretical results are established. First, conditions for existence and uniqueness of the least-squares problem are provided. Second, a maximum likelihood criteria is developed for a suitable definition of Gaussian errors on the manifold. While the method can be generally applied to data on any manifold, specific examples are given for a set of synthetically generated rotation data and an application to analyzing shape changes in the corpus callosum due to age.     

<Superscript>1</Superscript>H-NMR Spectroscopy as a New Tool in the Assessment of the Oxidative State in Edible Oils

Within the course of lipid peroxidation, hydroperoxides are formed as primary products. They can be used as analytical markers to assess the deterioration status of oils and fats. Here a new ¹H-NMR assay to determine the hydroperoxide amount in edible oils is presented. We were able to show that the analytical performance of the method is similar to that of the commonly used peroxide value (PV) according to Wheeler. A total of 290 edible oil samples were analyzed using both methods. For some oil varieties considerable discrepancies were found between the results obtained. In the case of black seed and olive oil, two substances could be identified that cause positive (black seed oil) and negative (olive oils) deviations from the theoretical PV expected from the NMR values.     

Digital image correlation analysis and modelling of the strain rate in metal cutting

In the last eight decades, considerable modelling and computational efforts have been made to predict the strain rate during cutting with the aim of optimizing machining processes. However, the validation of these modelling approaches on a local scale remains excessively limited due to the lack of in-situ measurements and the faulty existing quick-stop tests. This work presents the in-process analysis of the strain rate and strain in the primary shear zone using high speed Digital Image Correlation (DIC) techniques. The comparison of measured and computed results shows the suitability of the DIC techniques and the robustness of the modelling approaches.     

Thermal Boundary Resistance in GaN Films Measured by Time Domain Thermoreflectance with Robust Monte Carlo Uncertainty Estimation

In this work, we investigate the thermal boundary resistance and thermal conductivity of GaN layers grown on Si with 100 nm AlN transition layers using time domain thermoreflectance (TDTR). The GaN layers ranged from 0.31 to 1.27 μm. Due to the challenges in determining the thermal boundary resistance of the buried interfaces found in this architecture, a new data reduction scheme for TDTR that utilizes a Monte Carlo fitting method is introduced and found to dramatically reduce the uncertainty in certain model parameters. The results show that the GaN thermal conductivity does not change significantly with layer thickness, whereas the resistance of the AlN layer decreases slightly with GaN thickness.     

Dynamic modeling of the secondary drying stage of freeze drying reveals distinct desorption kinetics for bound water

In freeze drying, the desorption step for reaching a low target moisture content may take a significant fraction of the total process duration. Because the long-term stability of freeze-dried biological products strongly depends on the current moisture content, modeling the desorption process may help safely optimize the secondary drying step. Most published models assume a first-order desorption kinetic, but experimental evidence shows that strongly bound water in the monolayer takes a much longer time to be desorbed than less bound water in multilayer. The proposed model for desorption of freeze-dried lactic acid bacteria preparation accounts for monolayer and multilayer water state in the solid matrix, with very different desorption kinetics. Results showed that the ratio of characteristic desorption times (monolayer/multilayer) was almost 30. Temperature dependence was adequately described by an Arrhenius law in the range of 15 to 40°C. Model parameter identification used simultaneously gravimetric measurements with high time resolution and direct Karl-Fisher titration, from several experiments at different, time-varying temperatures.     

Understanding and Prediction of the Clouding Phenomenon by Spontaneous and Effective Packing Concepts

In this work, we show by which mechanism branching of the hydrocarbon chains influences the cloud point of nonionic, ethoxylated surfactants. The temperature-induced separation into a dilute and a concentrated liquid phase is of liquid–gas type and can be explained by the relative probability of endcaps and branching points of the cylindrical micelles in both phases. The influence of branches on the hydrocarbon chains can be easily understood by means of spontaneous and effective packing concepts, while quantification via hydrophilic/lipophilic balance (HLB), hydrophilic-lipophilic difference (HLD), and HLD-Net Average Curvature requires parametrization. The phase equilibrium above the cloud point phenomenon is equivalent to the Winsor I type phase equilibrium, one of the five known phase equilibria in ternary systems.     

Key Assumptions Used in the Calculation of Sustainability Parameters for Metals Processing Operations

JOM - No matter how sophisticated a model for prediction of important sustainability parameters, a number of assumptions must be made to yield the desired information. Some of these assumptions are...