Curvature-dependent parameterization of curves and surfaces

The death of insulin-producing beta-cells is a key step in the pathogenesis of type 2 diabetes. The amyloidogenic peptide Islet Amyloid Polypeptide (IAPP, also known as amylin) has been shown to disrupt beta-cell membranes leading to beta-cell death. Despite the strong evidence linking IAPP to the destruction of beta-cell membrane integrity and cell death, the mechanism of IAPP toxicity is poorly understood. In particular, the effect of IAPP on the bilayer structure has largely been uncharacterized. In this study, we have determined the effect of the amyloidogenic and toxic hIAPP(1-37) peptide and the nontoxic and nonamyloidogenic rIAPP(1-37) peptide on membranes by a combination of DSC and solid-state NMR spectroscopy. We also characterized the toxic but largely nonamyloidogenic rIAPP(1-19) and hIAPP(1-19) fragments. DSC shows that both amyloidogenic (hIAPP(1-37)) and largely nonamyloidogenic (hIAPP(1-19) and rIAPP(1-19)) toxic versions of the peptide strongly favor the formation of negative curvature in lipid bilayers, while the nontoxic full-length rat IAPP(1-37) peptide does not. This result was confirmed by solid-state NMR spectroscopy which shows that in bicelles composed of regions of high curvature and low curvature, nontoxic rIAPP(1-37) binds to the regions of low curvature while toxic rIAPP(1-19) binds to regions of high curvature. Similarly, solid-state NMR spectroscopy shows that the toxic rIAPP(1-19) peptide significantly disrupts the lipid bilayer structure, whereas the nontoxic rIAPP(1-37) does not have a significant effect. These results indicate IAPP may induce the formation of pores by the induction of excess membrane curvature and can be used to guide the design of compounds that can prevent the cell-toxicity of IAPP. This mechanism may be important to understand the toxicity of other amyloidogenic proteins. Our solid-state NMR results also demonstrate the possibility of using bicelles to measure the affinity of biomolecules for negatively or positively curved regions of the membrane, which we believe will be useful in a variety of biochemical and biophysical investigations related to the cell membrane.

High Local Curvature Reduces Migration Rate in Spreading Multi-Layer Tissues

Experiments conducted in the context of the strain-space formulation of plasticity

Elevated temperature fatigue crack growth in alloy 718. I. Effects of mechanical variables: Ghonem, H., Nicholas, T. and Pineau, A. Fatigue Fract Eng mater Struct (May 1993) 16 (5), 565–576

ESP operators are continually striving to reduce downhole equipment failure rates in order to maximize well uptime, which results in reduced well servicing costs and maximized production. ESP system run-life data tracking and analysis activities are critical for determining appropriate actions that can be taken towards these objectives. These activities have typically included collecting, validating and storing data for a relatively large set of parameters. However, in low-cost operating environments, comprehensive data collection activities are often ranked as a relatively low priority. This paper proposes a strategy to leverage a relatively smaller data collection effort and high-level analysis, covering only a limited number of critical run-life parameters, to narrow down the most severe reliability challenges. Additional efforts can then be focused on internal and collaborative activities specific to addressing the top challenges, therefore reducing total operating costs. The proposed strategy is based on work conducted within a joint industry project. This paper discusses two case studies where this strategy was successfully implemented. The first case study relates to the challenges associated with installing and operating ESP systems in horizontal wells and wells with regions of high curvature. Once substantially higher ESP equipment failure rates were confirmed for wells with regions of high curvature, a focused effort by several companies was initiated to correlate equipment failure rates with more detailed well and equipment characteristics to properly establish reasonable operating envelopes. The second case study relates to the identification of a critical equipment sub-component with a relatively high failure rate in certain applications. Upon the sub-component being identified, a focused industry effort was initiated through lab testing to determine which designs may be more robust, given the specific demands of the application. The above case studies have shown that, by structuring the data collection process to include an initial limited data collection effort, key challenges can be effectively identified and then limited available resources can be leveraged through industry collaboration to undertake actions that have the potential to lower operating costs and increase production.

Although rational polynomial curves and surfaces have become standard forms in computer-aided design, they have many problems. For example, a Newton-Raphson algorithm for dealing with rational polynomial curves tends to be non-robust. This is a fatal problem. In the past, we proposed a new Newton-Raphson method for dealing with the rational polynomial curves. In the method, we homogenize the coordinates of a rational curve when it is applied to the Newton-Raphson algorithm. Then it becomes very robust.This paper proposes a method of adapting the algorithm to the Newton-Raphson method for dealing with the surface-surface intersection problem. Like the case of a curve, the Newton-Raphson algorithm was found to be very robust when the coordinates of a curved surface are homogenized. In this paper, we discuss the reason why the conventional method tends to be non-robust while the new method is robust. The conventional method deals with a rational function that always has a horizontal asymptote as well as vertical ones while the new method deals with a non-rational function and thus has no asymptote. The result of our analysis points out that the cause of the non-robustness lies in the horizontal asymptote of the rational function inherent in the conventional Newton-Raphson method. Our numerical experiments show that our method is very robust.

Numerical simulations of inviscid capillary pinchoff

In fold-and-thrust belts rocks undergo deformation as fold geometries evolve. Deformation may be accommodated by brittle fracturing, which can vary depending on structural position. We use 2D forward modelling and 3D restorations to determine strain distributions throughout folds of the Achnashellach Culmination, Moine Thrust Belt, NW Scotland. Fracture data is taken from the Torridon Group; a thick, coarse grained fluviatile sandstone deposited during the Proterozoic. Modelling infers a correlation between strain and simple curvature; we use simple curvature to infer how structural position and strain control fracture attribute variations in a fold and thrust belt.In high curvature regions, such as forelimbs, fracture intensities are high and fractures are short and oriented parallel to fold hinges. In low curvature regions fractures have variable intensities and are longer. Fracture orientations in these regions are scattered and vary over short distances. These variations do not relate to strain; data suggests lithology may influence fracturing. The strain history of fold structures also influences fracturing; structures with longer deformation histories exhibit consistent fracture attributes due to moderate-high strain during folding, despite present day low curvature. This is in contrast to younger folds with similar curvatures but shorter deformation histories. We suggest in high strain regions fracturing is influenced by structural controls, whereas in low strain regions lithology becomes more important in influencing fracturing.

Geometry of Mediating Protein Affects the Probability of Loop Formation in DNA

It is often necessary to represent a hand-drawn shape accurately. Modeling such shapes manually is both cumbersome and commercially expensive. The user's concern for curves that are easy to manipulate has been a major influence on the development of free-form curves. Rational parametric curves have been receiving considerable attention in the area of geometric modeling because any parametric polynomial curve can be expressed as a rational curve and most polynomial splines have rational extensions. Rational parametric curves can be used to model any object, like ships and airplanes, and even in the medical field for modeling the heart or other parts of the body. In object modeling, the rational cubic spline is most popular because it is the lowest degree that can define space curves and curves with points of zero curvature. The foremost objective of this work is to show how conic sections can adequately be used to represent curves and objects that were previously thought to require rational cubic splines. A single rational cubic curve is represented by two conics by splitting the rational cubic at its mid-point. The degree of smoothness has been taken into account to have a visually pleasing effect. It has been realized that the conic representation is advantageous over the rational cubic one in terms of computational requirements and shape control. All of this work is carried out on both 2D curves and 3D objects.

Carotid geometry effects on blood flow and on risk for vascular disease

This paper describes a new approach by which a blind person can visualize the approximate shape of the image by hearing sound. Nowadays a lot of image shape approximation and representation algorithms are available, but these algorithms represent image contour as a sequence of straight line segments. This work proposed a digital image shape approximation method where a shape boundary is divided & approximated to a few numbers of half-elliptical arc segments. These half elliptical arc segments are then represented by three-phoneme speech sound pattern so that on hearing this sound a blind person can get information about the shape of an object.

Polarized-Tirf-Based Monitoring of Sub-Resolution Membrane Curvature Dynamics during Clathrin-Mediated Endocytosis

On the effect of constraint parameters on the generalized displacement control method

A Comparison of Layered Tetrahedral and Cartesian meshing in Additive Manufacturing Simulation