A Square Equal-Area Map Projection with Low Angular Distortion, Minimal Cusps, and Closed-Form Solutions

A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously published square equal-area projection. Thus, the new projection has lower angular distortion than any previously published square equal-area projection with a closed-form solution. Utilizing a quincuncial arrangement, the new projection places the north pole at the center of the square and divides the south pole between its four corners; the projection can be seamlessly tiled. The existence of closed-form solutions makes the projection suitable for real-time visualization applications, both in cartography and in other areas, such as for the display of panoramic images.

Image-Based Angular Distortion Metric of Map Projections by Using Surface Fitting for Noise Reduction

Measuring, analyzing, reducing, and optimizing distortions in map projections is important in cartography. In this study, we introduced a novel image-based angular distortion metric based on the previous spherical great circle arcs-based metric. Images with predefined patterns were used to generate distorted images using mapping software. The generated distorted images with known patterns were then exploited to calculate the proposed angular distortion metric. The mapping software performed the underlying transformation of map projections. Therefore, there was no direct explicit dependence on the forward equations of the map projections in our proposed metric. However, there were fairly large computation errors in the ordinary image-based approach without special correction. To reduce the error, we introduced surface-fitting-based noise reduction in our approach. We established and solved systems of linear equations based on bivariate polynomial functions in the process of noise reduction. Sufficient experiments were made to validate the proposed image-based metric and the accompanying noise reduction approach. In the experiment, the NASA G.Projector was employed as the mapping software for evaluating more than 200 map projections. Experimental results demonstrated that the proposed image-based approach and surface fitting-based noise reduction are feasible and practical for the evaluation of the angular distortion of map projections.

Karst Collapse Risk Zonation and Evaluation in Wuhan, China Based on Analytic Hierarchy Process, Logistic Regression, and InSAR Angular Distortion Approaches

The current study presents a detailed assessment of risk zones related to karst collapse in Wuhan by analytical hierarchy process (AHP) and logistic regression (LR) models. The results showed that the LR model was more accurate with an area under the receiver operating characteristic (ROC) curve of 0.911 compared to 0.812 derived from the AHP model. Both models performed well in identifying high-risk zones with only a 3% discrepancy in area. However, for the medium- and low-risk classes, although the spatial distribution of risk zoning results were similar between two approaches, the spatial extent of the risk areas varied between final models. The reliability of both methods were reduced significantly by excluding the InSAR-based ground subsidence map from the analysis, with the karst collapse presence falling into the high-risk zone being reduced by approximately 14%, and karst collapse absence falling into the karst area being increased by approximately 6.5% on the training samples. To evaluate the practicality of using only results from ground subsidence maps for the risk zonation, the results of AHP and LR are compared with a weighted angular distortion (WAD) method for karst risk zoning in Wuhan. We find that the areas with relatively large subsidence horizontal gradient values within the karst belts are generally spatially consistent with high-risk class areas identified by the AHP- and LR-based approaches. However, the WAD-based approach cannot be used alone as an ideal karst collapse risk assessment model as it does not include geological and natural factors into the risk zonation.

Bias deployable grids with horizontal compound scissor-like elements: A geometric study of the folding/deployment process

Bias deployable structural units are two-way structures arranged in a rotational pattern with respect to the edges. They have interesting advantages such as robust three-dimensional operation with supports around their entire base perimeter and the exclusive use of load-bearing scissor-like elements (SLEs). However, they do not have edge trims and their resistance to angular distortion is limited. This article proposes a series of deployable bi-stable structures that address these problems and incorporate new, resilient features. A method of analysing the incompatibilities of the structural unit is developed based solely on the geometric study of the deployment process, which allows the level of incompatibility of the proposal to be graduated, varying from stress-free structures to bi-stable structures. A kinematic model of one of the proposals allows the research undertaken to be contrasted.

Assessment of Reclamation-induced Consolidation Settlement Considering Stratigraphic Uncertainty and Spatial Variability of Soil Properties

Consolidation analysis is a key task for reclamation design. Although consolidation is a long-term process, acceleration of consolidation is often preferred for speeding up the reclamations. Before proposing measures to accelerate consolidation and reclamation process, it is imperative to have an accurate prediction of consolidation settlement for fine-grained materials, which is greatly affected by spatial distribution of subsurface zones with different soil types (i.e., stratigraphic heterogeneities and uncertainty) and spatial variability of soil properties. In current practice, calculation of consolidation settlement often uses simplified stratigraphic boundaries and deterministic consolidation parameters without considering stratigraphic uncertainty or soil property spatial variability. The oversimplified practice might result in unconservative estimations of consolidation settlement and pose threats to safety and serviceability of constructed facilities on reclaimed lands. In this study, a stochastic framework is proposed for consolidation settlement assessment with explicit modeling of stratigraphic uncertainty and spatial variability of soil properties by machine learning and random field simulation from limited site investigation data. The proposed method effectively generates multiple realizations of geological cross-section and random field samples of geotechnical properties from limited measurements and offers valuable insights into spatial distribution of the estimated total primary consolidation settlement curves and angular distortion.

Experimental Investigation on Turbulent Flow Deviation in a Gas-Particle Corner-Injected Flow

An experimental model of a corner-injected flow is built to investigate the turbulent flow behavior by employing the PIV technique. The influences of the ideal tangential circle, the additive particles and the initial gas mass flux on the corner-injected flow are analyzed systematically. To be specific, the flow deviation, the velocity profile, the vortex evolution and the turbulent flow development are discussed quantitatively. The influences of the increasing ideal tangential circle on the turbulent jet deviation are shortened gradually, and the impinging circles are obviously narrowed with the injection of particles. The gas-particle corner-injected flow can obtain a good rotation when the ideal tangential circle is 0.25 times the width of the impinging chamber. The momentum decay of the corner-injected flow diminishes with the increasing ideal tangential circle and the decreasing initial gas velocity. The rotation strength of the vortex is more affected by the injection of laden particles, while the angular distortion enhances when increasing the ideal tangential circle. The increasing initial gas mass flux plays a dominant role in the development of the corner-injected flow, secondly the increasing ideal tangential circle, and last the injection of particles. All these findings can provide theoretical support in the design of a corner-fired furnace.