Geometric Similarity Measurement Method for Micro Scene Generalization

Geometric similarity plays an important role in geographic information retrieval, map matching, and data updating. Many approaches have been developed to calculate the similarity between simple features. However, complex group objects are common in map and spatial database systems. With a micro scene that contains different types of geographic features, calculating similarity is difficult. In addition, few studies have paid attention to the changes in a scene’s geometric similarity in the process of generalization. In this study, we developed a method for measuring the geometric similarity of micro scene generalization based on shape, direction, and position. We calculated shape similarity using the hybrid feature description, and we constructed a direction Voronoi diagram and a position graph to measure the direction similarity and position similarity. The experiments involved similarity calculation and quality evaluation to verify the usability and effectiveness of the proposed method. The experiments showed that this approach can be used to effectively measure the geometric similarity between micro scenes. Moreover, the proposed method accounts for the relationships amongst the geometrical shape, direction, and position of micro scenes during cartographic generalization. The simplification operation leads to obvious changes in position similarity, whereas delete and merge operations lead to changes in direction and position similarity. In the process of generalization, the river + islands scene changed mainly in shape and position, the similarity change in river + lakes occurred due to the direction and location, and the direction similarity of rivers + buildings and roads + buildings changed little.

Revealing Free Energy Landscape from MD Data via Conditional Angle Partition Tree

Deciphering the free energy landscape of biomolecular structure space is crucial for understanding many complex molecular processes, such as protein-protein interaction, RNA folding, and protein folding. A major source of current dynamic structure data is Molecular Dynamics (MD) simulations. Several methods have been proposed to investigate the free energy landscape from MD data, but all of them rely on the assumption that kinetic similarity is associated with global geometric similarity, which may lead to unsatisfactory results. In this paper, we proposed a new method called Conditional Angle Partition Tree to reveal the hierarchical free energy landscape by correlating local geometric similarity with kinetic similarity. Its application on the benchmark alanine dipeptide MD data showed a much better performance than existing methods in exploring and understanding the free energy landscape. We also applied it to the MD data of Villin HP35. Our results are more reasonable on various aspects than those from other methods and very informative on the hierarchical structure of its energy landscape.

Integrating Geometric Data into Topology Optimization via Neural Style Transfer

This research proposes a novel topology optimization method using neural style transfer to simultaneously optimize both structural performance for a given loading condition and geometric similarity for a reference design. For the neural style transfer, the convolutional layers of a pre-trained neural network extract and quantify characteristic features from the reference and input designs for optimization. The optimization analysis is evaluated as a single weighted objective function with the ability for the user to control the influence of the neural style transfer with the structural performance. As seen in architecture and consumer-facing products, the visual appeal of a design contributes to its overall value along with mechanical performance metrics. Using this method, a designer allows the tool to find the ideal compromise of these metrics. Three case studies are included to demonstrate the capabilities of this method with various loading conditions and reference designs. The structural performances of the novel designs are within 10% of the baseline without geometric reference, and the designs incorporate features in the given reference such as member size or meshed features. The performance of the proposed optimizer is compared against other optimizers without the geometric similarity constraint.

The reflection of a blast wave by a very intense explosion

We demonstrate that the geometric similarity of Taylor’s blast wave persists beyond reflection from an ideal surface. Upon impacting the surface, the spherical symmetry of the blast wave is lost but its cylindrical symmetry endures. As the flow acquires dependence on a second spatial dimension, an analytic solution of the Euler equations becomes elusive. However, the preservation of axisymmetry, geometric similarity and planar symmetry in the presence of a mirror-like surface causes all flow solutions to collapse when scaled by the height of burst (HOB) and the shock arrival time at the surface. The scaled blast volume for any yield, HOB and ambient air density follows a single universal trajectory for all scaled time, both before and after reflection.

Effects of geometric similarity ratio on the disturbance amplitude of shock-wave front in viscosity measurement

Geometric similarity ratio is one of the important factors that affects the disturbance amplitude of shock-wave front in viscosity measurement. In this paper, the Euler difference scheme of two-dimensional (2D) equations of viscous fluid mechanics is used to simulate the disturbance amplitude damping curves under different geometric similarity ratios, and the corresponding numerical solutions are shown. The samples of aluminum shocked to 80 GPa are taken as an example. The simulation results show that the initial conditions, material viscosity, wavelength, and sample geometric similarity ratio affect the evolution of the shock front sine wave disturbance. For flyer-impact flow field, the phase shift increases from 0 to a certain value with the viscosity coefficient for sample with wavelength [Formula: see text] mm and geometric similarity ratio [Formula: see text], 0.1. So, the geometric similarity method can be used to measure the viscosity of material. But it is found that the phase shift is sensitive to the geometric similarity ratio, which should be considered in Zaidel’s equation. So, some flyer-impact experiments will be carried out to determine the simulation results, and find the quantity relation of phase shift and viscosity of material in the future investigation.

Geometric similarity of the twin collapsed glaciers in the west Tibet

Two adjacent glaciers collapsed consecutively in the Western Xizang Autonomous Region, China, on July 17 and September 21, 2016, presumably triggered by relatively intensive climate change in this region, leading to massive downstream ice and mud avalanches. After these twin glacier collapses, there have been many researches, which mainly focus on the physical characteristics of these two glaciers while lack the differences between them and the other glaciers. In this study, the geometric features and energy distribution along the glacier centerlines are investigated to identify the differences between these two collapsed glaciers and other glaciers in the western Tibetan Plateau. The anomaly of climate change is presumed to be the trigger of the twin glacier collapses in accordance with existing research results, whereas in this study, the striking geometric similarity between the centerlines of the twin glaciers, which is quantitatively interpreted by the Fréchet distance among the glacier centerlines, unearth some novel mechanisms. The essential point in these new mechanisms is the energy distribution along the glacier centerlines. A hypothesis based on the principle of energy conservation is derived to demonstrate the mechanisms and dynamic processes of the glacier collapses. Furthermore, on the basis of the geometric similarity and energy distribution of the glacier centerlines, a risk assessment of glacier collapse in the western Tibetan Plateau is implemented to facilitate glacier disaster prevention.