Verification of the Geometrical Representation of Buildings in Cadastre Using UAV Photogrammetry

The aim of this study was to determine the potential benefits of using UAV-based data to verify the accuracy of the geometry of the outlines of buildings registered in a cadastral database, and to investigate the potential use of data from UAV platforms in measuring the buildings.The authors examined whether the acquisition of data from UAVs can replace field measurements or only support them. The advantages and disadvantages of such data acquisition methods, compared with more well-established measurement methods, were identified.

Numerical Simulations of Red-Blood Cells in Fluid Flow: A Discrete Multiphysics Study

In this paper, we present a methodological study of modelling red blood cells (RBCs) in shear-induced flows based on the discrete multiphysics (DMP) approach. The DMP is an alternative approach from traditional multiphysics based on meshless particle-based methods. The proposed technique has been successful in modelling multiphysics and multi-phase problems with large interfacial deformations such as those in biological systems. In this study, we present the proposed method and introduce an accurate geometrical representation of the RBC. The results were validated against available data in the literature. We further illustrate that the proposed method is capable of modelling the rupture of the RBC membrane with minimum computational difficulty.

Modifications of class-shape transformation driven by aerodynamic concerns over leading-edge region

Geometrical representation method plays a fundamental role in aerodynamic design in that it makes preparation for design space. A good design space should be composed of design variables that are more likely to attain the solution to the problem than others. This study finds that due to the characteristics of Bernstein polynomials, a conventional class-shape transformation (CST) geometrical representation method is insufficiently focused on the leading-edge region of airfoils/wings. However, more aerodynamic attention is required there because it has strong relationship with the aerodynamic performance of whole geometry. The lack of design variables assigned to the leading-edge region is likely to compromise the effort in finding better optimization results in design space. While maintaining the convenience and accuracy of conventional CST, this study proposes two types of modifications to add more aerodynamic insights into the leading-edge region: (1) an approach of supplementary vertical CST aiming to describe the leading-edge region upon the fitting result of conventional CST; (2) an approach of globally transforming airfoil surfaces into a single-value function with respect to x-direction so that the leading-edge region avoids being split up into two separate parts. With those two modifications, the leading edge can be put to the center of geometric description by rotating the local coordinate system after tackling some other issues that come with the operation. Modification 1 is intuitive, although it requires additional attention to some parameters for the continuity between the leading-edge region and other regions of the airfoil. Modification 2 is convenient to implement, but has limitations on accuracy control because the result of shape error has to account for the introduction global transforming function. Two modifications are illustrated, and their applications are discussed in the study, showing the perspective of being utilized in aerodynamic design that involves delicate difference of aerodynamic performance brought by variations of leading-edge shape.

The procedure of the Section of Pieces of Areas in Li Ye and Yang Hui’s works: genealogy of diagrams and equations

ArgumentThe study of algebra in China has often focused on the algebraic “procedure of the Celestial Source.” Its geometrical ancestors are less known. The Yigu yanduan, authored by Li Ye (1192-1279), presents the procedure alongside its two geometrical counterparts, the “Section of Pieces [of Areas]” and the “Old Procedure.” The three procedures are known to represent three generations of algorithms used to set up quadratic equations. A similar geometrical procedure appears in a treatise written by Yang Hui (second half of thirteenth century). Although the procedures look alike at first glance, the two treatises reveal different moments in their work on the relation between counting materials and geometrical representation. This study challenges their chronology trying to identify the meander of the geometrical roots of the Celestial Source. The construction of negative coefficients plays a pivotal role in this mutation and shows several layers of composition.

Clusters in Atoms and Nuclei

Small aggregates of particles, possessing different properties than those in bulk (i.e., in crystals or in nuclear matter), are reviewed here. Specifically, while some categories of atomic clusters (regular or bosonic) are in a solid state of matter and their structure possesses, more or less, definite geometric picture of packing of spheres standing for atoms, some other categories of atomic clusters (quantum or fermionic) are in a liquid (or gas) state of matter and their structure follows quantum mechanics whose only the average forms have a geometrical representation. These quantum clusters can be extended to include nucléon clusters of spheres standing for the nucléon bags with rather impressive results. All families of clusters considered together could be seen as a fifth state of matter.

Geometrical Representation of Gas Properties

The perfect gas equation, laws, principles and processes as well as the van der Waals equation for real gases are represented geometrically. Intensive and extensive properties and the standard temperature and pressure (STP) condition are shown too. Plane geometry offers a supplementary method to the piston formulation for explaining and visualizing gas properties. Several difficulties and misconceptions of students may thus be resolved.