Geometric Definition Research Articles

Uniformization of metric surfaces using isothermal coordinates


 We establish a uniformization result for metric surfaces – metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be covered by quasiconformal images of Euclidean domains is quasiconformally equivalent to a Riemannian surface. To prove this, we construct an atlas of suitable isothermal coordinates.

Thermodynamic length, geometric efficiency and Legendre invariance

Thermodynamic length is a metric distance between equilibrium thermodynamic states that asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. By means of thermodynamic length, we first evaluate the departures from ideal to real gases in geometric thermodynamics with and without Legendre invariance. In particular, we investigate ideal and real gases in the Ruppeiner and geometrothermodynamic formalisms. Afterwards, we formulate a strategy to relate thermodynamic lengths to efficiency of thermodynamic systems in both the aforementioned frameworks in the working assumption of small deviations from ideality. In this respect, we propose a geometric efficiency definition built up in analogy to quantum thermodynamic systems. We show the result that this efficiency is higher for geometrothermodynamic fluids. Moreover, we stress this efficiency could be used as a novel geometric way to distinguish ideal from non-ideal thermal behaviors. In such a way, it could be useful to quantify deviations from ideality for a variety of real gases. Finally, we discuss the corresponding applications of our recipe to classical thermodynamic systems, noticing that our findings could help geometrically grasping the nature of different metrizations on manifolds of equilibrium thermal states.

3D Printing in Alginic Acid Bath of In-Situ Crosslinked Collagen Composite Scaffolds.

Bone-tissue regeneration is a growing field, where nanostructured-bioactive materials are designed to replicate the natural properties of the target tissue, and then are processed with technologies such as 3D printing, into constructs that mimic its natural architecture. Type I bovine collagen formulations, containing functional nanoparticles (enriched with therapeutic ions or biomolecules) or nanohydroxyapatite, are considered highly promising, and can be printed using support baths. These baths ensure an accurate deposition of the material, nonetheless their full removal post-printing can be difficult, in addition to undesired reactions with the crosslinking agents often used to improve the final structural integrity of the scaffolds. Such issues lead to partial collapse of the printed constructs and loss of geometrical definition. To overcome these limitations, this work presents a new alternative approach, which consists of adding a suitable concentration of crosslinking agent to the printing formulations to promote the in-situ crosslinking of the constructs prior to the removal of the support bath. To this aim, genipin, chosen as crosslinking agent, was added (0.1 wt.%) to collagen-based biomaterial inks (containing either 38 wt.% mesoporous bioactive glasses or 65 wt.% nanohydroxyapatite), to trigger the crosslinking of collagen and improve the stability of the 3D printed scaffolds in the post-processing step. Moreover, to support the material deposition, a 15 wt.% alginic acid solution was used as a bath, which proved to sustain the printed structures and was also easily removable, allowing for the stable processing of high-resolution geometries.

Graphic analytical optimization of design and operating parameters of tires for drive wheels of agricultural machinery

Historically, machinery with wheels and tires has dominated the agricultural machinery market, despite the rapidly growing popularity of rubber tracks. However, notwithstanding the rather long development history of wheels, unresolved problems remain. Most of these are associated with a reduction in the harmful effects on the soil. The aim of this study was to reduce the levels of load on agricultural soils by the drive wheels of agricultural machinery through optimization of the geometric dimensions of the flat and deformed soil surface contact areas of an elastic wheeled vehicle. The tire used for agricultural machinery was modeled mathematically, principally using the properties of Cassinian curves. Some tire dimensions and materials do not satisfy the folding condition, which specifies that the ratio of distances used in specifying Cassinian ovals, a/c, should not exceed 1.41. Based on the geometric definition of a Cassinian oval, the shape of the contact profile surface of an elastic tire–soil interaction is determined by the ratio a/c. Different a/c ratios correspond to different tire shapes. When a/c = 1.2, the profile shape of the undertread of the tire does not satisfy the folding condition. Using the geometric properties of a common circle and Cassinian ovals, it was possible to determine a value of angle α≈48°. This angle is optimal for the tire–soil contact surface and, also satisfies the without folding condition. The presented method may be applicable to bias-ply and radial-ply tires, so it is not specifically applicable for one of these over the other.

On the Geometric Definition of Quasiconformality

On the Geometric Definition of Quasiconformality

On the geometric definition of quasiconformality

On the geometric definition of quasiconformality

Interval Algebra and Region Connection Calculus for Ontological Spatiotemporal Assembly Product Motion Knowledge Representation

Over the last decades, noticeable efforts have been made to construct design knowledge during the detailed geometric definition phase systematically. However, physical products exhibit functional behaviors, which explain that they evolve over space and time. Hence, there is a need to extend assembly product knowledge towards the spatiotemporal dimension to provide more realistic knowledge models in assembly design. Systematic semantic knowledge representation via ontology enables designers to understand the anticipated product’s behavior in advance. In this article, Interval Algebra (IA) and Region Connection Calculus (RCC) are investigated to formalize and construct ontological spatiotemporal assembly product motion knowledge. IA is commonly used to represent the temporality between two entities, while RCC is more appropriate to represent the ‘part-to-part’ relationships of two topological spaces. This paper discusses the roles of IA and RCC and presents a case study of a nutcracker assembly model’s behavior. The assembly product motion ontology with the aid of IA and RCC is evaluated using a task-based approach. The evaluation shows the added value of the developed ontology compared to others published in the literature.

Development of Detailed FE Numerical Models for Assessing the Replacement of Metal with Composite Materials Applied to an Executive Aircraft Wing

This work provides a feasibility and effectiveness analysis, through numerical investigation, of metal replacement of primary components with composite material for an executive aircraft wing. In particular, benefits and disadvantages of replacing metal, usually adopted to manufacture this structural component, with composite material are explored. To accomplish this task, a detailed FEM numerical model of the composite aircraft wing was deployed by taking into account process constraints related to Liquid Resin Infusion, which was selected as the preferred manufacturing technique to fabricate the wing. We obtained a geometric and material layup definition for the CFRP components of the wing, which demonstrated that the replacement of the metal elements with composite materials did not affect the structural performance and can guarantee a substantial advantage for the structure in terms of weight reduction when compared to the equivalent metallic configuration, even for existing executive wing configurations.

Distinguishing Weak and Strong Hydrogen Bonds in Liquid Water-A Potential of Mean Force-Based Approach.

The ability to form hydrogen bonds is one of the most important factors behind water's many anomalous properties. However, there is still no consensus on the hydrogen bond structure of liquid water, including the average number of hydrogen bonds in liquid water. We use molecular dynamics simulations of the polarizable iAMOEBA water model for investigating the hydrogen bond characteristics of liquid water over a wide range of temperatures and pressures. Geometric definitions of a hydrogen bond often use a rectangular region on the plane of hydrogen bond distances and angles. In this work, we find that an elliptical region is more appropriate for the identification of hydrogen bonds, based on statistically favorable molecular configurations. The two-dimensional potential of mean force (PMF) landscape along the hydrogen bond distance (O-H) and angle (O-H-O) is calculated for identifying the statistically favored molecular configurations, which is then used for defining hydrogen bond formation as well as the strength of a hydrogen bond. We further propose a new approach to characterize the hydrogen bonds as strong when the PMF is lower than -2 kT. Using this definition, a consistent explanation for the different average numbers of hydrogen bonds in water is obtained in agreement with the literature. Simulations are also performed with the rigid and nonpolarizable TIP4P/2005 water model. Both water models are qualitatively consistent in predicting the distribution of double-, single-, and non-donor configurations, in line with experimental data, while the iAMOEBA water model yields more quantitatively precise results, including a 10-15% double-donor fraction at 90 °C and 1 atm. The method is also demonstrated to be applicable to the recent, and more general, three-dimensional PMF-based definition of hydrogen bonds.

Moving mesh methods for two-phase flow systems: Assessment, comparison and analysis

We seek to assess the key aspects of two modern moving mesh approaches for simulating two-phase flows where a thin explicit interface separates the two fluids within the context of “one-fluid” formulation. Both methods discretize the fluid equations through the Finite Element (FE) method using the Arbitrary Lagrangian-Eulerian (ALE) framework, therefore a complex moving mesh scheme is achieved. These methods are supported by a spatial Heaviside function which locates the interface between fluids in the domain of interest. Despite a sharp geometrical definition of the tracked interface, one methodology requires a smooth regularization of the Heaviside function to avoid undesirable numerical instabilities. On the other hand, the second method bypass such an artificial requirement but an advanced remeshing algorithm is demaded to maintain the simulation. Several important test cases are used as benchmark to assess the capabilities of both approaches such as the oscillating drop and the Zalesak’s disk test where fundamental parameters are evaluated and more challenging two-phase flows such as the rising of single bubbles and microscale flows in capillaries. A comparison is then made to evaluate the important aspects of each model and an accurate analysis is made to quantify the errors associated to important parameters in two-phase flows such as surface tension, liquid film thickness, interfacial waves, interface deformation and bubble/drop shape.

FWMR-II: a modular link-type rope-climbing robot with the finger-wheeled mechanism

Purpose The rope-climbing robot that can cling to a rope for locomotion has been a popular piece of equipment for some overhead applications due to its high flexibility. In view of problems left by existing rope-climbing robots, this paper aims to propose a new-style rope-climbing robot named Finger-wheeled mechanism robot (FWMR)-II to improve their performance. Design/methodology/approach FWMR-II adopts a modular and link-type mechanical structure. With the finger-wheeled mechanism (FWM) module, the robot can achieve smooth and quick locomotion and good capability of obstacle-crossing on the rope and with the link module based on a spatial parallel mechanism, the robot adaptability for rope environments is improved further. The kinematic models that can present configurations of the FWM module and link module of the robot are established and for typical states of the obstacle-crossing process, the geometric definitions and constraints that can present the robot position relative to the rope are established. The simulation is performed with the optimization calculating method to obtain the robot adaptability for rope environments and the experiment is also conducted with the developed prototype to verify the robot performance. Findings From the simulation results, the adaptability for rope environments of FWMR-II are obtained and the advantage of FWMR-II compared with FWMR-I is also proved. The experiment results give a further verification for the robot design and analysis work. Practical implications The robot proposed in this study can be used for inspection of power transmission lines, inspection and delivery in mine and some other overhead applications. Originality/value An ingenious modular link-type robot is proposed to improve existing rope-climbing robots and the method established in this study is worthy of reference for obstacle-crossing analysis of other rope-climbing robots.

Structural design of reinforced concrete buildings based on deep neural networks

In shear wall building design, the initial process requires the interaction between the architectural and structural engineering groups to define the adequate wall layout, usually done with a trial-and-error procedure to fulfill architectural and engineering needs, slowing down the design process. For the engineering analysis, first, the wall thickness and length are required to check the building deformation limits, base shear strength, among other parameters. For this reason, the present investigation develops a structural design platform for reinforced concrete wall buildings that uses a deep neural network to predict the wall’s thickness and length based on previous architectural and engineering projects. The study includes, in the first place, the surveying of the architectural and engineering plans for a total of 165 buildings constructed in Chile; the generated database has the geometric and topological definition of the walls and the slabs. As a second stage, a model was trained for the regression of the wall segments’ thickness and length, making use of a feature vector that models the variation between the architectural and the engineering plans for a set of conditions such as the thickness, connectivity (vertical and horizontal), area, wall density, the distance between elements, wall angles, foundation soil type, among other engineering parameters. The regression model results in terms of R2-value are 0.995 and 0.994 for the predicted wall thickness and length, respectively, proving to be a reliable method for the initial engineering wall definition.

Turbopump Design: Comparison of Numerical Simulations to an Already Validated Reduced-Order Model

The article expands on the ongoing assessment of the reduced order model proposed by some of the authors for the geometric definition and noncavitating performance evaluation in the preliminary design and parametric optimization of mixed-flow centrifugal turbopumps. Some of the dynamically most significant predictions of the model are compared with the experimentally validated URANS (Unsteady Reynolds-Averaged Navier-Stokes) simulations of the non-cavitating flow through a typical six-bladed unshrouded mixed-flow turbopump for liquid propellant rocket engines operating at both design and off-design flow conditions and different values of the impeller clearance. The observed discrepancies can be explained in terms of the simplifying assumptions introduced for the development of the model and their relative magnitude (< ±10%) does not adversely interfere with the accurate prediction of the turbopump performance over a wide range of operating conditions above and below design flow rate. Together with earlier experimental validations, the results dramatically confirm the capability of the proposed model to generate useful engineering solutions of the turbopump preliminary design problem at a negligible fraction of the computational cost required by 3D numerical simulations.

Design and analysis of a modular rope-climbing robot with the finger-wheeled mechanism

The rope-climbing robot that can cling to a rope for locomotion has been a popular equipment for some inspection applications due to its high flexibility. In this study, a modular rope-climbing robot with the finger-wheeled mechanism is proposed. Due to the ingenious finger-wheeled mechanism and the modular structure, the robot can achieve smooth and quick movement and good capability of obstacle-crossing on the rope and has a high adaptability for different rope environments. On the basis of introducing the robot mechanism, the geometric definitions and descriptions that can present the robot configuration and position relative to the rope are established. Aiming at three typical states during obstacle-crossing, the geometric and force analysis is performed to establish the constraint equations for the robot, and then the simulation is carried out with the optimization calculating method to solve the geometric variables and external forces of the robot that can be used for the robot design work. Finally, the robot prototype is developed based on the design and analysis work, and the experiment is conducted to verify the performance of the robot.

SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions

We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form A, by a superalgebra-valued polyform tilde{A} mixing exterior-forms of all degrees and satisfying the chiral self-duality condition tilde{A} =^{ast }{tilde{A}}_{chi } , where χ denotes the superalgebra grading operator. This superconnection contains Yang-Mills vectors valued in the even Lie subalgebra, together with scalars and self-dual tensors valued in the odd module, all coupling only to the charge parity CP-positive Fermions. The Fermion quantum loops then induce the usual Yang-Mills-scalar Lagrangian, the self-dual Avdeev-Chizhov propagator of the tensors, plus a new vector-scalar-tensor vertex and several quartic terms which match the geometric definition of the supercurvature. Applied to the SU(2/1) Lie-Kac simple superalgebra, which naturally classifies all the elementary particles, the resulting quantum field theory is anomaly-free and the interactions are governed by the super-Killing metric and by the structure constants of the superalgebra.

The braid group and its presentation

In this paper, we recall the geometric definition of the braid group by Emil Artin and we give a complete, elementary geometric/topological proof of the standard presentation of the braid group on [Formula: see text] strings.

Students' conceptions of the definitions of congruent and similar triangles

This study addresses high school students’ conceptions of mathematical definitions of congruent and similar triangles. The findings indicate that many of the participants differentiated between definitions and theorems and did not always accept the congruent and similar triangles theorems as formal definitions of congruency and similarity. Based on the participants’ explanations of their responses and from the interviews performed, it appears that two issues prevented some participants from accepting or preferring these theorems as definitions. The first was a concern for uniformity: there is only one known and accepted definition of each concept. The second was a focus on the essence of the concepts: the essence of the concepts of similarity and congruency lies primarily in the lengths of the sides of a triangle. The students who accepted these theorems as formal definitions explained their reaction as arising from the equivalence and from the theorems including necessary and sufficient attributes. Students’ difficulties in understanding the characteristics and roles of mathematical definitions of geometric concepts affected their understandings of mathematical and geometric definitions. This behaviour indicates a tendency to interpret the content of theorems incorrectly and an inability to unpack the logical structure of the theorem.

Open data repositories and Geo Small Data for mapping the wildfire risk exposure in wildland urban interface (WUI) in Spain: A case study in the Valencian Region

The risk of forest fires in areas of wildland urban-interface (WUI.) is increasing due to the increase in urbanized areas and the progressive abandonment of traditional farming and forest uses. The global increase in catastrophic episodes in regions with a Mediterranean climate is worrying. Resilient towns and villages have given way to extensive and scattered residential estates that are in contact with forest fuel. These changes in the landscape when added to those of the climate, increase the danger of what some call ‘igneous storms’. The risk in many areas has increased greatly in the last few decades. It is necessary to limit the growing exposure to this type of risk – and geographical information resources are essential for determining the territorial magnitude of the problem. Official libraries offering remote sensing data or geographical databases on land use and land cover (LULC) may be the best option (although accessing this data is complex for many end users). This research proposes identifying areas exposed to fire risk in the wildland-urban interface (WUI) through the automated integration of massive data from official geographic information sources. The application of this study to the region of Valencia (Spain) shows that the integration of these official sources of geographical information can achieve the objective at a detailed scale with relatively short processing times and for large geographical areas (approximately 8 h required to process about 70 Gb of LIDAR data). Geo Small Data techniques for the process of large datasets and its application to the objective of the study have been the best way to automate the analysis of lidar point clouds, with more than 5 billion echoes, through the use of free and open tools, containerization technologies, parallel processing and specific python libraries for geospatial data management. The LIDAR data has provided the necessary geometric definition to complement and improve the WUI area map from the reclassification of hundreds of thousands of polygons from the official Spanish land use geodatabase (SIOSE), achieving a map scale of more than 1: 25,000, for its part, the quality of the SIOSE geodatabase has allowed us to reduce the total LIDAR data to process by 97.8%.

Can Boosted Randomness Mimic Learning Algorithms of Geometric Nature? Example of a Simple Algorithm That Converges in Probability to Hard-Margin SVM.

In the light of the general question posed in the title, we write down a very simple randomized learning algorithm, based on boosting, that can be seen as a nonstationary Markov random process. Surprisingly, the decision hyperplanes resulting from this algorithm converge in probability to the exact hard-margin solutions of support vector machines (SVMs). This fact is curious because the hard-margin hyperplane is not a statistical solution, but a purely geometric one-driven by margin maximization and strictly dependent on particular locations of some data points that are placed in the contact region of two classes, namely the support vectors. The proposed algorithm detects support vectors probabilistically, without being aware of their geometric definition. We give proofs of the main convergence theorem and several auxiliary lemmas. The analysis sheds new light on the relation between boosting and SVMs and also on the nature of SVM solutions since they can now be regarded equivalently as limits of certain random trajectories. In the experimental part, correctness of the proposed algorithm is verified against known SVM solvers: libsvm, liblinear, and also against optimization packages: cvxopt (Python) and Wolfram Mathematica.

Sexual dimorphism from third cervical vertebra (C3) on lateral cervical radiograph: A 2-dimensional geometric morphometric approach

Abstract Sex identification is essential for the establishment of an accurate biological profile from skeletal remains in forensic anthropology. Conventional method using calipers is time-consuming and associated with a high margin of error especially in the case of highly fragmented skeletal remains. Geometric morphometric method is an approach which utilizes qualitative and quantitative description of biological forms according to geometric definitions of their shape. This study aimed to determine sexual dimorphism of third cervical (C3) vertebra on the lateral cervical radiograph by geometric morphometric method. Lateral cervical radiographs of 432 samples comprising of 262 males and 170 females of known individuals were retrieved retrospectively. The samples were adult Malaysian population aged from 20 to 60 years old. Eleven 2-dimensional (2D) landmarks were applied on the digitalized radiographs by TPSDig2 (Version 2.31) software. Geometric morphometric analysis was performed by MorphoJ software. Procrustes ANOVA showed that centroid size and shape are significantly different with p