Dynamic Geometry Research Articles

Investigation of Lost Circulation and Wellbore Strengthening During Drilling Petroleum Wells: An Overview

Lost circulation is the partial or complete loss of drilling fluid into a formation. It is among the major non-productive time events in drilling operations. Most of the lost circulation events are fracture initiation and propagation problems, occurring when the fluid pressure in a wellbore is high enough to create fractures in a formation. Wellbore strengthening is a common method to prevent or remedy lost circulation problems. Although many successful field applications have been reported, the fundamental mechanisms of wellbore strengthening are still not fully understood. There is still a lack of functional models in the drilling industry that can sufficiently describe fracture behavior in lost circulation events and wellbore strengthening. A finite-element framework was first developed to simulate lost circulation while drilling. Fluid circulation in the well and fracture propagation in the formation were coupled to predict dynamic fluid loss and fracture geometry evolution in lost circulation events. There are two common wellbore strengthening treatments, namely, preventive treatments based on plastering wellbore wall with mudcake before fractures occur and remedial treatments based on bridging/plugging lost circulation fractures. Two analytical models were developed for the investigation of preventive and remedial wellbore strengthening. The models developed and analyses conducted in this paper present a useful step towards the understanding of the fundamentals of lost circulation and wellbore strengthening, and provide improved guidance for lost circulation prevention and remediation.

Shaking table study on seismic behavior of MSE wall with inclined backfill soils reinforced by polymeric geostrips

In this study, the seismic behavior of a mechanically stabilized earth (MSE) wall with inclined backfill is investigated under sinusoidal acceleration excitations using a series of 1-g shaking table tests performed on the MSE model of 150 cm in height reinforced with polymeric geostrips. The effects of the stiffness of the reinforcement and slope angles of the backfill soil on the acceleration amplification factor (RMSA), the lateral displacement of the wall, the surface displacement of the backfill, the distribution of dynamic earth pressure along the height of reinforced wall and the strain distributions on the surfaces of the polymeric geostrips in three planes of the wall are investigated. The experimental results show that the dynamic earth pressure determined by traditional pseudo-static approaches leads to overestimated values. In addition, increasing the inclination angle of backfill soil results in the increase of surface settlement, lateral wall displacements, soil dynamic earth pressures, acceleration amplification factors and strains on the polymeric geostrip materials. The stiffness of the polymeric geostrip material has a negligible effect on the displacement, dynamic earth pressures and failure surface geometry.

Una orquestación instrumental para un curso en línea a nivel universitario

In this article, we present a proposal for instrumental orchestration that organizes the use of technological environments in online mathematics education, in the synchronous mode for the concepts of eigenvalue and eigenvector of a first linear algebra course with engineering students. We used the instrumental orchestration approach as a theoretical framework to plan and organize the artefacts involved in the environment (didactic configuration) and the ways in which they are implemented (exploitation modes). The activities were designed using interactive virtual didactic scenarios, in a dynamic geometry environment, guided exploration worksheets with video and audio recordings of the work of the students, individually or in pairs. The results obtained are presented and the orchestrations of a pedagogical sequence to introduce the concepts of eigenvalue and eigenvector are briefly discussed. This work allowed us to identify new instrumental orchestrations for online mathematics education.

Connecting Digital and Physical Resources for Enriching Heuristic Strategies in Geometry Problem Solving. Theoretical Considerations and Empirical Findings

There has been a large amount of research about the impact of dynamic geometry software (DGS) on the learning of mathematics mainly related to different representations of mathematical concepts and functional dependences. This paper goes beyond these investigations by suggesting meaningful connection and integration of DGS with physical resources as 3D prints. It is evocative to investigate which students’ general and subject-specific heuristic strategies in geometry problem solving can be identified when connecting diverse types of resources. Though the importance of diverse heuristic strategies in problem solving has already been acknowledged in literature, effects of a meaningful connection of different digital and tangible resources on the widening and broadening the spectrum of strategies have not been explored to a satisfactory amount. Empirical results of this undertaken design based research with prospective high school mathematics teachers contribute to consolidation of the existing body of theoretical knowledge and open new question for further research about the relation: resources-strategies.

SolCelSim: simulation of charge transport in solar cells developed in Comsol Application Builder

ABSTRACT A user-friendly software SolCelSim is introduced for the simulation of the charge transport in a solar cell with an arbitrary number of layers. Various recombination mechanisms, types of transport through internal layer interfaces and conditions at the contacts can be chosen. A wide range of the measurement methods available for the solar cells such as photocurrent-voltage, incident photon-to-current efficiency and impedance spectroscopy can be simulated with SolCelSim. Any parameter of the layers can be swept automatically during the simulation in order to obtain the dependence of the simulation results on the particular parameter values. Import/export buttons for the experimental/simulated data are provided to facilitate comparison between the measurements and simulations. The application provides a convenient entry-point for the experimentally oriented researchers in order to execute the drift-diffusion simulation of their solar cell devices. Furthermore, SolCelSim provides an example of advanced use of Comsol Application Builder in the development of complex Comsol applications with dynamic geometry, import/export and error handling features.

Using Technology With Future Teachers Of Primary School Mathematics: A Glimpse Into An American Experience

The paper describes the author’s experience in using technology within mathematics content and methods (undergraduate and graduate) courses for prospective teachers of primary grades (age 5–10). The main pedagogical idea behind the courses is to change pre-teachers’ perception of mathematics as a subject matter most people predictably dislike. It is suggested that technology can assist instructors in making mathematics an enjoyable subject matter without sacrificing content. The paper provides examples of using Excel, Wolfram Alpha, dynamic geometry software, computer graphing program, and the Online Encyclopedia of Integer Sequences. In conclusion, solicited comments by teacher candidates about their experience of learning computer assisted mathematics are shared.

Dealing with Degeneracies in Automated Theorem Proving in Geometry

We report, through different examples, the current development in GeoGebra, a widespread Dynamic Geometry software, of geometric automated reasoning tools by means of computational algebraic geometry algorithms. Then we introduce and analyze the case of the degeneracy conditions that so often arise in the automated deduction in geometry context, proposing two different ways for dealing with them. One is working with the saturation of the hypotheses ideal with respect to the ring of geometrically independent variables, as a way to globally handle the statement over all non-degenerate components. The second is considering the reformulation of the given hypotheses ideal—considering the independent variables as invertible parameters—and developing and exploiting the specific properties of this zero-dimensional case to analyze individually the truth of the statement over the different non-degenerate components.

A Virtual-Reality Imaging Analysis of the Dynamic Aortic Root Anatomy

PurposeTo measure and explore complex cardiac anatomy in research and preoperative simulation, a virtual imaging technology—the Vesalius 3D suite (PS Medtech, Amsterdam, Netherlands)—combines Vesalius three-dimensional (3D) image-processing software with an optic-tracking navigation system running PST-Client software. We present a novel method of evaluating dynamic aortic root geometry in vivo using this visualization system. DescriptionBased on electrocardiography-gated cardiac computed tomography data in systole and diastole, images of the aortic root in a healthy adult were reconstructed for 3D visualization. Virtual interaction tools were used to explore and measure the aortic root structures. EvaluationVirtually reconstructed images revealed the aortic root internal structures in exquisite detail. Highly accessible 3D interpretation promptly permitted precise measurements of repair-relevant anatomic parameters, including geometrically complex curves of the aortic root wall and dynamic changes in the aortic valves. Measurement accuracy examined against a known prosthesis showed within 1 mm of error (less than 0.5%). ConclusionsThis technology may promote understanding of aortic root form and function, and facilitate valve-sparing surgery, and seems valuable for 3D exploration and measurement of cardiac anatomy in vivo.

Using Dynamic Geometry Software to Enhance Specialized Content Knowledge: Pre-Service Mathematics Teachers’ Perceptions

The study aimed to expose how pre-service teachers perceived the value of an inquiry-based geometrical task with dynamic geometry software for increasing and deepening their understanding of the task itself, and for heightening their mathematical, pedagogical, and technological knowledge in the case of reflection and transformation. Twenty-seven pre-service teachers studying to become middle-school (junior high) mathematics teachers were assigned an inquiry-based geometrical task to explore – both by conventional, low-tech means (paper and pencil) and then in a dynamic geometry software (DGS) environment – the properties of objects formed by reflections in polygons (triangles and quadrilaterals) and to offer conjectures and proofs regarding the final polygon’s shape and area concerning the original. The results show that the majority of participants indicated that DGS provided a valuable instrument for revising and expanding their knowledge, that the assignment demonstrated the value that technological tools have in teaching and learning processes, and the importance of adapting learning tasks in geometry to a dynamic geometry environment for expanding and deepening geometrical and pedagogical knowledge and reasoning skills.

Developing the meaning of volume and deriving the volume of hemispheres with dynamic geometry

ABSTRACT In this paper, we introduce a technology-enhanced pedagogical sequence for supporting lower secondary school students’ sense-making of the concept of volume in a non-procedural and non-formula-driven way. Specifically, we illustrate a novel approach of using dynamic geometric environment (DGE) to introduce the meaning of volume and then deriving the volume of a hemisphere with minimal algebra but simple trigonometry. This method aims to support students’ geometrical reasoning through comparing the volume of different three-dimensional shapes and analysing their cross sections two-dimensionally, thus drawing on the concept of area. We highlight the affordances of the designed DGE sketches for fostering a dynamic conception of volume.

Construction of cyclic quadrilateral: A pre-service teacher’s journey from subsets to the generic concept through instrumentation of a dynamic technology

This case study examines instrumented techniques of a pre-service mathematics teacher when utilising a dynamic geometry system (DGS) for the construction of cyclic quadrilaterals. Equally, it investigates her understanding of the hierarchical relations between the constructed cyclic quadrilaterals. For this aim, the hierarchical classification and instrumental genesis constitute the theoretical framework of our study. The data was collected through task-based interviews in which the participant was asked to construct the cyclic quadrilateral without using the circle tool in DGS. Data analysis was carried out to examine the participant’s development of construction strategies related to her instrumented techniques and her reasoning regarding the properties of different cyclic quadrilaterals. The analysis showed that the participant’s initial instrumented techniques enabled her to construct subsets of the cyclic quadrilaterals. Also, the process of reaching the most inclusive cyclic quadrilateral affected both her instrumented techniques and her understanding about the hierarchical relations between the constructed quadrilaterals.

Method for Processing Graph Degeneracy in Dynamic Geometry Based on Domain Design

Method for Processing Graph Degeneracy in Dynamic Geometry Based on Domain Design

On the 3D Nature of the Magpie (Aves: Pica pica) Functional Hindlimb Anatomy During the Take-Off Jump.

Take-off is a critical phase of flight, and many birds jump to take to the air. Although the actuation of the hindlimb in terrestrial birds is not limited to the sagittal plane, and considerable non-sagittal plane motion has been observed during take-off jumps, how the spatial arrangement of hindlimb muscles in flying birds facilitates such jumps has received little attention. This study aims to ascertain the 3D hip muscle function in the magpie (Pica pica), a bird known to jump to take-off. A musculoskeletal model of the magpie hindlimb was developed using μCT scans (isotropic resolution of 18.2 μm) to derive bone surfaces, while the 3D muscle path definition was further informed by the literature. Function was robustly characterized by determining the 3D moment-generating capacity of 14 hip muscles over the functional joint range of motion during a take-off leap considering variations across the attachment areas and uncertainty in dynamic muscle geometry. Ratios of peak flexion-extension (FE) to internal-external rotation (IER) and abduction-adduction (ABD) moment-generating capacity were indicators of muscle function. Analyses of 972 variations of the 3D muscle paths showed that 11 of 14 muscles can act as either flexor or extensor, while all 14 muscles demonstrated the capacity to act as internal or external rotators of the hip with the mean ratios of peak FE to IER and ABD moment-generating capacity were 0.89 and 0.31, respectively. Moment-generating capacity in IER approaching levels in the FE moment-generating capacity determined here underline that the avian hip muscle function is not limited to the sagittal plane. Together with previous findings on the 3D nature of hindlimb kinematics, our results suggest that musculoskeletal models to develop a more detailed understanding of how birds orchestrate the use of muscles during a take-off jump cannot be restricted to the sagittal plane.

Validation of a multicomponent reactive-transport model at pore scale based on the coupling of COMSOL and PhreeqC

Pore scale modelling in porous media is a field of research where interfaces such as the fluid – mineral boundary are explicitly represented and avoids volume-averaged properties such as porosity, permeability and reaction rates as required in a continuum scale approach. Setting up, running and extracting data from a pore scale model can be complex involving multiple software packages and coding for each problem. A new implementation of a multicomponent reactive-transport model at pore scale is presented using a java interface combining COMSOL and PhreeqC (iCP). The new model is tested using benchmark problems recently published and by simulating a laboratory experiment. The main advantages of this model are the implementation of the aqueous speciation, easy incorporation of different reaction mechanisms and rate laws, parallelization of geochemical calculations and a user-friendly interface. The iCP results agree with the benchmark and experimental results very well confirming its application to reactive-transport problems with dynamic pore geometry evolution. The importance of aqueous speciation and the chosen rate constants are demonstrated for calcite dissolution. Given the model transfers data between two codes and computes the aqueous speciation for every time step, the model is computationally expensive. Its advantages are the user-friendliness and its accuracy in computing local reaction rates and fluid composition.

Problem-Based Geometry in Seventh Grade: Examining the Effect of Path-Based Vs. Conventional Instruction on Learning Outcomes

This experimental study examined the impact of learning and teaching ge-ometry in seventh-grade geometry education comparing learning-path and conventional instruction. According to constructivism, a learning path with the use of learning objects should enhance learner autonomy and self-directedness by providing differentiated instruction. We designed a model of path-based geometry learning in a learning management system–based learning environment with the use of dynamic geometry programs and applets, which fosters visualisation and the exploration of geometric concepts through the manipulation of interactive virtual representations. The results show that the experimental group (EG) achieved higher scores on all levels of knowledge and statistically significantly better results in taxonomy level-III tasks (problem-solving knowledge) and overall score than the control group (CG). There was initial equivalence between the EG and CG in prior knowledge. The authors concluded that path-based geometry learning empirically develops knowledge at higher cognitive levels.

Reinventing Geometric Linear Transformations in a Dynamic Geometry Environment: Multimodal Analysis of Student Reasoning

This paper reports the multimodal resources that attached to students’ reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we design a task (in ℝ2) referring to specific tools and functions of GeoGebra. Task-based interviews were conducted with a pair of linear algebra students, by way of a computer and a teacher. Data was collected using a video camera observing the students’ working environment, screen recorder software, student production and field notes. The data was analysed according to the multimodal paradigm focusing on all semiotic resources, such as gestures and artefact use, in addition to written signs. According to the findings, the artefact use, verbal and written mathematical expressions all interlaced with the emergence of gestures. The students mostly gestured when they faced a new reflection situation and when describing associated geometric actions. Finally, a shared environment with action, production and communication conveyed student reasoning and they managed to reinvent a number of geometric linear transformations.

Instrumentation Schemes for Solving Systems of Linear Equations with Dynamic Geometry Software

In this paper we focus on the link between the use of dynamic geometry software and student understanding for the solution of systems of linear equations from an instrumental genesis perspective. Three task-based interviews were conducted with an undergraduate linear algebra student majoring in mathematics education and proficient in using dynamic geometry software. Data included video recordings, student written work and screen recordings. The data analysis was guided by the theoretical lens of instrumental genesis, to elaborate on how student thinking was shaped by the use of the digital artefacts. The digital technology supported the participant’s solution steps and over time the student developed four interrelated instrumentation schemes, which are parameter scheme, combined algebra and geometry scheme, the intersection of figures scheme and echelon form scheme.

Research on trajectory smoothing algorithm of dynamic geometry software

As a kind of mathematical geometry education software, dynamic geometry software is an application software that can interactively create and manipulate geometric objects. Its vivid image changes and colorful geometric objects provide teachers with an efficient Geometry teaching tool. Comparing and analyzing the existing geometry software, we found that there is a curve smoothness problem in its trajectory drawing. In this article, we propose the uniform point selection method based on the principle of the trajectory generation geometric method. Under the premise of ensuring rendering efficiency, extensive case studies have shown that the smoothness of the trajectory curve generated by this method has been improved.

Nondestructive Approach for Complex-Shaped Cracks in Concrete Structures by Electromagnetic Waves with FDTD Technique

Concrete cracks have no specific shape and do not show linearity. Since the natural occurrences of concrete cracks make simulation identification difficult, rectangular step function and a dynamic geometry are used to define a concrete surface crack in the natural process. A novel interior crack expression is obtained by accepting the area between two curves as a crack filled by air in concrete and modeling this area like a Riemann integral domain. Taking the partition of this integral domain, the most realistic definition of the crack is made. Electromagnetic (EM) waves are utilized for numerical simulation after identifying the defects, cracks, rebars, and geometry of concrete. Three different simulation setups with complex geometries with two different surface cracks and one internal crack are simulated using a finite-difference time-domain (FDTD) method with Gaussian pulse wave excitation. Simulations are obtained using both transverse electric (TEz) waves and transverse magnetic (TMz) waves and the results are compared with each other. Air-dried concrete specimens are molded following simulation setups with surface cracks and measurements are made nondestructively with a Vivaldi antenna array in the frequency range of 0.4–4.0 GHz. The reflection and transmission coefficients are validated by comparing the data obtained using the measurement with the results obtained from numerical simulation.

Visualization of Selected Sangaku Problem as Didactical Phenomenon in GeoGebra

In this article, we will focus on visualization solutions within specific geometric problem of the category Sangaku - historical mathematical problems from Japan. We also highlight didactical advantages of experimental activities in the teaching of mathematics and the role of the visualization via using dynamical geometry software GeoGebra.