Cartesian Meshing Spherical Earth (CMSE): A Code Package to Incorporate the Spherical Earth in SPECFEM3D Cartesian Simulations

The SPECFEM3D_Cartesian code package is widely used in simulating seismic wave propagation on local and regional scales due to its computational efficiency compared with the one-chunk version of the SPECFEM3D_Globe code. In SPECFEM3D_Cartesian, the built-in meshing tool maps a spherically curved cube to a rectangular cube using the Universal Transverse Mercator projection (UTM). Meanwhile, the geodetic east, north, and up directions are assigned as the local x–y–z directions. This causes coordinate orientation issues in simulating waveform propagation in regions larger than 6° × 6° or near the Earth’s polar regions. In this study, we introduce a new code package, named Cartesian Meshing Spherical Earth (CMSE), that can accurately mesh the 3D geometry of the Earth’s surface under the Cartesian coordinate frame, while retaining the geodetic directions. To benchmark our new package, we calculate the residual amplitude of the CMSE synthetics with respect to the reference synthetics calculated by SPECFEM3D_Globe. In the regional scale simulations with an area of 1300 km × 1300 km, we find a maximum of 5% amplitude residual for the SPECFEM3D_Cartesian synthetics using the mesh generated by the CMSE, much smaller than the maximum amplitude residual of 100% for the synthetics based on its built-in meshing tool. Therefore, our new meshing tool CMSE overcomes the limitations of the internal mesher used by SPECFEM3D_Cartesian and can be used for more accurate waveform simulations in larger regions beyond one UTM zone. Furthermore, CMSE can deal with regions at the south and north poles that cannot be handled by the UTM projection. Although other external code packages can be used to mesh the curvature of the Earth, the advantage of the CMSE code is that it is open-source, easy to use, and fully integrated with SPECFEM3D_Cartesian.

Analisis Kemampuan Pemecahan Masalah pada Materi Sistem Koordinat Kartesius Ditinjau dari Perbedaan Pola Pikir Divergen dan Konvergen Siswa Kelas VIII SMP

This study aims to determine how the ability of mathematical problem solving in the Cartesian coordinate system material in terms of differences in divergent and convergent thinking patterns in class VIII students in semester 1 of SMP Negeri 1 Kediri in the 2019/2020 academic year. This research is a descriptive study using a quantitative approach. The instruments used in this study were the thinking character questionnaire instrument and the problem solving ability test instrument. The thinking character questionnaire instrument was used to select research samples that met the criteria for divergent thinking and convergent thinking. In this study, 11 students thought divergent and 12 students thought convergent. The problem-solving ability test instrument was used to determine the problem-solving ability of the research sample as measured by Polya's assessment guidelines, namely (1) understanding the questions, (2) planning solutions, (3) solving problems, and (4) checking. The results showed that there was no difference in the average score of problem-solving abilities between students with divergent and convergent thinking patterns, namely 66.19 and 66.73. The only difference lies in the steps each student takes. This shows that different mindsets do not affect a person's ability to solve a problem.

Pengembangan Media Pembelajaran Matematika Berbasis Macromedia Flash pada materi koordinat kartesius kelas VIII SMP

The purpose of this research are to develop macromedia flash-based mathematics learning media for cartesian coordinate material for class VIII SMPN 19 Mataram. Macromedia flash-based learning media is an audio-visual media presented in the form of software consisting of basic competencies, learning objectives, materials and quizzes. This development aims to overcome the weaknesses in the learning process that have occurred due to the lack of use of media in classroom, besides that it can also assist students in learning the concept of cartesian coordinates, especially in visualizing the objects in the material. The research methodology used in developing this learning media is 4D (Define, Design, Developement, Dissemination). Data collection techniques using interview guidelines and questionnaires. The result of this research is a software product of learning media for cartesian coordinates based on macromedia flash in the CD form. The product has been declared valid with good criteria by 4 validators. Based on the limited trial, it is known that the response of class VIII students of SMPN 19 Mataram that use the macromedia flash-based learning media cartesian coordinate is good.

Evaluasi Program Pemberdayaan Usaha Mikro Kecil dan Menengah (UMKM) LAZISMU Magetan dengan Pendekatan Diagram Kartesius

This study aimed to determine the effect of zakat empowerment with MSMEs on the economic people empowerment according to the mustahik perceptions. This research used descriptive analysis with Cartesian coordinate approach. The results showed that the quality of LAZISMU in the MSMEs empowerment program in each dimension of tangible, reliability, responsiveness, assurance, and empathy was almost entirely good quality. The tangible dimension can be shown through the ease of procedures for submitting assistance and the period of its realization. The suitability between everything described by the officer with the reality on the reliable dimension is the main priority factor. The politeness, friendliness and communication skill of officers in the empathy dimension are factors that must be maintained. While transparency in providing information on survey results on the assurance dimension is a low priority factor. The monitoring on the impact of empowerment on the responsiveness dimension and the strategic location of the LAZISMU office on the tangible dimension was considered excessive. There is an effect of zakat empowerment with MSMEs on increasing the people's economic income in terms of service quality according to the perceptions of mustahik. This research suggests LAZISMU Magetan for accelerates the realization of assistance proposals and the ease in applying for assistance.

Maximum Allowable Pressure Calculation of Water Tube Boiler during Operation

In the steam boiler industrial sector, pressure and temperature of the water tube are the two main factors that affect the safety and efficiency of a steam boiler. Explosions may be occurring because of a sudden drop in pressure without a corresponding drop in temperature. Therefore, understanding the temperature distribution of the water tube boiler is essential to control the failure and explosion of the boiler. Once the temperature distribution is known than the limiting factors that affect the water tube life such as the maximum allowable pressure can be determined. ANSYS software will be used to determine the temperature distribution in the water tube of a utility boiler during operation at elevated inlet water and furnace temperature. The theory of axisymmetric has been utilized since the water- tube is cylindrical in shape. In axisymmetric theory, a three-dimensional cylindrical problem like a water tube can be reduced to two-dimensional by ignoring the circumferential Ө, while the r-axis and z-axis became x-axis and y-axis or Cartesian coordinate. Then two-dimensional rectangular elements meshing for the profile cross-section along the water tube in r and z axes were implemented in a computerized simulation using ANSYS 10 to find out the steady-state temperature distribution of the water tube.

BALLU2: A Safe and Affordable Buoyancy Assisted Biped

This work presents the first full disclosure of BALLU, Buoyancy Assisted Lightweight Legged Unit, and describes the advantages and challenges of its concept, the hardware design of a new implementation (BALLU2), a motion analysis, and a data-driven walking controller. BALLU is a robot that never falls down due to the buoyancy provided by a set of helium balloons attached to the lightweight body, which solves many issues that hinder current robots from operating close to humans. The advantages gained also lead to the platform’s distinct difficulties caused by severe nonlinearities and external forces such as buoyancy and drag. The paper describes the nonconventional characteristics of BALLU as a legged robot and then gives an analysis of its unique behavior. Based on the analysis, a data-driven approach is proposed to achieve non-teleoperated walking: a statistical process using Spearman Correlation Coefficient is proposed to form low-dimensional state vectors from the simulation data, and an artificial neural network-based controller is trained on the same data. The controller is tested both on simulation and on real-world hardware. Its performance is assessed by observing the robot’s limit cycles and trajectories in the Cartesian coordinate. The controller generates periodic walking sequences in simulation as well as on the real-world robot even without additional transfer learning. It is also shown that the controller can deal with unseen conditions during the training phase. The resulting behavior not only shows the robustness of the controller but also implies that the proposed statistical process effectively extracts a state vector that is low-dimensional yet contains the essential information of the high-dimensional dynamics of BALLU’s walking.

Characterization of Rectifying Curves by Their Involutes and Evolutes

A rectifying curve is a twisted curve with the property that all of its rectifying planes pass through a fixed point. If this point is the origin of the Cartesian coordinate system, then the position vector of the rectifying curve always lies in the rectifying plane. A remarkable property of these curves is that the ratio between torsion and curvature is a nonconstant linear function of the arc-length parameter. In this paper, we give a new characterization of rectifying curves, namely, we prove that a curve is a rectifying curve if and only if it has a spherical involute. Consequently, rectifying curves can be constructed as evolutes of spherical twisted curves; we present an illustrative example of a rectifying curve obtained as the evolute of a spherical helix. We also express the curvature and the torsion of a rectifying spherical curve and give necessary and sufficient conditions for a curve and its involute to be both rectifying curves.

Research on the Trajectory Planning and Control Technology of Industrial Robots Guided by Computer Visualization

With the popularization of computers, the development of all walks of life has become more rapid. This article mainly analyzes the mechanical structure design of the Cartesian coordinate robot system, it also studies the motion control.

A structure of the solenoidal 2D vector and 2-tensor fields given in a domain with the conformal Riemannian metric

The Helmholtz decomposition of a vector field on potential and solenoidal parts is much more natural from physical and geometric points of view then representations through the components of the vector in the Cartesian coordinate system of Euclidean space. The structure, representation through potentials and detailed decomposition for 2D symmetric m-tensor fields in a case of the Euclidean metric is known. For the Riemannian metrics similar results are known for vector fields. We investigate the properties of the solenoidal vector and 2-tensor two-dimensional fields given in the Riemannian domain with the conformal metric and establish the connections between the fields and metrics.

Contravariant tensor algebra for anisotropic hyperelasticity

Analysis of tensors in oblique Cartesian coordinate systems always requires the definition of a set of orthogonal covariant basis vectors called the Reciprocal basis. This increases the complexity of the analysis and hence makes the method cumbersome. In this work a novel method is presented to effectively carry out the various transformations of tensors to and between oblique coordinate system/s without the need to create the covariant reciprocal basis. This will simplify the procedure of transformations involving problems where tensors are required to be defined in the oblique coordinate system. This work also demonstrates how the analysis of contravariant tensors can be applied to hyperelasticity. Continuum material and damage models can integrate this approach to model anisotropy and non linearity using a much simpler approach. The accuracy of the models was illustrated by matching the predictions to experimental results. A finite element analysis of material and damage model based on contravariant tensors was also carried out on a simple geometry with a re-entrant corner.