GNU Octave Research Articles

More on the Fascinating Characterizations of Mulatu’s Numbers

Background The discoveries of Mulatu’s numbers, better known as Mulatu’s sequence, represent revolutionary contributions to the mathematical world. His best-known work is Mulatu’s sequence, in which each new number is the sum of the two preceding numbers. When various operations and manipulations are performed on the numbers in this sequence, beautiful and incredible patterns begin to emerge. This study aimed to identify novel characterizations of Mulatu’s numbers. Methods This study employed a multi-faceted approach to investigate characterizations of Mulatu’s numbers. Mathematical proof techniques such as principle of mathematical induction, proof by contradiction and direct proof were utilized to substantiate findings. GNU Octave (version 9, (1)) software was applied to verify the existence, classify, and conduct computational investigations of findings prior to formal proofs. Results In this study, we provided several characterizations of Mulatu’s numbers. We also investigated the properties and patterns of these fascinating numbers. Moreover, we have also shown that, similar to Fibonacci’s numbers, Mulatu’s numbers also give the so-called golden ratio, which is most applicable in numerical optimization. Furthermore, we formulated a relation among Mulatu’s numbers, Fibonacci numbers, and Lucas numbers. Finally, we provided a generating function for the Mulatu numbers. Conclusions In this study, we uncovered novel characterizations of Mulatu’s numbers and introduced a generating function for them. We investigated relationship between Mulatu’s numbers and the golden ratio. The results discussed offer valuable insights and enhance our understanding of their properties. Furthermore, these findings play a vital role in the boarder context of mathematical sequences, contributing significantly to the field.

Bridging external and attenuated total reflection infrared spectroscopies through computational simulations

Abstract This work provides an integrated view of Attenuated Total Reflection (ATR) and External Reflection (ER) for advanced undergraduate and postgraduate students beginning their study of infrared spectroscopy. The theoretical framework of reflectance is reviewed, and a computational tool developed using GNU Octave is presented to model ER and ATR spectra. Simulating spectra demonstrates how ER spectra evolve to ATR spectra by modifying relevant parameters. This unified approach offers advanced students a deeper understanding of infrared spectroscopy, enhancing their ability to correctly interpret ATR spectra and avoid common pitfalls. The computational exercises and provided code serve as valuable educational resources for exploring reflectance behaviour under different conditions.

Three-Dimensional Mapping of the Rotation of Interactive Virtual Objects with Eye-Tracking Data.

We present a method for real-time recording of human interaction with three-dimensional (3D) virtual objects. The approach consists of associating rotation data of the manipulated object with behavioral measures, such as eye tracking, to make better inferences about the underlying cognitive processes. The task consists of displaying two identical models of the same 3D object (a molecule), presented on a computer screen: a rotating, interactive object (iObj) and a static, target object (tObj). Participants must rotate iObj using the mouse until they consider its orientation to be identical to that of tObj. The computer tracks all interaction data in real time. The participant's gaze data are also recorded using an eye tracker. The measurement frequency is 10 Hz on the computer and 60 Hz on the eye tracker. The orientation data of iObj with respect to tObj are recorded in rotation quaternions. The gaze data are synchronized to the orientation of iObj and referenced using this same system. This method enables us to obtain the following visualizations of the human interaction process with iObj and tObj: (1) angular disparity synchronized with other time-dependent data; (2) 3D rotation trajectory inside what we decided to call a "ball of rotations"; (3) 3D fixation heatmap. All steps of the protocol have used free software, such as GNU Octave and Jmol, and all scripts are available as supplementary material. With this approach, we can conduct detailed quantitative studies of the task-solving process involving mental or physical rotations, rather than only the outcome reached. It is possible to measure precisely how important each part of the 3D models is for the participant in solving tasks, and thus relate the models to relevant variables such as the characteristics of the objects, cognitive abilities of the individuals, and the characteristics of human-machine interface.

Systematic Review of Consumer Price Index Methods and Software: Evidence from ASEAN Countries and Scholarly Research

This comprehensive systematic review provides an in-depth analysis of consumer price index (CPI) methods and software use in Asian countries. The study looks at the practises used by countries to calculate CPI, with an overwhelming preference for monthly calculations, reflecting the dynamic economic growth of the region. The use of household expenditure surveys and weighting sources ensures that CPI accurately captures changes in consumer spending patterns and the relative importance of different goods and services. Applications of CPI in Asian countries cover a wide range, including indexation of wages, pensions and social security contributions, as well as its central role as a main indicator for monetary policy decisions, macroeconomic modelling and various analytical purposes. The systematic review highlights various calculation methods for CPI, including the Carli index, the Laspeyres index, the chained Jevons index and the Dutot index, each of which has different strengths and weaknesses that affect the accuracy and reliability of CPI's measurements. In terms of software, the study encounters a range of applications, including Microsoft Excel, SAS, STATA, R, Python, EViews and SPSS, each offering versatile capacities for statistical analysis and econometric modelling. In addition, the study explores potential software alternatives such as Gretl, Julia, EpiData, GNU Octave, Tableau, Matplotlib, Seaborn and QGIS, whose suitability for CPI calculations should be considered. The research findings highlight the importance of transparent and accurate CPI calculations in shaping effective policy decisions. Policy makers can use these findings to refine CPI measurements to enable well-informed strategies to steer the economy. The study suggests avenues for future research that include assessing specific impacts of CPI calculations, further developing software tools, and incorporating consumer perceptions into CPI development.

Analysis of Naturally Occurring Radioactive Material (NORM) in shifting earth layers in Piyungan, Bantul

In recent decades, understanding the correlation between radon gas emissions and geodynamic processes has been pivotal in enhancing geophysical monitoring. This study advances current methodologies by refining radon data analysis and employing mathematical models to further elucidate this relationship. We developed a radon well geometry for Piyungan using Finite Element Method principles, and conducted simulations via GNU Octave to assess normal and anomalous conditions. The results indicate a basal radon concentration of 2.2420 Bq/L at a depth of 14.2308 m. Notably, radon levels inversely correlate with the water volume and diffusivity, yet proportionally increase with soil moisture. These findings offer a nuanced understanding of radon behavior in response to geodynamic activity, paving the way for improved environmental monitoring.

COMPARING SCIENTIFIC COMPUTING ENVIRONMENTS FOR SIMULATING 2D NON-BUOYANT FLUID PARCEL TRAJECTORY UNDER INERTIAL OSCILLATION: A PRELIMINARY EDUCATIONAL STUDY

This study presents a preliminary numerical investigation of the two-dimensional trajectory of a non-buoyant fluid parcel subjected to inertial oscillations and abrupt external forcing events. The simulations were implemented using Python, GNU Octave, R, Julia, and Fortran open-source scientific computing environments. By running 1,000 iterations in each environment, we evaluated the computational performance of these languages in tackling this idealized problem. The results, visualized through static plots and animation, validate the numerical model's ability to represent the fundamental physics governing fluid motion. Statistical analysis using the Kruskal-Wallis test and Dunn's post-hoc test with Bonferroni correction revealed that Fortran exhibits significantly faster execution times than other environments. However, the choice of programming language should also consider factors such as coding expertise, library availability, and scalability requirements. This study focuses on the performance of scientific computing environments within each language rather than the languages themselves. The observed execution times should be interpreted in the context of the specific environments used, as they often leverage optimized libraries written in lower-level languages. Despite the limitations of this work, such as the simplified 2D model and the use of a single hardware configuration, this study provides valuable insights into selecting appropriate computational tools. It contributes to educational resources for teaching idealized fluid dynamics models. Future studies could explore more complex scenarios, a more comprehensive range of programming environments, and the impact of different numerical schemes and physical parameterizations.

Simulation of Massive MIMO Antennas for Improved Link Throughput

Massive MIMO technology involves deploying multiple antennas on both ends of a communication link, which boosts spatial diversity and signal-to-noise ratio. By using multi-user MIMO transmission and techniques like spatial multiplexing and beamforming, it increases capacity, spectral efficiency, and data rates. Simulations conducted with tools like Octave software help engineers to optimize designs, predict system behavior, and assess the impact of antenna quantity on downlink throughput. This study addresses the increasing demand for high downlink data rates within modern communication networks. It explores the performance of Massive MIMO systems through simulations using Octave software, focusing on the quantity of antenna elements (M), and considering both spectral efficiency (SE) and data throughput. Results show higher M enhances both spectral efficiency and data rates. Efficiency dips at M=10, surges at M=40, and slowly, but steadily grows from M=50 to 100. Similar trends in data rates indicate M's impact on transmission performance. SE values range from 5.8442 bps/Hz (M = 10) to 24.1608 bps/Hz (M = 100), while data rates range from 116.8834 Mbps (M = 10) to 483.2158 Mbps (M = 100). These insights offer practical guidance for engineers and could facilitate the optimization of wireless communication setups and addressing the imperative for improved data rates. The study advances the understanding of Massive MIMO's potential, providing a roadmap for effectively leveraging its capabilities across diverse communication network scenarios.

Multicentral Agent-Based Model of Six Epidemic Waves of COVID-19 in the Nizhny Novgorod Region of Russian Federation

Relevance. To investigate the characteristics of the COVID-19 pandemic and introduce timely and effective measures, there is a need for models that can predict the impact of various restrictive actions or characteristics of disease itself on COVID-19 spread dynamics. Employing agent-based models can be attractive because they take into consideration different population characteristics (e.g., age distribution and social activity) and restrictive measures, laboratory testing, etc., as well as random factors that are usually omitted in traditional modifications of the SIR-like dynamic models. Aim. Improvement of the previously proposed agent-based model [23,24] for modeling the spread of COVID-19 in various regions of the Russian Federation. At this stage, six waves of the spread of COVID-19 have been modeled in the Nizhny Novgorod region as a whole region, as well as in its individual cities, taking into account restrictive measures and vaccination of the population. Materials and Methods. In this paper we extend a recently proposed agent-based model for Monte Carlo-based numerical simulation of the spread of COVID-19 with consideration of testing and vaccination strategies. Analysis is performed in MATLAB/ GNU Octave. Results. Developed multicentral model allows for more accurate simulation of the epidemic dynamics within one region, when a patient zero usually arrives at a regional center, after which the distribution chains capture the periphery of the region due to pendulum migration. Furthermore, we demonstrate the application of the developed model to analyze the epidemic spread in the Nizhny Novgorod region of Russian Federation. The simulated dynamics of the daily newly detected cases and COVID-19-related deaths was in good agreement with the official statistical data both for the region as whole and different periphery cities. Conclusions. The results obtained with developed model suggest that the actual number of COVID-19 cases might be 1.5–3.0 times higher than the number of reported cases. The developed model also took into account the effect of vaccination. It is shown that with the same modeling parameters, but without vaccination, the third and fourth waves of the epidemic would be united into one characterized by a huge rise in the morbidity rates and the occurrence of natural individual immunity with the absence of further pandemic waves. Nonetheless, the number of deaths would exceed the real one by about 9–10 times.

Evaluation of reaction rate of thermogravimetric analysis data using periodic sinc function interpolation

AbstractThe periodic sinc function interpolation offers a compelling solution to address the issue of noise in the analysis of thermogravimetric analysis (TGA) data, thereby enhancing the outcomes of differential techniques such as the Friedman isoconversional method. In this study, we introduce a novel approach that leverages the periodic sinc function interpolation to directly obtain smooth reaction rates from TGA data, eliminating the reliance on numerical differentiation methods. The efficacy of this method has been confirmed through its application to noisy experimental data derived from the thermal decomposition of various polymers, showcasing its robustness. Readers are provided with the corresponding code for Gnu Octave, serving as a free alternative to MATLAB. Additionally, the activation energies calculated from the experimental data using both the Friedman method and periodic sinc function interpolation closely align with those determined by the integral Vyazovkin method, emphasizing the validity and reliability of this new approach.

Enabling support for Octave within the FOCUS software package

FOCUS, the “Fast Object-Oriented C+ + Simulator” (https://www.egr.msu.edu/∼fultras-web/), is a free software package that enables rapid calculations of continuous-wave and transient pressure fields generated by single transducers and phased arrays. FOCUS achieves small errors in relatively short computation times through linear memory-efficient calculations with the fast nearfield method. This capability extends to quick and accurate biomedical imaging simulations within FOCUS. Moreover, FOCUS supports some nonlinear pressure calculations, such as the continuous-wave and transient Khokhlov-Zabolotskaya-Kuznetsov (KZK) equations for circular and spherical transducers. Additionally, the Angular Spectrum Approach (ASA), a frequency-domain solution to linear computational methods, ideal for large volumetric field computations, is also included within the FOCUS package. Initial success with MATLAB motivates the creation of an Octave version that replicates the core functionalities of the original FOCUS package. GNU Octave is similar to MATLAB, but unlike MATLAB, Octave is a free software. Building and compiling FOCUS in Octave required a few minor alterations due to discrepancies in syntax and function calls. The use of Octave-compiled MEX files simplified the conversion process while introducing addition memory overhead compared to rewriting C+ + code for Oct-file structuring. The performance and capabilities of FOCUS in Octave are demonstrated and discussed.

Development and application of a mesh generator intended for unsteady vortex-lattice method simulations of wind turbines and wind farms

Abstract. In the last decades, the unsteady vortex-lattice method (UVLM) has gained a lot of acceptance to study large onshore–offshore wind turbines (WTs). Furthermore, and due to the development of more powerful computers, parallelization strategies, and algorithms like the fast multipole method, it is possible to use vortex-based methods to analyze and simulate wind farms (WFs). However, UVLM-based solvers require structured meshes, which are generally very tedious to build using classical mesh generators, such as those utilized in the context of finite element methods (FEMs). Wind farm meshing is further complicated by the large number of design parameters associated with the wind turbine (coning angle, tilt angle, blade shape, etc.), farm layout, modeling of the terrain topography (for onshore WFs), and modeling of the sea level surface (for offshore WFs), which makes the use of FEM-oriented meshing tools almost inapplicable. In the literature there is a total absence of meshing tools when it comes to building aerodynamic grids of WTs and WFs to be used along with UVLM-based solvers. Therefore, in this work, we present a detailed description of the geometric modeling and computational implementation of an interactive UVLM-oriented mesh generator, named UVLMeshGen, developed entirely in MATLAB® and easily adaptable to GNU OCTAVE, for wind turbines and onshore–offshore wind farms. The meshing tool developed here consists of (i) a geometric processor in charge of designing and discretizing an entire wind farm and (ii) an independent module in charge of computing the kinematics for the entire WF. The output data provided by the UVLMeshGen consist of nodal coordinates and connectivity arrays, making it especially attractive and useful to be used by other flow potential solvers using vortices, sources and sinks, or dipoles/doublets, among others. The work is completed by providing a series of aerodynamic results related to WTs and WFs to show the capabilities of the mesh generator, without going into detailed discussions of wind turbine aerodynamics, which are not the focus of this paper. The meshing tool developed here is freely available under a Creative Commons Attribution 4.0 International License (Roccia, 2023).

Graph plotting of 1-D motion in introductory physics education using scripts generated by ChatGPT 3.5

Introductory physics courses often necessitate students to graphically represent one-dimensional (1-D) motion and derive various physical parameters. Physical quantities are often solved by calculating either slope or the area under the graph. Instructors and students who do not have access to paid software must plot graphs by hand. This paper explores three introductory physics examples related to 1-D motion, and employs ChatGPT 3.5 to generate scripts that will produce graphs from raw data. It can generate scripts, based on accurate user inputs, in free programming languages like Python and/or GNU Octave to enable efficient graph plotting. Examples will be provided on calculating the slope of a distance–time graph and determining the area under a velocity–time graph. Given raw data, ChatGPT 3.5 may exhibit occasional inaccuracies when solving for physical parameters. However, user can communicate in English to modify the output. The author does not endorse the use of ChatGPT for academic misconducts such as assisting students to cheat in problem solving. Instead, ChatGPT is presented as a tool to enhance data visualisation for both instructors and students, which can potentially improve learning environments in introductory physics. This paper lays the groundwork for future initiatives, beyond the plotting of 1-D motion graphs, aiming to integrate artificial intelligence to assist more complex motion studies in physics learning environments.

An Image-Processing Tool for Size and Shape Analysis of Manufactured Irregular Polyethylene Microparticles

Microplastics (MPs) pose a significant risk to humans and animals due to their ability to absorb, adsorb, and desorb organic pollutants. MPs catchment from either sediments or water bodies is crucial for risk assessment, but fast and effective particle quantification of irregularly shaped particles is only marginally addressed. Many studies used microscopy methods to count MP particles, which are tedious for large sample sizes. Alternatively, this work presents an algorithm developed in the free software GNU Octave to analyze microscope images of MP particles with variable sizes and shapes. The algorithm can detect and distinguish different particles, compensate for uneven illumination and low image contrast, find high-contrast areas, unify edge regions, and fill the remaining pixels of stacked particles. The fully automatic algorithm calculates shape parameters such as convexity, solidity, reciprocal aspect ratio, rectangularity, and the Feret major axis ratio and generates the particle size distribution. The study tested low-density polyethylene particles with sizes of 50–100 µm and 200–300 µm. A scanning electron microscope image series analyzed with Octave was compared to a manual evaluation using ImageJ. Although the fully automatic algorithm did not identify all particles, the comprehensive tests demonstrate a qualitatively accurate particle size and shape monitoring applicable to any MPs, which processes larger data sets in a short time and is compatible with MATLAB-based codes.

Mathematical Model of Impact Projectile Flight Dynamics as an Element of its Digital Twin

This paper gives the analysis of the structure and characteristics of the mathematical model of the impact projectile’s flight dynamics. The model is designed for being used as an element of the projectile’s digital twin. The model is based on differential motion equations of a gyro-stabilized solid with an axisymmetric mass distribution. Different types of angle variables were chosen for describing aerodynamics and formulating equations of motion. Non-linear (considering the nutation angle) dependences for aerodynamic coefficients are proposed. They are created by applying proven scientific concepts and research methods in aerodynamics of axisymmetric body and by comparing with known numerical and experimental results obtained in exterior ballistics of gyro-stabilized aviation and artillery projectiles. Special aspects of initial conditions for angles and angular velocity were also studied. Since the impact projectile is considered as an axially symmetric body, its self-rotation angle is not of practical inte rest. Using algebraic manipulations, the differential equation for this angle was eliminated from the set of equations. This has made it possible to significantly reduce stiff of the remaining system of differential equations. The Dormand-Prince method is recommended as a method of numerical integration. The method of the eight-order (with seventh-order uncertainty estimate) allows getting the high accurate solution of the differential equations set under relatively small computing costs. The model allows computing the projectile trajectory under various initial conditions, including the flight with high nutation angles up to 87°—89°. As a result, there is a possibility to determine the nature of the interaction between impact projectiles and typical targets (ricochet, surface effect, after-penetration effect) within a wide range of approach angles to the target’s surface (skin) unattainable during the full-scale tests. The possibility of solving similar problems allows to recommend the designed model as an element of the impact projectile’s digital twin intended for testing its exterior ballistics on the digital (virtual) test range. All testing calculations and final modeling were made by using the "GNU Octave" computational software package.

APPLICATION OF NUMERICAL MODELING TO PIPE LEAKS IN FLUID FLOW

Pipes are a medium used to move flowing fluids and are very dependent on pressure and speed. Leaks in pipes can cause physical loss of water. This can be caused by many things, one of which is a leak caused by a hole in the pipe which can disrupt the flow of water so that the flow of water or fluid will change, including the pressure and speed. A fluid flow can be visualized using simulation or mathematical modeling using finite differences. By using the GNU Octave application, namely numerical computing which can be accessed for free without a license which is used as data visualization, it can provide an overview of fluid flow including the occurrence of leaks in pipes, namely by visually representing the state of fluid flow when a leak occurs in a pipe. With this visualization, a fluid flow pattern is produced where leaks occur at several different points. From the research results, it was found that the pipe before it got a leak would be laminar, but when it got a leak, the fluid flow would become a fluid flow that switched to transitional fluid flow or turbulence. Apart from that, the placement of coordinate variations slightly affects the fluid flow line

SYSTEM IDENTIFICATION OF AIRCRAFT LONGITUDINAL MOTION BY MEANS OF FLIGHT SIMULATOR DATA

In presented article, an exemplary problem of identifying parameters of an aircraft's motion within the vertical plane of symmetry is solved. The data was collected by FlightGear simulator for a Pilatus PC-9M aircraft flight case. After submitting a sequence of commands to pitch elevator and engine thrust, the simulator records five parameters of longitudinal motion at certain frequency. The collected data are further used to build a state-space model of the flight through least-squares estimation. The obtained numerical results are compared with the experimental ones and are overlaid graphically. Charts depicting elevator angle to trim are derived in addition. A source code developed in GNU Octave is applied with the help of which the problem was solved.

Performance analysis of proportional feedback control and integral control in DC motors and speed control

Control systems play a crucial role in modern engineering and technology, and their stability and performance are vital for the success of various applications. This paper aims to explore the application and performance analysis of proportional feedback control (P control) in DC motors and integral control (PI control) in speed control. The following section provides an exposition of the fundamental principles underpinning P control and PI control, alongside an exhaustive account of their practical implementations within the Tinkercad and Octave software environments. The simulations carried out in Tinkercad serve as the basis for evaluating step responses associated with varying values, leveraging a 1Hz function generator. Subsequent analysis pertains to proportional-integral control through the utilization of Octave's PZmap and root locus methodologies, with specific regard to their implications for system stability and control performance in the context of speed control. The experimental outcomes reveal the aptitude of P control in scenarios demanding rapid responses, while establishing the superiority of PI control in the context of steady-state error mitigation. In the experimental analysis conducted, an evident trend emerged as Kp values were systematically increased within the framework of proportional feedback control. The primary observation related to the reduction in system response times, along with the concurrent rise in overshooting tendencies.

The Study on the Spectral Analysis of Fiber Bragg Grating (FBG) as a Strain Sensor

Abstract: By adjusting the grating length and refractive index change, parameters of the Fibre Bragg grating which are the effective refractive index, Bragg wavelength, grating period, and strain-optic constant are provided and discussed, along with the characterization of the grating, including strain, Bragg wavelength shift, spectral response, and bandwidth. The coupled mode equations form the basis for data analysis and acquisition. This research uses a high-level computer language, such as GNU Octave software, to simulate FBG spectral responses.

Baseflow: a MATLAB and GNU Octave package for baseflow recession analysis

baseflow: a MATLAB and GNU Octave package for baseflow recession analysis

ROE (Radiotherapy Outcomes Estimator): An open-source tool for optimizing radiotherapy prescriptions

Background and objectivesRadiotherapy prescriptions currently derive from population-wide guidelines established through large clinical trials. We provide an open-source software tool for patient-specific prescription determination using personalized dose-response curves. MethodsWe developed ROE, a plugin to the Computational Environment for Radiotherapy Research to visualize predicted tumor control and normal tissue complication simultaneously, as a function of prescription dose. ROE can be used natively with MATLAB and is additionally made accessible in GNU Octave and Python, eliminating the need for commercial licenses. It provides a curated library of published and validated predictive models and incorporates clinical restrictions on normal tissue outcomes. ROE additionally provides batch-mode tools to evaluate and select among different fractionation schemes and analyze radiotherapy outcomes across patient cohorts. ConclusionROE is an open-source, GPL-copyrighted tool for interactive exploration of the dose-response relationship to aid in radiotherapy planning. We demonstrate its potential clinical relevance in (1) improving patient awareness by quantifying the risks and benefits of a given treatment protocol (2) assessing the potential for dose escalation across patient cohorts and (3) estimating accrual rates of new protocols.