Two-dimensional Graphical Representation Research Articles

Educational interactive graphics tool for teaching Mohr Circle

Mohr Circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. The components of the Cauchy stress tensor at a specific material point are known with respect to a coordinate system. Mohr Circle graphically determines the stress components acting in a rotated coordinate system, i.e., acting on a differently oriented plane passing through that point. The e-Mohr program is an interactive graphics tool that explains the Mohr Circle to Solid Mechanics (Strength of Materials) students in engineering courses. The program demonstrates how the Mohr Circle works for plane stress states, allowing users to interactively manipulate the plane's orientation where the stress tensor components are calculated. Furthermore, e-Mohr involves determining a point in the Mohr Circle called the pole or origin of the planes. Any straight line drawn from the pole will intersect the Mohr Circle at a point representing the state of stress on an inclined plane in the same orientation (parallel) in space as that line.

Optoelectronic and photoacoustic waves in rotating excited semiconductor subjected to thermal shock

In this study, the impact of rotation on the transmission of optical acoustic waves, arising from the movement of the optical carrier within an elastic thermal environment, is examined through theoretical analysis. The theoretical framework incorporates the interaction between acoustic waves and thermomechanics to formulate governing equations specific to a semiconductor medium. The fundamental equations of the physical model, influenced by photothermal and thermoelastic principles, are deduced mathematically while considering the presence of rotation. The model studied the medium under a thermal shock wave from thermal stress resulting from light-induced temperature elevation that is not fixed but decaying over time. The mathematical model is solvable using the normal mode method. The model’s numerical solutions provide access to all physical fields within the physical domain, encompassing displacement, temperature, acoustic pressure, mechanical stress, and carrier density diffusion. Utilizing the harmonic wave method, a two-dimensional graphical representation of the rotation parameter with and without the influence of the decay parameter is obtained. The theoretical analysis involves comparison, analysis, and discussion of the effects of these parameters investigated.

Dynamics and wave analysis in longitudinal motion of elastic bars or fluids

We look at the bifurcation analysis, chaotic behavior, multistability, and sensitivity analysis of the van der Waals equation, which is used in science and engineering to study the dynamics of various structures. The variant van der Waals equation covers one-dimensional longitudinal isothermal motion in elastic bars or fluids, which is the main focus of this research. The Galilean transformation transfers the given model into a planar dynamical system. The power series methodology produces exact wave solutions. In addition, after accounting for the perturbation component, sensitivity analysis for various initial value problems is used to investigate quasi-periodic, chaotic, and time series behavior. Numerical simulation results show that influencing viscosity and the coefficient of interfacial capillarity influence the dynamical factors of the examined model. We are observing what happens with viscosity and the interface coefficients to the wave solution. In some cases, for different parameter values, we present plots of both one-dimensional and two-dimensional graphical representations of individual solutions.

Electromagnetohydrodynamic (EMHD) flow of Jeffrey fluid through a rough circular microchannel with surface charge-dependent slip.

This research examines the electromagnetohydrodynamic (EMHD) flow of Jeffrey fluid in a rough circular microchannel while considering the effect of surface charge on slip. The channel wall corrugations are described as periodic sinusoidal waves with small amplitudes. The perturbation method is employed to derive solutions for velocity and volumetric flow rate, and a combination of three-dimensional (3D) and two-dimensional (2D) graphical representations is utilized to effectively illustrate the impacts of relevant parameters on them. The significance of the Reynolds number in investigations of EMHD flow is particularly emphasized. Furthermore, the effect of wall roughness and wave number on velocity and the influence of wall roughness and surface charge density on volumetric flow rate are primarily focused on, respectively, at various Reynolds numbers. The results suggest that increasing the wall roughness leads to a reduction in velocity at low Reynolds numbers ( ) and an increment at high Reynolds numbers ( ). For any Reynolds number, a roughness with an odd multiple of wave number ( ) will result in a more stable velocity profile compared to one with an even multiple of wave number ( ). Decreasing the relaxation time while increasing the retardation time and Hartmann number can diminish the impact of wall roughness and surface charge density on volumetric flow rate, independent of the Reynolds number. Interestingly, in the existence of wall roughness, further consideration of the effect of surface charge on slip leads to a 15% drop in volumetric flow rate at and a 32% slippage at . However, in the condition where the effect of surface charge on slip is considered, further examination of the presence of wall roughness only results in a 1.4% decline in volumetric flow rate at and a 1.6% rise at . These findings are crucial for optimizing the EMHD flow models in microchannels.

The nonlinear wave dynamics of fractional foam drainage and Boussinesq equations with Atangana’s beta derivative through analytical solutions

The space–time fractional foam drainage and the Boussinesq equations are valuable mathematical models to describe different complex physical phenomena, including the drainage of soap films in bubbles and foams, the behavior of surface water waves in oceans and rivers, the propagation of long waves, etc. In this research, we explore several unrivaled and some existing analytical soliton solutions to the above-stated equations using an effective expansion scheme, known as the G′/(G′+G+A)-expansion scheme within the framework of Atangana’s beta derivative. A fractional composite transformation is used to interpret the considered equations into nonlinear equations of a single independent variable. The wave dynamics of the outcomes are illustrated through three- and two-dimensional graphical representations and contour plots. The solutions include kink, flat kink-shaped, the parabolic-shaped, the bell-shaped, and the compacton solitons. The study reveals that the fractional-order derivative in the projected equations influences the wave behavior, providing deeper insights into wave composition when the fractional derivative approaches larger. The comparison table demonstrates the effectiveness of the method across various fractional orders, with results approaching accuracy as the fractional-order approaches integer values. This study emphasizes the computational robustness and adaptability of the proposed method for investigating various phenomena across a wide range of physical science and engineering disciplines.

Use of 2D FFT and DTW in Protein Sequence Comparison.

Protein sequence comparison remains a challenging work for the researchers owing to the computational complexity due to the presence of 20 amino acids compared with only four nucleotides in Genome sequences. Further, protein sequences of different species are of different lengths; it throws additional changes to the researchers to develop methods, specially alignment-free methods, to compare protein sequences. In this work, an efficient technique to compare protein sequences is developed by a graphical representation. First, the classified grouping of 20 amino acids with a cardinality of 4 based on polar class is considered to narrow down the representational range from 20 to 4. Then a unit vector technique based on a two-quadrant Cartesian system is proposed to provide a new two-dimensional graphical representation of the protein sequence. Now, two approaches are proposed to cope with the varying lengths of protein sequences from various species: one uses Dynamic Time Warping (DTW), while the other one uses a two-dimensional Fast Fourier Transform (2D FFT). Next, the effectiveness of these two techniques is analyzed using two evaluation criteria-quantitative measures based on symmetric distance (SD) and computational speed. An analysis is performed on five data sets of 9 ND4, 9 ND5, 9 ND6, 12 Baculovirus, and 24 TF proteins under the two methods. It is found that the FFT-based method produces the same results as DTW but in less computational time. It is found that the result of the proposed method agrees with the known biological reference. Further, the present method produces better clustering than the existing ones.

On topological polynomials and indices for metal-organic and cuboctahedral bimetallic networks

Abstract A molecular graph consists of bonds and atoms, where atoms are present as vertices and bonds are present as edges. We can look at topological invariants and topological polynomials that furnish bioactivity and physio-chemical features for such molecular graphs. These topological invariants, which are usually known as graph invariants, are numerical quantities that relate to the topology of a molecular graph. Let m pq (X) be the number of edges in X such that (ζ a , ζ b ) = (p, q), where ζ a (or ζ b ) present the degree of a (or b). The M-polynomial for X can be determined with the help of relation M ( X ; x , y ) = ∑ p ≤ q m p q ( X ) x p y q M(X;x,y)={\sum }_{p\le q}{m}_{pq}(X){x}^{p}{y}^{q} . In this study, we calculate the M-polynomial, forgotten polynomial, sigma polynomial and Sombor polynomial, and different topological invariants of critical importance, referred to as first, second, modified and augmented Zagreb, inverse and general Randić, harmonic, symmetric division; forgotten and inverse invariants of chemical structures namely metal-organic networks (transition metal-tetra cyano benzene organic network) and cuboctahedral bimetallic networks (MOPs) are retrieved using a generic topological polynomial approach. We also draw the two-dimensional graphical representation of outcomes that express the relationship between topological indices and polynomial structural parameters.

High-Definition Survey of Architectural Heritage Fusing Multisensors—The Case of Beamless Hall at Linggu Temple in Nanjing, China

Following the development of digital measurement technology in recent years, the information contained in the measurement outcomes have become increasingly rich. However, the traditional graphical representation method based on vector graph needs to be updated. In this study, we use the Beamless Hall of Linggu Temple as an example. Measurements are conducted by using digital techniques, including three-dimensional (3D) laser scanning, close-range photogrammetry, and infrared thermal imaging. The pseudocolours that express spatial information and moisture distribution are calculated and generated through point clouds, which are used to express the land subsidence, wall deformation, moisture distribution, and other effects of the Beamless Hall. Furthermore, combining it with two-dimensional (2D) graphical representation, such as the plan, elevation, and section, damage-related information can be expressed intuitively and efficiently. This method can combine the advantages of graphics and images to provide a comprehensive and intuitive representation of the digital measurement results of brick architecture heritage. It can also provide a reference for surveying similar monuments and buildings of our architectural heritage.

IMGT® Immunoinformatics Tools for Standardized V-DOMAIN Analysis.

The variable domains (V-DOMAIN) of the antigen receptors, immunoglobulins (IG) or antibodies and Tcell receptors (TR), which specifically recognize the antigens show a huge diversity in their sequences. This diversity results from the complex mechanisms involved in the synthesis of these domains at the DNA level (rearrangements of the variable (V), diversity (D), and joining (J) genes; N-diversity; and, for the IG, somatic hypermutations). The recognition of V, D, and J as "genes" and their entry in databases mark the creation of IMGT by Marie-Paule Lefranc, and the origin of immunoinformatics in 1989. For 30years, IMGT®, the international ImMunoGeneTics information system® http://www.imgt.org , has implemented databases and developed tools for IG and TR immunoinformatics, based on the IMGT Scientific chart rules and IMGT-ONTOLOGY concepts and axioms, and more particularly, the princeps ones: IMGT genes and alleles (CLASSIFICATION axiom) and the IMGT unique numbering and IMGTCollierdePerles (NUMEROTATION axiom). This chapter describes the online tools for the characterization and annotation of the expressed V-DOMAIN sequences: (a) IMGT/V-QUEST analyzes in detail IG and TR rearranged nucleotide sequences, (b) IMGT/HighV-QUEST is its high throughput version, which includes a module for the identification of IMGT clonotypes and generates immunoprofiles of expressed V, D, and J genes and alleles, (c) IMGT/StatClonotype performs the pairwise comparison of IMGT/HighV-QUEST immunoprofiles, (d) IMGT/DomainGapAlign analyzes amino acid sequences and is frequently used in antibody engineering and humanization, and (e) IMGT/Collier-de-Perles provides two-dimensional (2D) graphical representations of V-DOMAIN, bridging the gap between sequences and 3D structures. These IMGT® tools are widely used in repertoire analyses of the adaptive immune responses in normal and pathological situations and in the design of engineered IG and TR for therapeutic applications.

Television as a Source of Cultural Inspiration: Measuring Impact of Television Programs on Cultural Values of Youth

Television is cheap source of information that provides various programs regarding to social, political, cultural and entertainment. Where television has become part of every home, there it has also caused of various effects. These effects have already discussed in the past and vast literature is available that shows strong relationship among public. The objective of this article was to examine the impact of television on cultural values of adolescents. This research study was developed based on the survey and data was collected from n=200 university students using self-designed questionnaire. The results presented by applying statistical tests and two-dimensional graphic representation using a software visualization approach. It is observed that excessive use of electronic media (mainly television) among young people leads to a conventional diminution of the cultural and traditional virtues, whereas it found lack of presentation of women image according to the religious concept.

Invariance analysis for determining the closed-form solutions, optimal system, and various wave profiles for a (2+1)-dimensional weakly coupled B-Type Kadomtsev-Petviashvili equations

In the case of negligible viscosity and surface tension, the B-KP equation shows the evolution of quasi-one-dimensional shallow-water waves, and it is growingly used in ocean physics, marine engineering, plasma physics, optical fibers, surface and internal oceanic waves, Bose-Einstein condensation, ferromagnetics, and string theory. Due to their importance and applications, many features and characteristics have been investigated. In this work, we attempt to perform Lie symmetry reductions and closed-form solutions to the weakly coupled B-Type Kadomtsev-Petviashvili equation using the Lie classical method. First, an optimal system based on one-dimensional subalgebras is constructed, and then all possible geometric vector yields are achieved. We can reduce system order by employing the one-dimensional optimal system. Furthermore, similarity reductions and exact solutions of the reduced equations, which include arbitrary independent functional parameters, have been derived. These newly established solutions can enhance our understanding of different nonlinear wave phenomena and dynamics. Several three-dimensional and two-dimensional graphical representations are used to determine the visual impact of the produced solutions with determined parameters to demonstrate their dynamical wave profiles for various examples of Lie symmetries. Various new solitary waves, kink waves, multiple solitons, stripe soliton, and singular waveforms, as well as their propagation, have been demonstrated for the weakly coupled B-Type Kadomtsev-Petviashvili equation. Lie classical method is thus a powerful, robust, and fundamental scientific tool for dealing with NPDEs. Computational simulations are also used to prove the effectiveness of the proposed approach.

The second and third waves in India: when will the pandemic be culminated?

An unprecedented upsurge of COVID-19-positive cases and deaths is currently being witnessed across India. According to WHO, India reported an average of 3.9 lakhs of new cases during the first week of May 2021 which equals 47% of new cases reported globally and 276 daily cases per million population. In this letter, the concept of SIR and fractal interpolation models is applied to predict the number of positive cases in India by approximating the epidemic curve, where the epidemic curve denotes the two-dimensional graphical representation of COVID-19-positive cases in which the abscissa denotes the time, while the ordinate provides the number of positive cases. In order to estimate the epidemic curve, the fractal interpolation method is implemented on the prescribed data set. In particular, the vertical scaling factors of the fractal function are selected from the SIR model. The proposed fractal and SIR model can also be explored for the assessment and modeling of other epidemics to predict the transmission rate. This letter investigates the duration of the second and third waves in India, since the positive cases and death cases of COVID-19 in India have been highly increasing for the past few weeks, and India is in a midst of a catastrophizing second wave. The nation is recording more than 120 million cases of COVID-19, but pandemics are still concentrated in most states. In order to predict the forthcoming trend of the outbreaks, this study implements the SIR and fractal models on daily positive cases of COVID-19 in India and its provinces, namely Delhi, Karnataka, Tamil Nadu, Kerala and Maharashtra.

Optimization of electronic nose drift correction applied to tomato volatile profiling.

E-noses can be routinely used to evaluate the volatile profile of tomato samples once the sensor drift and standardization issues are adequately solved. Short-term drift can be corrected using a strategy based on a multiplicative drift correction procedure coupled with a PLS adaptation of the component correction. It must be performed specifically for each sequence, using all sequence signals data. With this procedure, a drastic reduction of sensor signal %RSD can be obtained, ranging between 91.5 and 99.7% for long sequences and between 75.7 and 98.8% for short sequences. On the other hand, long-term drift can be fixed up using a synthetic reference standard mix (with a representation of main aroma volatiles of the species) to be included in each sequence that would enable sequence standardization. With this integral strategy, a high number of samples can be analyzed in different sequences, with a 94.4% success in the aggrupation of the same materials in PLS-DA two-dimensional graphical representations. Using this graphical interface, e-noses can be used to developed expandable maps of volatile profile similitudes, which will be useful to select the materials that most resemble breeding objectives or to analyze which preharvest and postharvest procedures have a lower impact on the volatile profile, avoiding the costs and sample limitations of gas chromatography.

The design heatmap: A simple visualization of -optimality design problems.

Optimal experimental designs are often formal and specific, and not intuitively plausible to practical experimenters. However, even in theory, there often are many different possible design points providing identical or nearly identical information compared to the design points of a strictly optimal design. In practical applications, this can be used to find designs that are a compromise between mathematical optimality and practical requirements, including preferences of experimenters. For this purpose, we propose a derivative-based two-dimensional graphical representation of the design space that, given any optimal design is already known, will show which areas of the design space are relevant for good designs and how these areas relate to each other. While existing equivalence theorems already allow such an illustration in regard to the relevance of design points only, our approach also shows whether different design points contribute the same kind of information, and thus allows tweaking of designs for practical applications, especially in regard to the splitting and combining of design points. We demonstrate the approach on a toxicological trial where a -optimal design for a dose-response experiment modeled by a four-parameter log-logistic function was requested. As these designs require a prior estimate of the relevant parameters, which is difficult to obtain in a practical situation, we also discuss an adaption of our representations to the criterion of Bayesian -optimality. While we focus on -optimality, the approach is in principle applicable to different optimality criteria as well. However, much of the computational and graphical simplicity will belost.

BAROQUE BANDED VAULTS: SURVEYING AND MODELING. THE CASE STUDY OF A NOBLE PALACE IN TURIN

Abstract. This paper presents the methodological framework set up for the analysis, interpretation, and representation of the banded vaulted systems recognized in eleven Baroque atria in Turin. In these atria, the banded vaults, locally named “a fascie”, are featured by a series of arches orthogonal to the perimeter walls on which they rest. The arches divide the room’s ceiling into spaces that can accommodate small vaults of different shapes. The atria have been the subject of bibliographical, historical and documentary analyses, laser scanner metric survey, two-dimensional graphic representations, and interpretative hypotheses through three-dimensional modeling of the design’s geometries of the vaults.The integration between terrestrial laser scanning (TLS) technique, architectural drawing and three-dimensional modeling methods led to the definition of new workflows, aimed at optimizing the use of data. From these procedures new opportunities for the research arise, such as the comparison (metric and geometric) through the superimposition of design ideal models and point clouds.

The Networks Infection Contagious Diseases Positioning System (NICDP-System): The Case of Wuhan-COVID-19

This paper formulates an analytical framework to understand the spatiotemporal patterns of epidemic disease occurrence, its relevance and implications to economic activity, their impact on the vulnerability of different populations, and to develop public health policy decisions on disease prevention issues. The paper suggests a paradigm shift: a new multidimensional geometric approach to capture all symmetrical and asymmetrical strategic graphical movements in real space and time. The Networks Infection Contagious Diseases Positioning System (NICDP-System) extends the traditional two-dimensional graphical representation into a multidimensional graphical framework that synchronizes the optimal virus behavior in real-time. The model investigates the epidemic 2019 novel coronavirus (COVID-19) identified in Wuhan City, Hubei Province, China.

Adaptive structure modeling and prediction for swarm unmanned system

In recent years, swarm unmanned systems (SUSs) have become crucial in the military field, both at home and abroad. This has promoted the evolution of the unmanned combat mode from single-platform remote-control to intelligent-swarm combat. SUSs support the cooperative, autonomous, and flexible characteristics of the combat system under uncertain tasks and environments. The overall swarm performance depends on the system and structure among its members and also dynamically evolves with the time and the environment. Thus, new intelligence emerges from the interaction among systems. Starting from the evolution of the SUS structure, this paper proposes the model of a three-layer structure and a relationship involving the data-link layer, the SUS, and the task requirements. The multidimensional spatial relationship model is transformed into a two-dimensional graphical representation model by using a graph neural network; then, the dependency graph of the relationships of the systems and layers of the SUS is constructed. The integral network is classified according to a task-based standard. The recursive neural network algorithm is derived from the intra- and interlayer relationships. The SUS structure is predicted via some examples of training data sets and the attribute labels of task-based nodes. The impact of the system or data layer damage can be evaluated according to the weight parameters of the structure dependence relationship. Finally, the autonomous decision of the SUS from the task to the swarm structure is realized.

Design, construction, and implementation of an inexpensive underwater passive SONAR

For almost 20 years, the University of Florida’s Machine Intelligence Laboratory (MIL) at the University of Florida (UF) has been creating SONAR systems for locating underwater transmitters. These systems have helped UF teams achieve significant success in international robotic competitions. However, when students graduate, their knowledge is often lost. This paper documents the process of developing a highly accurate, inexpensive SONAR system for future UF projects.A four-hydrophone array SONAR simulator was created to test a time difference of arrival approach used to estimate the location of a sound sources. The software was then applied to an actual SONAR system built in the laboratory. Two-dimensional graphic representations of the SONAR’s accuracy were created to visualize the system’s performance. This article summarizes the results.

Squiggle: a user-friendly two-dimensional DNA sequence visualization tool.

Squiggle is a software tool that automatically generates interactive web-based two-dimensional graphical representations of raw DNA sequences. Built with ease of use in mind, Squiggle implements several prior sequence visualization algorithms and introduces novel visualization methods designed to maximize human usability. Squiggle is written in Python 3 and freely available under the permissive MIT license. The open-source code can be downloaded from github.com/Lab41/squiggle as well as the Python Package Index. The installation instructions and user guide are available at squiggle.readthedocs.org.

Monitoring a Francis turbine operating conditions

Francis turbines are designed for a specific set of operating conditions that is particular to each hydropower plant site. It allows this type of turbine to extract as much hydraulic power as possible, as long as they are operating in the right conditions. For this reason, power plant operators must know in advance what are the best conditions for operating their generating units and, naturally, in which exact conditions these units are actually operating. Detailed information about the turbine behavior in any operating condition can be obtained by performing measurements in a reduced scale physical model of the turbine prototype. These tests provide what is known as the turbine hill chart: a two-dimensional graphical representation of the most relevant turbine properties showing, for instance, the power output, the discharge, the efficiency and the cavitation conditions. This paper presents a method to monitor the operating conditions of a Francis turbine by locating it on the hill chart. To do so, it requires the generation of polynomial bi-variate functions based on Hermite polynomials that can calculate the turbine discharge and efficiency from its guide vanes angle and power output. A test case is presented with a turbine prototype of 444 MW of rated power operating through a wide range of operating conditions. The validation is done by comparisons between the measured and estimated values of gross head, leading to similar values.