3D Graphical Representation Research Articles

GENERALISED TWO-COMPONENT MODIFIED WEAKLY DISSIPATIVE DULLIN-GOTTWALD-HOLM SYSTEM: INVARIANCE ANALYSIS AND CONSERVATION LAWS

The Dullin-Gottwald-Holm equation models the unidirectional propagation of shallow regime water waves. In this work, the Lie symmetry analysis of the generalised two-component modified weakly dissipative Dullin-Gottwald-Holm system is performed. Using symmetry reduction, the exact solutions are obtained in the form of power series and trigonometric functions. Also using multiplier approach, the conservation laws are obtained. The 3D graphical representations are also shown for obtained solutions.

Mitigation of transient ground potential rise in gas insulated substations during very fast transient overvoltage

• The paper proposes PEEC based a simulation technique the allow to take into account the complex 3D structure and the various electromagnetic coupling phenomena that take place between the metallic structure of a complex GIS and the associated earthing system during VFTO events. • The proposed GIS modeling and simulation technique is applied in case of 110 kV GIS in order to identify the grounding grid area that mostly effect the clearance of VFTO fault. • A mitigation procedure is show cased for the identified grounding grid area in order to accelerate the clearance of VFTO faults. This paper is focused on the assessment and mitigation of the transient response of a Gas Insulated Substation's (GIS) grounding grid to the fault due to voltage breakdown using the Partial Element Equivalent Circuit (PEEC) numerical approach. The adopted analysis methodology considers the magnetic induction by quantifying the electromagnetic couplings generated within the metallic components contained by the GIS configuration. The Transient Ground Potential Rise (TGPR) and transient current are computed and analyzed at several locations inside of GIS housing. With the aid of 3D graphical representation, the maximum amplitudes of the TGPR across the substation are illustrated. The mitigation efforts are considerably optimized by assuming the grounding grid sub-system is responsible for high frequency fault energy clearance based on identification method. By adopting several simplifications of the earthing system during the computational process, from a step-by-step analysis, it has been discovered that the grid located beneath the GIS enclosure will mostly attenuate the TGPR across the GIS building. Based on the aforementioned findings a successful mitigation technique is implemented.

Rational W-shape solitons on a nonlinear electrical transmission line with Josephson junction

This paper examines envelope solitons, rational W-shape solitons to a Nonlinear Electrical Transmission Line (NETL) with Josephson junction (JJ) that consist of the Nth cells of circuits. By employing the reductive perturbation approach in the semi-discrete approximation, we obtain the nonlinear Schrödinger equation (NLSE). From this equation, the frequency ranges of propagation of bright and dark solitons were obtained. As in most of the works, the NLSE obtained is well known as the seat of rogue waves and Peregrine solitons. The nonlinearity provided by the JJ, combined with the dispersion, made it possible to study the Modulation Instability (MI) gain spectrum. The 3D and 2D graphical representations illustrated the instability zones and the W-rational solutions have followed by using numerical simulation. The results obtained in this paper are of a very capital contribution for the study of rogue waves in nonlinear transmission lines or other physical problems.

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

The Ivancevic option pricing model comes as an alternative to the Black‐Scholes model and depicts a controlled Brownian motion associated with the nonlinear Schrodinger equation. The applicability and practicality of this model have been studied by many researchers, but the analytical approach has been virtually absent from the literature. This study intends to examine some dynamic features of this model. By using the well‐known ARS algorithm, it is demonstrated that this model is not integrable in the Painlevé sense. He’s variational method is utilized to create new abundant solutions, which contain the bright soliton, bright‐like soliton, kinky‐bright soliton, and periodic solution. The bifurcation theory is applied to investigate the phase portrait and to study some dynamical behavior of this model. Furthermore, we introduce a classification of the wave solutions into periodic, super periodic, kink, and solitary solutions according to the type of the phase plane orbits. Some 3D‐graphical representations of some of the obtained solutions are displayed. The influence of the model’s parameters on the obtained wave solutions is discussed and clarified graphically.

Analyzing the Influence of Harmonic Parameters on Accuracy Indices When Applying Wavelet Transform

The paper deals with the evaluation of root mean square deviations and maximum absolute relative errors associated to the decomposition followed by recomposition based on Wavelet Packet Transform (WPT) of signals pol-luted with harmonics. Subtrees associated to sets of harmonics presenting practical interest for industrial applications are addressed. The study uses artificial signals generated through the superposition of perfect sinusoids with pairs of harmonics which proved to be related in an almost exclusive manner to pairs of nodes from the bottom level of a WPT tree. 4 parameters had to be considered when determining the maximum and minimum values of errors for each set: the clustered harmonics’ magnitudes and their phase-shifts relative to the component of fundamental frequency. The decomposition/recomposition are time-efficient due to an original system of flags labeling each node from the WPT tree. For each analyzed set of harmonics, 3d graphical representation of minimum and maximum errors along with the associated 3d graphical representation of the phase-shifts are provided. At the same time, per set limits of errors ranges were established and discussed while specific patterns were deduced for the context in which extreme errors appear (phase-shifts and harmonic magnitudes). The results were commented, and conclusions were drawn.

Applications of the Sub Equation Method for the High Dimensional Nonlinear Evolution Equation

In this article, Generalized (3+1)-dimensional Shallow Water-Like (SWL) equation is taken into consideration and exact solutions have been constructed of the SWL equation using sub equation method. This method is an easier and efficient method for finding analytic solutions of nPDEs. The method appears to be easier and faster for symbolic computation. Moreover 2D, 3D and contour graphical representation of the obtained results of the specified equation is made using ready-made package program for certain values and thus the conformity of the founded results has been demonstrated.

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

This work is interested in constructing new traveling wave solutions for the coupled nonlinear Schrödinger type equations. It is shown that the equations can be converted to a conservative Hamiltonian traveling wave system. By using the bifurcation theory and Qualitative analysis, we assign the permitted intervals of real propagation. The conserved quantity is utilized to construct sixteen traveling wave solutions; four periodic, two kink, and ten singular solutions. The periodic and kink solutions are analyzed numerically considering the effect of varying each parameter keeping the others fixed. The degeneracy of the solutions discussed through the transmission of the orbits illustrates the consistency of the solutions. The 3D and 2D graphical representations for solutions are presented. Finally, we investigate numerically the quasi-periodic behaviour for the perturbed system after inserting a periodic term.

On the solutions and conservation laws of the Yu–Toda–Sasa–Fukuyama equation of plasma physics

In this work, we investigate the two-dimensional Yu–Toda–Sasa–Fukuyama equation, which has many applications in plasma physics and other fields of study in natural sciences. Exact analytical solutions of this model are presented by invoking Lie symmetry analysis technique. Moreover, the power series expansion method is also used to construct exact analytical solutions. We present the 2D and 3D graphical representations of the obtained solutions for some parametric values so as to demonstrate the dynamic behaviour of the solutions. Furthermore, conserved vectors are derived by making use of two methods, namely the multiplier method and Noether’s theorem.

Topological Analysis of PAHs using Irregularity based Indices

Topological descriptors are non-empirical graph invariants that characterize the structures of chemical molecules. The structural descriptors are vital components of QSAR/QSPR studies which form the basis for theoretical chemists to design and investigate new chemical structures. Irregularity indices are a class of topological descriptors that have been employed to study certain chemical properties of compounds. This article aims to compute analytical expressions of irregularity indices for three important classes of polycyclic aromatic hydrocarbons. The intriguing properties of these classes of compounds have several potential applications in wide-raging fields, which warrant a study of their properties from a structural perspective. Additionally, the 3D graphical representations of a few indices are presented, which will aid in analyzing the similarity of behavior among the indices.

On Degree-Based Topological Indices for Strong Double Graphs

A topological index is a characteristic value which represents some structural properties of a chemical graph. We study strong double graphs and their generalization to compute Zagreb indices and Zagreb coindices. We provide their explicit computing formulas along with an algorithm to generate and verify the results. We also find the relation between these indices. A 3D graphical representation and graphs are also presented to understand the dynamics of the aforementioned topological indices.

Surgical workflow simulation for the design and assessment of operating room setups in orthopedic surgery

BackgroundThe design and internal layout of modern operating rooms (OR) are influencing the surgical team’s collaboration and communication, ergonomics, as well as intraoperative hygiene substantially. Yet, there is no objective method for the assessment and design of operating room setups for different surgical disciplines and intervention types available. The aim of this work is to establish an improved OR setup for common procedures in arthroplasty.MethodsWith the help of computer simulation, a method for the design and assessment of enhanced OR setups was developed. New OR setups were designed, analyzed in a computer simulation environment and evaluated in the actual intraoperative setting. Thereby, a 3D graphical simulation representation enabled the strong involvement of clinical stakeholders in all phases of the design and decision-making process of the new setup alternatives.ResultsThe implementation of improved OR setups reduces the instrument handover time between the surgeon and the scrub nurse, the travel paths of the OR team as well as shortens the procedure duration. Additionally, the ergonomics of the OR staff were improved.ConclusionThe developed simulation method was evaluated in the actual intraoperative setting and proved its benefit for the design and optimization of OR setups for different surgical intervention types. As a clinical result, enhanced setups for total knee arthroplasty and total hip arthroplasty surgeries were established in daily clinical routine and the OR efficiency was improved.

2D Graphical Representation of DNA Sequences Based on Variant Map

Mining and analyzing the information and structure of DNA sequences is an important method of exploring and explaining the mysteries of biology. In addition to traditional biological detection methods for DNA sequences, technological advances have allowed researchers to utilize computers to analyze DNA sequences, such as in DNA visualization. However, DNA visualization techniques have disadvantages, such as difficult operation and complex calculation. Therefore, in this paper, we propose an algorithm called VARCH based on a variant map that is a part of variant logic construction. VARCH is a high-efficiency and concise visualization algorithm for DNA sequences. The principle of this approach is that the number of base combinations in each DNA subsequence is counted, and a matrix is constructed based on the full arrangement of different base combinations. Finally, the matrix is mapped to the 2D coordinate plane, obtaining the image of DNA sequences. The experimental results demonstrate that VARCH can effectively display features of DNA sequences.

MicroRNA prediction based on 3D graphical representation of RNA secondary structures.

MicroRNAs (miRNAs) are posttranscriptional regulators of gene expression. While a miRNA can target hundreds of messenger RNA (mRNAs), an mRNA can be targeted by different miRNAs, not to mention that a single miRNA might have various binding sites in an mRNA sequence. Therefore, it is quite involved to investigate miRNAs experimentally. Thus, machine learning (ML) is frequently used to overcome such challenges. The key parts of a ML analysis largely depend on the quality of input data and the capacity of the features describing the data. Previously, more than 1000 features were suggested for miRNAs. Here, it is shown that using 36 features representing the RNA secondary structure and its dynamic 3D graphical representation provides up to 98% accuracy values. In this study, a new approach for ML-based miRNA prediction is proposed. Thousands of models are generated through classification of known human miRNAs and pseudohairpins with 3 classifiers: decision tree, naïve Bayes, and random forest. Although the method is based on human data, the best model was able to correctly assign 96% of nonhuman hairpins from MirGeneDB, suggesting that this approach might be useful for the analysis of miRNAs from other species.

Enhancing Civil Engineering teaching through 3D Computer Aided Design

3D interpretation of 2D drawing is not easy for most of the Civil Engineering first-year students. Some do it naturally but most need to be trained to master this skill. In this paper, the implemented teaching methodologies aiming to facilitate the acquisition of three-dimensional project visualization skills are presented. These methodologies were developed during the last two years targeting first-year Civil Engineering students at the University of Beira Interior (Portugal). After a first contact with 2D project representation through manual drawing, students progressively elaborate computer-aided design (CAD) project starting with simple 2D drawings and culminating with a 3D project of a pre-existing building. Students are also motivated to improve their 3D graphic representation skills through a classroom contest where the winning project is printed in 3D. The training in 2D and 3D graphic representation is complemented during the second year with several in situ surveys and computer-aided drawing of topographic data. This approach proved to be very interesting for competence acquisition, qualifying students for a better 3D representation and interpretation. Students also found this methodology to be motivating.

Subject-Specific Surgical Planning for Hip Replacement: A Novel 2D Graphical Representation of 3D Hip Motion and Prosthetic Impingement Information

Prosthetic impingement (PI) following total hip arthroplasty (THA), which arises due to the undesirable relative motion of the implants, results in adverse outcomes. Predicting PI through 3D graphical representation is difficult to comprehend when all activities are combined for different implant positions. Therefore, the aim of the paper was to translate this 3D information into a 2D graphical representation for improved understanding of the patient’s hip motion. The method used planned implanted geometry, positioned onto native bone anatomy, and activity definitions as inputs to construct the 2D polar plot from 3D hip motion in four steps. Three case studies were performed to highlight its potential use in (a) combining different activities in a single plot, (b) visualising the effect of different cup positions and (c) pelvic tilt on PI. A clinical study with 20 ‘Non-Dislocators’ and 20 ‘Dislocators’ patients after 2 years of THA was performed to validate the method. The results supported the study hypothesis, in that the incidence of PI was always higher in the ‘Dislocators’ compared to the ‘Non-Dislocators’ group. The proposed 2D graphical representation could assist in subject-specific THA planning by visualising the effect of different activities, implant positions, pelvic tilt and related aspects on PI.

A New Numerical Method for DNA Sequence Analysis Based on 8-Dimensional Vector Representation

Background: The multiple sequence alignment (MSA) algorithms are the traditional ways to compare and analyze DNA sequences. However, for large DNA sequences, these algorithms require a long time computationally. Objective: Here we will propose a new numerical method to characterize and compare DNA sequences quickly. Method: Based on a new 2-dimensional (2D) graphical representation of DNA sequences, we can obtain an 8-dimensional vector using two basic concepts of probability, the mean and the variance. Results: We perform similarity/dissimilarity analyses among two real DNA data sets, the coding sequences of the first exon of beta-globin gene of 11 species and 31 mammalian mitochondrial genomes, respectively. Conclusion: Our results are in agreement with the existing analyses in our literatures. We also compare our approach with other methods and find that ours is more effective.

Two phospholipid scramblase 1–related proteins (PLSCR1like-a & -b) from Liza haematocheila: Molecular and transcriptional features and expression analysis after immune stimulation

Phospholipid scramblases (PLSCRs) are a family of transmembrane proteins known to be responsible for Ca2+-mediated bidirectional phospholipid translocation in the plasma membrane. Apart from the scrambling activity of PLSCRs, recent studies revealed their diverse other roles, including antiviral defense, tumorigenesis, protein–DNA interactions, apoptosis regulation, and cell activation. Nonetheless, the biological and transcriptional functions of PLSCRs in fish have not been discovered to date. Therefore, in this study, two new members related to the PLSCR1 family were identified in the red lip mullet (Liza haematocheila) as MuPLSCR1like-a and MuPLSCR1like-b, and their characteristics were studied at molecular and transcriptional levels. Sequence analysis revealed that MuPLSCR1like-a and MuPLSCR1like-b are composed of 245 and 228 amino acid residues (aa) with the predicted molecular weights of 27.82 and 25.74 kDa, respectively. A constructed phylogenetic tree showed that MuPLSCR1like-a and MuPLSCR1like-b are clustered together with other known PLSCR1 and -2 orthologues, thus pointing to the relatedness to both PLSCR1 and PLSCR2 families. Two-dimensional (2D) and 3D graphical representations illustrated the well-known 12-stranded β-barrel structure of MuPLSCR1like-a and MuPLSCR1like-b with transmembrane orientation toward the phospholipid bilayer. In analysis of tissue-specific expression, the highest expression of MuPLSCR1like-a was observed in the intestine, whereas MuPLSCR1like-b was highly expressed in the brain, indicating isoform specificity. Of note, we found that the transcription of MuPLSCR1like-a and MuPLSCR1like-b was significantly upregulated when the fish were stimulated with poly(I:C), suggesting that such immune responses target viral infections. Overall, this study provides the first experimental insight into the characteristics and immune-system relevance of PLSCR1-related genes in red lip mullets.

Base Distribution in Dengue Nucleotide Sequences Differs Significantly from Other Mosquito-Borne Human-Infecting Flavivirus Members.

Among the mosquito-borne human-infecting flavivirus species that include Zika, West Nile, yellow fever, Japanese encephalitis and Dengue viruses, the Zika virus is found to be closest to Dengue virus, sharing the same clade in the Flavivirus phylogenetic tree. We consider these five flaviviruses and on closer examination in our analyses, the nucleotide sequences of the Dengue viral genes (envelope and NS5) and genomes are seen to be quite widely different from the other four flaviviruses. We consider the extent of this distinction and determine the advantage and/or disadvantage such differences may confer upon the Dengue viral pathogenesis. We have primarily used a 2D graphical representation technique to show the differences in base distributions in these five flaviviruses and subsequently, obtained quantitative estimates of the differences. Similarity/dissimilarity between the viruses based on the genes were also determined which showed that the differences with the Dengue genes are more pronounced. We found that the Dengue viruses compared to the other four flaviviruses spread rapidly worldwide and became endemic in various regions with small alterations in sequence composition relative to the host populations as revealed by codon usage biases and phylogenetic examination. We conclude that the Dengue genes are indeed more widely separated from the other aforementioned mosquito-borne human-infecting flaviviruses due to excess adenine component, a feature that is sparse in the literature. Such excesses have a bearing on drug and vaccine, especially peptide vaccine, development and should be considered appropriately.

On the Usage of Different Coordinate Systems for 3D Plots of Functions of Two Real Variables

Students learning towards a degree in a STEM related domain learn quite early a course in Advanced Calculus, i.e. a course where the main object of study are multivariate functions. It happens that students do not see the connection between the properties of the function such as continuity or differentiability and the 3-dimensional graphical representation. In particular, difficulties appear in classroom for functions having different limits at a point, according to the path approaching the point. One of the ways for this analysis is to use different coordinate systems to study the behavior of the function. Constraints exist on the hardware, the software and on the numerical approximation methods, which may lead to completely different graphs for the same function, when using two different coordinate systems. In this contribution we analyze the different types of graphs created with a CAS such as MATLAB 14 and Maple 2017 for different coordinate systems, in terms of properties of the 2-variable function under study. We prove that when the function is continuous, the 3D graphical representation does not depend on the coordinate system in use. However, when the function is discontinuous,the graphical representation depends strongly on the coordinate system and on the type of discontinuity (point singularity, line singularity, multiple singularity, etc.). Moreover, without a suitable analysis prior to plotting, the 3D graph may be uncorrect. The software shows a strange behavior around the singular points. It happens also that a line singularity is replaced either by a point singularity or by no singularity. We analyse the software behavior using numerical analysis of the meshing algorithm.

Rogue wave solutions in nonlinear optics with coupled Schrödinger equations

In this article, the first and second-order rogue wave solutions are obtained which are localized in both space and time that appear from nowhere and disappear without a trace. The coupled NLSEs with time-dependent coefficients are considered that describe the effects of ultrashort optical pulse propagation in nonlinear optics and quantum physics. The similarity transformation is used to investigate these rational-like (rogue wave) solutions. Moreover, the 3D graphical representations and contour plots have depicted with different parameters of gravity field and external magnetic field.