Dimensional Graphics Research Articles

Exact Solutions for the Modified Burgers Equation with Additional Time-dependent Variable Coefficient

In this article, we investigated new travelling wave solutions for the modified Burgers equation with additional time-dependent variable coefficient via the functional variable method. The performance of this method is reliable and effective and gives the exact solitary wave solutions. All solutions of this equation have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab program. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena. This method presents a wider applicability for handling nonlinear wave equations.

Metaverse: Trend, emerging themes, and future directions

AbstractMetaverse is going to change human life in a profound way because it offers an opportunity to merge our physical world with the digital/virtual worlds. Yet, how much effort has the research community across the world and disciplines contributed and what are the emerging themes of metaverse? The study aims to answer these important research questions using a bibliometric approach. Using a search of (“metaverse” OR “metaverses”) in “Article Title, Abstract, Keywords” and the date range up to 2022 on March 15, 2023 in Scopus, 1031 journal articles, reviews, and conference papers were identified. Among the 1031 identified documents, 816 (i.e., around 80%) were published in 2022. Feiyue Wang of the Institute of Automation, Chinese Academy of Sciences was found to be the most productive author with 17 metaverse publications, followed by Elif Ayiter of Sabancı Üniversitesi with 11 metaverse publications. The Chinese Academy of Sciences (with its Institute of Automation) was found to be the most productive affiliation with 29 publications. China, the United States, South Korea, and the United Kingdom were the most productive countries that contributed to over 58% of metaverse publications. Co‐occurrence of keywords analysis revealed that seven clusters were emerged. The clusters included “artificial intelligence and human perception,” “metaverses and blockchain,” “e‐learning and students,” “metaverse, avatar and immersive,” “virtual reality, virtual worlds, and Second Life,” “three dimensional computer graphics and deep learning,” and “augmented reality, mixed reality, and human computer interaction.” Implications and future directions are given.

Origin of the elastic anisotropy of silica particles: Insights from first-principles calculations and nanoindentation molecular dynamic simulations

To better elucidate and comprehend the origin of the elastic anisotropy observed in silica sand, this study investigates the nanoscale mechanical properties of α-quartz (the main component of silica sand) using the first-principles calculations (density functional theory, DFT) and nanoindentation molecular dynamics (MD) simulations. The cell parameters and elastic constants (Cij) of α-quartz are obtained by DFT with PBESOL functional. The electron density difference of the most commonly exposed crystal surfaces {100}, {001}, and {101}, exhibits significant distinction, which is considered as the underlying cause of α-quartz's elastic anisotropy. This study reveals a significant difference in Young's modulus E, Poisson's ratio v, and hardness H along different directions, which are also visualized in three dimensional graphics. Notably, E{100} = 81.576 GPa < E{001} = 101.198 GPa < E{101} = 113.323 GPa, and H{001} = 9.068 GPa < H{100} = 11.258 GPa < H{101} = 19.870 GPa. The change in E calculated by MD simulations is consistent with DFT calculations. Additionally, this study observed distinct initiation of yielding during nanoindentation for different crystal surfaces, with the corresponding indentation yielding depth following the trend D{100} > D{001} > D{101}. Furthermore, both DFT and MD simulation results indicate that the negative v effect on E is negligible in α-quartz.

On the dynamics of exact solutions to a (3+1)-dimensional YTSF equation emerging in shallow sea waves: Lie symmetry analysis and generalized Kudryashov method

This paper focuses on obtaining a large number of exact solutions to the highly nonlinear (3+1)-dimensional Yu–Toda–Sassa–Fukuyama (YTSF) equation, which is important in fluid dynamics, plasma physics, nonlinear sciences, and weakly dispersive media, among other things. The primary goal of this research is to obtain a variety of exact soliton solutions and different dynamical wave-forms of the YTSF equation using two different techniques: Lie symmetry and generalized Kudryashov (GK) methods. These techniques reduce the considered partial differential equation (PDE) into ordinary differential equations (ODEs). Hereafter, a variety of exact solutions are derived with the help of the associated subalgebras and wave transformation by the Lie symmetry technique and GK technique, respectively. The obtained exact solutions involve various arbitrary constants, parameters, and arbitrary functionals that enhance the dynamic representation of the derived solutions in the research area. We use numerical simulations to generate 3-dimensional graphics and contour plots to determine the dynamical behavior of the obtained exact solutions. The physical interpretation of interaction soliton solutions demonstrates a rich diversity of attained solutions, such as solitons, kink waves, kink wave interaction with solitons, and others.

The Future Cities that Were Shaped by Visual Culture of 1980’s SCI-FI Movies

At the turn of the 20th century modernism was it’s own way. Futurism has its manifesto by expressing of the celebration of the new era. It was underlining the fact that new era should destroy all previous ties of traditionalism and one should turn its head to the developments of industrial revolution. Architecture created its own dynamics by examining the tradition, later combining it with revolution and at the end creating the vocabulary of its own language. As Pioneer architect Le Corbusier illustrated the appearance of feature cities in his sketches some other new art forms were on its way. Meanwhile; cinema as the new art form, visualised and rather prophecisied future cities as architects of the new world foreseen the facts of the future appearance of the cities. The aim of this paper is to investigate the effects of the cinema industry of 1980’s on future cities and the reflections of three dimensional graphics on architectural facades of the future cities by examining the movie based sci-fi hallucinations that come to be true in today’s cities.

The role of virtual reality in hepato-pancreato-biliary surgical education: A systematic review

Background: Virtual reality (VR) is a technology that can be used as a tool to create 3-dimensional graphics for surgical education, including anatomy and surgical skills teaching. Hepato-pancreato-biliary (HPB) surgery requires specialized surgical skill training and is characterized by cases of complex anatomical variations, which might be difficult to appreciate and conceptualize for trainees in their early stages of education. We performed this systematic review to summarize evidence on real-world VR implementation in surgical education for HPB surgical trainees and to understand the effects of VR on HPB trainees.

Fuzzy Logic Modelling Of The Effect Of Tool Tip Radius On Surface Roughness In Machining Co28Cr6Mo Wrought Steels In CNC Turning

This study includes fuzzy logic modeling of surface roughness experimental values obtained as a result of machining Co28Cr6Mo medical alloy in CNC turning (rotational speed (n), feed rate (f), depth of cut (a) and tool tip radius (r)) depending on cutting parameters. According to the hardness of the material to be cut and the type of cutting tool used, fuzzy logic solution models that can determine the most suitable tool tip radius for the surface roughness (Ra) were created. In the model created using fuzzy logic, experimental studies on the rule base created by using the membership functions of the input parameters and the output parameters, the membership function foot widths and the relations between the membership functions were used. Triangle (trimf) membership function was chosen with Mamdani approach on the rule base. The results obtained using the established model are interpreted with 2 and 3 dimensional graphics for tool tip radius. We can say that a good surface quality (minimum surface roughness) is obtained on the material with the most suitable (optimal) tool tip radius determined by models established with fuzzy logic.

New Solutions for IOPM and (3+1)-Dimensional NLWE in Liquid with Gas Bubbles

Generalized Kudryashov method (GKM), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been used to obtain some solutions of Ivancevic option pricing model (IOPM) and (3+1)-dimensional nonlinear wave equation (NLWE) in liquid with gas bubbles. Thus, some solutions of the discussed equations have been found such as dark soliton, trigonometric and hyperbolic solutions. Two dimensional (2D) and three dimensional (3D) graphics of these solutions have been drawn with the help of Wolfram Mathematica 12.

Zurich Appearance Score for Hands: Development and Validation of an Instrument for Assessing Hand Appearance in Congenital Upper Limb Differences

The appearance of the hand is relevant to individual activity and participation. Improving appearance is often one of the essential goals of hand surgery. The aim of this study was to describe and validate an instrument for quantitatively assessing hand appearance in congenital upper limb differences (CULD). The Zurich Appearance Score for Hands (ZASH) was developed as a summed score of 6 items: 1 for overall appearance and 5 specific items for the skin, proportions of the hand, the number of digits, the shape of fingers and the thumb, and the position of the thumb. Each item can be rated on an 11-point Likert scale. Here, 448 participants (age, 14-83 years) were asked to rate the images of 17 hands, including standardized 3-dimensional photorealistic computer graphics and photographs of children's hands with or without CULDs, some after surgical correction. The sociodemographic characteristics of the participants were measured using a short questionnaire. The ZASH score for all CULDs was significantly lower than the ZASH score for normal hands. Correlations for overall appearance and the ZASH score were high (r= 0.77-0.87). The internal consistency of all ZASH scores was good to excellent (Cronbach α= 0.82-0.94). The test-retest reliability in a subgroup of 54 participants was good (r= 0.53-0.79). The interrater reliability of the ZASH score was moderate (intraclass correlation= 0.47). The ZASH is a valid and moderately reliable instrument for assessing hand appearance in children with CULDs. Achieving the best possible appearance is the one of the most relevant goals of hand surgery. Assessment with validated instruments provides evidence on how to approach this goal. Further studies may clarify whether the ZASH can be recommended for all hand conditions and to what extent observers' sociocultural and professional backgrounds affect perception.

Simulation of Magnetic Anisotropy Energy Surfaces for Cubic Crystals Using MATLAB in Remote Material Physics Lectures

The physical characteristics of a crystal can be viewed from the distribution of magnetic energy contained in it so that a simulation is needed which helps in visualizing the magnetic energy of the crystals. This study aims to present a simple solution for constructing a simulation of the physical properties of cubic crystals using MATLAB software. MATLAB can also be used to help organize physics lectures remotely. This is because MATLAB can be operated by anyone, anytime, and anywhere without being connected to the internet network to help visualize the material magnetization concept in the form of 2- and 3-dimensional graphics. The simulation aims to visualize the magnetic anisotropy energy surface for cubic crystals. This simulation can visualize the magnetic anisotropy energy surface of 3 types of cubic crystals, namely simple cubic, body-centered cubic, and face-centered cubic. In this simulation, the difference between the 3 types of crystals is the anisotropy energy constant. The mathematical equations in the magnetic anisotropy energy surface for cubic crystals are quite complicated. This simulation can help students in exploring mathematical equations and studying the magnetic anisotropy energy surface for cubic crystals more. Students can also develop mathematical representation skills and creative visual representations of the magnetic anisotropy energy surface for cubic crystals.&#x0D; HIGHLIGHTS&#x0D; &#x0D; The uniaxial anisotropy energy equation is closely related to helping to realize the behavior of materials&#x0D; Visualization of magnetic anisotropy energy surfaces in a crystal is influenced by the shape of the crystal and the value of its anisotropy constant&#x0D; Physics lectures during the Covid-19 pandemic require a variety of lectures that utilize the computational program-based physics equation simulation media&#x0D; Magnetic anisotropy energy surfaces on a crystal can be visualized through the help of computational programs to support physics lectures during the Covid-19 pandemic&#x0D; MATLAB can be used to visualize magnetic anisotropy energy surfaces because it can be operated by anyone, anytime, and anywhere without being connected to the internet network&#x0D; &#x0D; GRAPHICAL ABSTRACT

Solitary and periodic wave solutions of the loaded modified Benjamin-Bona-Mahony equation via the functional variable method

In this article, we established new travelling wave solutions for the loaded Benjamin-Bona-Mahony and the loaded modified Benjamin-Bona-Mahony equation by the functional variable method. The performance of this method is reliable and effective and gives the exact solitary wave solutions and periodic wave solutions. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab program. We get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations.

A new (3 + 1) dimensional Hirota bilinear equation: Periodic, rogue, bright and dark wave solutions by bilinear neural network method

This study deals with a new (3 + 1) dimensional Hirota equation that emerges in shallow water waves theory. Considering the bilinear form of this equation, the bilinear neural network method was applied. At this point, new activation functions have been proposed by using both single-layer and multi-layer neurons such as 4-2-2 and 4-2-3 types. As a result, a periodic type I–II, rogue, bright, and dark wave solutions with physical properties have been systematically produced via Maple symbolic software. In order to better consider the characteristics and dynamic structure of these revealed solution forms, 3D, contour, density, and 2D dimensional graphics are drawn for the appropriate values of the parameters. Bilinear neural network method includes many existing classical test functions and is an effective, robust and systematic approach.

Capabilities of the T-Scan 10 Novus System in the Diagnosis of Occlusion

The physiological restoration of occlusal relationships is important for the normal functioning of the masticatory system. Currently, qualitative and quantitative occlusal indicators are used in clinical practice for occlusion registration. In the past, articulation paper, foil, silk marks, waxes, etc. were the only tools available to access and balance the bite force. However, these methods do not detect simultaneous contact, nor do they quantify time and force. With the introduction of T-Scan, this changes. The evolution of T-Scan from the 1st generation to the 8th generation (1987-2016) has revolutionized the concept of occlusal analysis. The latest version of the T-Scan Novus system, is software version 10.0 that was released in 2018. The T-Scan Novus system is made up of hardware (handpiece, sensor) and Microsoft Windows-based software. &#x0D; Тhe registered occlusion is transformed by a computer into a dynamic film (dynamic occlusion video). Recorded occlusal contacts are then illustrated as 2- and 3-dimensional graphics. The improved features of the software provide detailed digital information about the occlusal relationships, which enhances the quality of their analysis.&#x0D; T-Scan Novus helps to avoid errors in the subjective judgment of the dentist and to control changes in occlusal contacts.

Kinetic and thermodynamic examinations for the unsteady couette flow problem of a plasma using the BGK cylindrical model

We aim to investigate the kinetic and irreversible thermodynamic treatment of the Couette flow of gaseous plasma (GP) confined between two coaxial rotating circular rigid cylinders. The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann kinetic equation (BKE) is solved by applying the perturbation method coupled with the moments' approach with a two-stream Maxwellian distribution function (MDF). Nonlinear partial differential equations are precisely solved. As an actual application, we are considering the laboratory Argon GP. An interesting comparison between the non-equilibrium electron velocity distribution function (EVDF) and the equilibrium EVDF is made carefully with 3-Dimensional graphics in various time values. We found that the system goes to an equilibrium state (ES) with time compatible with Le Chatelier's principles. Moreover, we determined with very high precision the value of the system equilibrium time, which is tequ.≅2.4. That great advantage cannot be reached by solving other macroscopic magnetohydrodynamic models. The relations between the various macroscopic variables of the GP are studied. The irreversible non-equilibrium thermodynamics (NT) properties of the system are presented. We present the extended Gibbs equation (EGE) for the internal energy variation (IEV) in cylindrical geometry for GP for the first time, to the best of our knowledge. We have shown that our model is compatible with the H-theorem of Boltzmann and the Onsager-Casimir relations. The various participations in IEV are introduced. The significance of this search is due to its vast implementations in various fields, such as in GP physics, electrical engineering, medicine, biological systems, and numerous commercial and industrial deployments.

Use of virtual reality during scalp injections: A randomized interventional crossover study

To the Editor: Intradermal injection of platelet-rich plasma is regularly used to treat pattern hair loss. Multiple treatment sessions are often required, and the injections can be painful. The potential interaction between local anesthetic and active drug precludes the use of numbing agents.1 Various sensory distraction techniques, including virtual reality (VR), have been investigated in the outpatient procedure setting.2-4 VR is a computer-simulated immersive environment of moving 3-dimensional graphics.

Simulation of Wave Solutions of a Mathematical Model Representing Communication Signals

In this study, the Lonngren-wave equation is considered to be analyzed for its wave solutions. To implement this purpose the modified exponential function method is used and ultimately new hyperbolic, trigonometric and rational forms of the exact solutions are obtained. Furthermore, it was tested whether these forms satisfy the Lonngren-wave equation or not and it was seen that they verify the equation. Besides this, the two and three dimensional graphics together with the contour and density plots are presented.

Development of a New Image-Guided Neuronavigation System: Mixed-Reality Projection Mapping Is Accurate and Feasible.

Image-guided systems improve the safety, functional outcome, and overall survival of neurosurgery but require extensive equipment. To develop an image-guided surgery system that combines the brain surface photographic texture (BSP-T) captured during surgery with 3-dimensional computer graphics (3DCG) using projection mapping. Patients who underwent initial surgery with brain tumors were prospectively enrolled. The texture of the 3DCG (3DCG-T) was obtained from 3DCG under similar conditions as those when capturing the brain surface photographs. The position and orientation at the time of 3DCG-T acquisition were used as the reference. The correct position and orientation of the BSP-T were obtained by aligning the BSP-T with the 3DCG-T using normalized mutual information. The BSP-T was combined with and displayed on the 3DCG using projection mapping. This mixed-reality projection mapping (MRPM) was used prospectively in 15 patients (mean age 46.6 yr, 6 males). The difference between the centerlines of surface blood vessels on the BSP-T and 3DCG constituted the target registration error (TRE) and was measured in 16 fields of the craniotomy area. We also measured the time required for image processing. The TRE was measured at 158 locations in the 15 patients, with an average of 1.19±0.14 mm (mean±standard error). The average image processing time was 16.58 min. Our MRPM method does not require extensive equipment while presenting information of patients' anatomy together with medical images in the same coordinate system. It has the potential to improve patient safety.

Investigation of new waves in chemical engineering

Modelling of wave motion and propagation characteristics of waves is of great significant in chemical engineering. Waves are the major source of chemical actions in various real life applications. We apply an efficacious solver to give exact traveling wave solutions of the Hirota-maccari model. This solver introduces closed-form wave structures of the solutions. The traveling wave solutions are expressed by hyperbolic function solutions. These solutions may be applicable for some real life problems in chemical engineering, biological engineering, plasma physics and etc. Some two and three dimensional graphics are plotted for certain parameter values to describe the propagation of traveling wave solutions. Finally, it is pondered that the proposed approach can also be applied to another sort of complex models.

Development of Integrated 3-Dimensional Computer Graphics Human Head Model

Understanding the complex anatomy of neurostructures is very important in various stages of medical education, from medical students to experienced neurosurgeons, and, ultimately, for the knowledge of human beings. To develop an interactive computer graphics (CG) anatomic head model and present the current progress. Based on the prior head 3-dimensional CG (3DCG) polygon model, 23 additional published papers and textbooks were consulted, and 2 neurosurgeons and 1 CG technician performed revision and additional polygon modeling. Three independent neurosurgeons scored the clear visibility of anatomic structures relevant to neurosurgical procedures (anterior petrosal and supracerebellar infratentorial approaches) in the integrated 3DCG model (i model) and patients' radiological images (PRIs) such as those obtained from computed tomography, magnetic resonance imaging, and angiography. The i model consisted of 1155 parts (.stl format), with a total of 313 763 375 polygons, including 10 times more information than the foundation model. The i model was able to illustrate complex and minute neuroanatomic structures that PRIs could not as well as extracranial structures such as paranasal sinuses. Our subjective analysis showed that the i model had better clear visibility scores than PRIs, particularly in minute nerves, vasculatures, and dural structures. The i model more clearly illustrates minute anatomic structures than PRIs and uniquely illustrates nuclei and fibers that radiological images do not. The i model complements cadaveric dissection by increasing accessibility according to spatial, financial, ethical, and social aspects and can contribute to future medical education.

Higher Dimensional Graphics: Conceiving Worlds in Four Spatial Dimensions and Beyond

AbstractWhile the interpretation of high‐dimensional datasets has become a necessity in most industries, the spatial visualization of higher‐dimensional geometry has mostly remained a niche research topic for mathematicians and physicists. Intermittent contributions to this field date back more than a century, and have had a non‐negligible influence on contemporary art and philosophy. However, most contributions have focused on the understanding of specific mathematical shapes, with few concrete applications. In this work, we attempt to revive the community's interest in visualizing higher dimensional geometry by shifting the focus from the visualization of abstract shapes to the design of a broader hyper‐universe concept, wherein 3D and 4D objects can coexist and interact with each other. Specifically, we discuss the content definition, authoring patterns, and technical implementations associated with the process of extending standard 3D applications as to support 4D mechanics. We operationalize our ideas through the introduction of a new hybrid 3D/4D videogame called Across Dimensions, which we developed in Unity3D through the integration of our own 4D plugin.