Three-dimensional Depictions Research Articles

Introducing Novel Geometric Insights and Three-Dimensional Depictions of the Pythagorean Theorem for any Triangles

Introducing Novel Geometric Insights and Three-Dimensional Depictions of the Pythagorean Theorem for any Triangles

Evolution and Deepening of Antagonistic Characters in Films: A Typological Analysis and Exploration of Empathy Construction

This paper explores antagonistic characters in films, specifically focusing on the concept of “empathetic antagonists.” Through a review of relevant literature, the paper defines empathetic antagonists, examines their evolutionary processes, categorizes them, and elucidates their significance in film narratives and how they evoke empathy in the audience. Firstly, the paper reviews prior studies related to empathetic antagonists and provides a conceptual framework. Secondly, it traces the evolution of antagonist characters from simple, one-dimensional evil personas to complex, multifaceted characters with depth. Thirdly, the paper classifies empathetic antagonists into four main types: Complex Motivation, Moral Struggle, Complicated Relationships, and Diverse Backgrounds. Additionally, it offers suggestions for scriptwriting and actor interpretation in shaping these characters. Finally, by synthesizing these aspects, the paper concludes that antagonistic characters in films have transitioned from initially simplistic and flat representations to complex and three-dimensional depictions, evolving from uni-dimensional evil to profound humanity. This trend not only enhances the artistic quality of films but also prompts audiences to contemplate issues of humanity, morality, and emotions. In the future, filmmakers can continue exploring the multifaceted qualities of antagonist characters to enrich character experiences and create more captivating works. Simultaneously, actors need to accurately convey the emotions and complexities of these characters during performances, leaving a lasting impression on the audience. This research is instrumental in understanding the role and impact of antagonist characters in film narratives and offers guidance for creating in-depth and empathetic antagonist characters.

A comparative investigation on the fundamental physical properties of UX2 (X = O, N, C, Si and S) solid nuclear fuel materials: A DFT + U study

This study investigates and compares the physical properties of various UX2 (X = O, N, C, Si and S) nuclear fuels using a combination of Density Functional Theory (DFT) and Hubbard U correction parameter (U) to accurately model the electronic structure and account for strong correlation effects among 5f orbital electrons. Spin-polarized DFT + U method is employed to optimize the structures of the considered compounds. The computational analysis reveals that UO2 and UN2 exhibit Mott-insulating properties, while the remaining UX2 compounds demonstrate metallic nature. To assess the mechanical aspects of these materials, the study evaluates their mechanical stability, Vickers hardness and machinability index through calculations of elastic constants. Notably, all the UX2 fuels are found to be mechanically stable and possess ductility. Both the two-dimensional (2D) and three-dimensional (3D) depictions of the elastic moduli for the analyzed solid fuels demonstrate the presence of elastic anisotropy. The famous Slack's equation is used to determine the lattice thermal conductivity of the UX2 fuels, providing valuable insights into their thermal properties. Among the investigated materials, UC2 exhibits the highest values of Debye temperature and lattice thermal conductivity, which amount to 412 K and 15.73 Wm−1 K−1 at 300 K, respectively. Furthermore, UN2 demonstrates the highest melting temperature. Among the compounds under investigation, UC2 and UN2 fuels exhibit the most minimal thermal expansion and the greatest heat capacity. Based on these findings, UC2 and UN2 emerge as promising alternative fuel materials to UO2 for potential use in nuclear power reactors. This research contributes to the ongoing efforts in identifying alternative fuel materials.

New Analytical Solutions for Coupled Stochastic Korteweg–de Vries Equations via Generalized Derivatives

In this paper, the coupled nonlinear KdV (CNKdV) equations are solved in a stochastic environment. Hermite transforms, generalized conformable derivative, and an algorithm that merges the white noise instruments and the (G′/G2)-expansion technique are utilized to obtain white noise functional conformable solutions for these equations. New stochastic kinds of periodic and soliton solutions for these equations under conformable generalized derivatives are produced. Moreover, three-dimensional (3D) depictions are shown to illustrate that the monotonicity and symmetry of the obtained solutions can be controlled by giving a value of the conformable parameter. Furthermore, some remarks are presented to give a comparison between the obtained wave solutions and the wave solutions constructed under the conformable derivatives and Newton’s derivatives.

On the application of $ G_\alpha $ integral transform to nonlinear dynamical models with non-integer order derivatives

<abstract><p>The current study uses an essential and integrated form of Laplace-type integral transform coupled with the Adomian's approach to study nonlinear evolution equations endowed with non-integer derivatives. More so, of particular interest here is to demonstrate the application of this transform to a wider class of nonlinear problems. Three test models have been examined by the presented method, and their closed-form solutions have been reported iteratively. Lastly, the variational effect of the non-integer order derivatives on the evolution of these models has been studied via the two and three-dimensional depictions.</p></abstract>

Prediction of factors affecting activation of soil erosion by mathematical modeling at pedon scale under laboratory conditions

Soil degradation due to erosion is a significant worldwide problem at different spatial (from pedon to watershed) and temporal scales. All stages and factors in the erosion process must be detected and evaluated to reduce this environmental issue and protect existing fertile soils and natural ecosystems. Laboratory studies using rainfall simulators allow single factors and interactive effects to be investigated under controlled conditions during extreme rainfall events. In this study, three main factors (rainfall intensity, inclination, and rainfall duration) were assessed to obtain empirical data for modeling water erosion during single rainfall events. Each factor was divided into three levels (− 1, 0, + 1), which were applied in different combinations using a rainfall simulator on beds (6 × 1 m) filled with soil from a study plot located in the arid Sistan region, Iran. The rainfall duration levels tested were 3, 5, and 7 min, the rainfall intensity levels were 30, 60, and 90 mm/h, and the inclination levels were 5, 15, and 25%. The results showed that the highest rainfall intensity tested (90 mm/h) for the longest duration (7 min) caused the highest runoff (62 mm3/s) and soil loss (1580 g/m2/h). Based on the empirical results, a quadratic function was the best mathematical model (R2 = 0.90) for predicting runoff (Q) and soil loss. Single-factor analysis revealed that rainfall intensity was more influential for runoff production than changes in time and inclination, while rainfall duration was the most influential single factor for soil loss. Modeling and three-dimensional depictions of the data revealed that sediment production was high and runoff production lower at the beginning of the experiment, but this trend was reversed over time as the soil became saturated. These results indicate that avoiding the initial stage of erosion is critical, so all soil protection measures should be taken to reduce the impact at this stage. The final stages of erosion appeared too complicated to be modeled, because different factors showed differing effects on erosion.

Demonstrative simulations of L-PEACH: a computer-based model to understand how peach trees grow

L-PEACH is a computer-based model that simulates the distribution of light in the peach canopy as the tree grows and carbohydrate assimilation of each leaf. The model integrates important concepts to simulate water and carbon transport within the tree with real environmental input data collected from weather stations. Tree architecture is based on developmental principles governing tree growth and detailed measurements of shoots of peach trees. While running L-PEACH, realistic three-dimensional depictions of simulated growing trees can be displayed on the computer screen for visualization of tree architecture. The L-PEACH model has been widely reported in the literature along with quantitative data generated during simulations. However, demonstrative simulations were never disseminated to the scientific community and they are an essential component for understanding the model and demonstrating principles of tree growth. Along with the modeling work several movies with demonstrative simulations of L-PEACH have been made public in a scientific repository to complement existing references. Demonstrative simulations are related with overall tree growth and the movement of carbon within the tree, detailed growth of leaves and fruit and responses of tree growth to pruning intensity, drought and size-controlling rootstocks. In this work each demonstrative simulation will be accompanied by a physiological and/or horticultural description to demonstrate the value of L-PEACH to study, understand and teach how trees grow.

Applying Hand-Held 3D Printing Technology to the Teaching of VSEPR Theory

The use of hand-held 3D printing technology provides a unique and engaging approach to learning VSEPR theory by enabling students to draw three-dimensional depictions of different molecular geometries, giving them an appreciation of the shapes of the building blocks of complex molecular structures. Students are provided with 3D printing pens and two-dimensional templates which allows them to construct three-dimensional ABS models of the basic VSEPR shapes. We found that the learning curve associated with manipulating the pen accurately and the time required to draw a structure is sufficiently high that this exercise would need to be limited in a laboratory setting to students each being tasked with drawing a different molecule; however, in the correct setting, hand-held 3D printing pens are a potentially powerful tool for the teaching of VSEPR theory.

Magnetic Resonance Reporter Gene Imaging

Molecular imaging has undergone an explosive advancement in recent years, due to the tremendous research efforts made to understand and visualize biological processes. Molecular imaging by definition assesses cellular and molecular processes in living subjects, with the targets of following metabolic, genomic, and proteomic events. Furthermore, reporter gene imaging plays a central role in this field. Many different approaches have been used to visualize genetic events in living subjects, such as, optical, radionuclide, and magnetic resonance imaging. Compared with the other techniques, magnetic resonance (MR)-based reporter gene imaging has not occupied center stage, despite its superior three-dimensional depictions of anatomical details. In this article, the authors review the principles and applications of various types of MR reporter gene imaging technologies and discuss their advantages and disadvantages.

L-PEACH: A Computer-based Model to Understand How Peach Trees Grow

L-PEACH is a computer-based model that simulates the growth of peach [Prunus persica (L.) Batsch] trees. The model integrates important concepts related to carbon assimilation, distribution, and use in peach trees. It also includes modeling of the responses to horticultural practices such as tree pruning and fruit thinning. While running L-PEACH, three-dimensional (3D) depictions of simulated growing trees can be displayed on the computer screen and the user can easily interact with the model. Quantitative data generated during a simulation can be saved to a file or printed for visualization and analysis. L-PEACH is a powerful tool for understanding how peach trees function in the field environment, and it can be used as an innovative method for dissemination of knowledge related with carbohydrate assimilation and partitioning. In this study, we describe the version of L-PEACH that runs on a daily time-step (L-PEACH-d) and how users can run the model and interact with it. To demonstrate how L-PEACH-d works, different pruning and fruit thinning strategies were analyzed. Regarding pruning, model outputs showed 3D depictions of unpruned trees and pruned trees trained to a perpendicular V system. For the fruit thinning studies, we simulated different intensities and dates of fruit thinning in mature peach trees. Total simulated yield increased with crop load but the opposite was observed for average fruit weight. An optimal balance between simulated total yield and average fruit weight was obtained by leaving 150 fruit per tree. Simulating different dates of fruit thinning indicated that fruit weight at harvest was higher on earlier compared with later-thinned trees. The model indicates that fruit thinning should be therefore carried out early in the season to maximize fruit size. The simulation results demonstrate that L-PEACH-d can be used as an educational tool and facilitate the adoption of suitable cultural practices for efficient production.

L-PEACH: A Computer-based Model to Understand How Peach Trees Grow

L-PEACH is a computer-based model that simulates the growth of peach [Prunus persica (L.) Batsch] trees. The model integrates important concepts related to carbon assimilation, distribution, and use in peach trees. It also includes modeling of the responses to horticultural practices such as tree pruning and fruit thinning. While running L-PEACH, three-dimensional (3D) depictions of simulated growing trees can be displayed on the computer screen and the user can easily interact with the model. Quantitative data generated during a simulation can be saved to a file or printed for visualization and analysis. L-PEACH is a powerful tool for understanding how peach trees function in the field environment, and it can be used as an innovative method for dissemination of knowledge related with carbohydrate assimilation and partitioning. In this study, we describe the version of L-PEACH that runs on a daily time-step (L-PEACH-d) and how users can run the model and interact with it. To demonstrate how L-PEACH-d works, different pruning and fruit thinning strategies were analyzed. Regarding pruning, model outputs showed 3D depictions of unpruned trees and pruned trees trained to a perpendicular V system. For the fruit thinning studies, we simulated different intensities and dates of fruit thinning in mature peach trees. Total simulated yield increased with crop load but the opposite was observed for average fruit weight. An optimal balance between simulated total yield and average fruit weight was obtained by leaving 150 fruit per tree. Simulating different dates of fruit thinning indicated that fruit weight at harvest was higher on earlier compared with later-thinned trees. The model indicates that fruit thinning should be therefore carried out early in the season to maximize fruit size. The simulation results demonstrate that L-PEACH-d can be used as an educational tool and facilitate the adoption of suitable cultural practices for efficient production.

FMRI Data Visualization with BrainBlend and Blender

The visualization and exploration of neuroimaging data is important for the analysis of anatomical and functional magnetic resonance (MR) images and thresholded statistical parametric maps. While two-dimensional orthogonal views of neuroimaging data are used to display statistical analyses, real three-dimensional (3d) depictions are helpful for showing the spatial distribution of a functional network, as well as its temporal evolution. However, viewers that are freely available on the internet offer only limited rendering capabilities and depictions of temporal changes of the blood oxygen level-dependent (BOLD) response. In this article, we present BrainBlend, a toolbox for the software package Statistical Parametric Mapping (SPM), that generates voxeldata files to be used with the open-source 3d-software "Blender". Our interface between SPM and Blender permits the use of any Analyze- and Nifti-file for the creation of images and animations of transparent volumetric objects. Different kinds of anatomical, functional and statistical data can be rendered as volumetric objects in order to convey an immediate understanding of the three-dimensional shape. Representations of functional networks can be animated using a time course extracted from the general linear model or the independent component analysis. Relative BOLD activations of functional MR-images can be calculated for a time-resolved depiction of hemodynamic changes. The resulting animation can be displayed along with its corresponding paradigm matrix and the presented stimuli. BrainBlend is particularly suitable for the visual exploration of interactions between functional networks, for time-resolved animations of BOLD changes and meets high demands on visual quality in images and animations.

Human White Matter Atlas

Human White Matter Atlas

Designing a Virtual Reality Model for Aesthetic Surgery

Aesthetic surgery deals in large part with the manipulation of soft-tissue structures that are not amenable to visualization by standard technologies. As a result, accurate three-dimensional depictions of relevant surgical anatomy have yet to be developed. This study presents a method for the creation of detailed virtual reality models of anatomy relevant to aesthetic surgery. Two-dimensional histologic sections of a cadaver from the National Library of Medicine's Visible Human Project were imported into Alias's Maya, a computer modeling and animation software package. These two-dimensional data were then "stacked" as a series of vertical planes. Relevant anatomy was outlined in cross-section on each two-dimensional section, and the resulting outlines were used to generate three-dimensional representations of the structures in Maya. A detailed and accurate three-dimensional model of the soft tissues germane to aesthetic surgery was created. This model is optimized for use in surgical animation and can be modified for use in surgical simulators currently being developed. A model of facial anatomy viewable from any angle in three-dimensional space was developed. The model has applications in medical education and, with future work, could play a role in surgical planning. This study emphasizes the role of three-dimensionalization of the soft tissues of the face in the evolution of aesthetic surgery.

SCOTOMAS OF AGE-RELATED MACULAR DEGENERATION DETECTED AND CHARACTERIZED BY MEANS OF A NOVEL THREE-DIMENSIONAL COMPUTER-AUTOMATED VISUAL FIELD TEST

We used the recently devised three-dimensional computer-based threshold Amsler grid test to acquire and identify typical patterns of visual field defects (scotomas) caused by age-related macular degeneration (AMD). Patients with AMD traced on a computer touch screen the borders of those areas on an Amsler grid that were missing from their field of vision. Scotomas were repeatedly outlined and recorded at different grid contrast levels. The resulting three-dimensional "hole" in the central 25 degrees of the visual field was further characterized by its slope, location, shape, and depth. The results were compared with fundus photographs and fluorescein angiograms. Twenty-five patients and 41 eyes were examined. The three-dimensional depictions consistently demonstrated central scotomas with "scallop"-shaped borders and steplike patterns, with either steep slopes or a combination of steep and shallow slopes. The steep slopes corresponded to nonexudative AMD, while the shallow slopes indicated exudative AMD. The three-dimensional computer-automated threshold Amsler grid test may demonstrate characteristic scotoma patterns in patients with AMD that conform to the respective fluorescein angiograms. The test shows promise as an effective tool in accurately evaluating, characterizing, and monitoring scotomas in patients with AMD. It may have the potential as a screening tool for the early diagnosis of AMD.

Visual mediation and the haptic recognition of two-dimensional pictures of common objects

A set of three experiments was performed to investigate the role of visual imaging in the haptic recognition of raised-line depictions of common objects. Blindfolded, sighted (Experiment 1) observers performed the task very poorly, while several findings converged to indicate that a visual translation process was adopted. These included (1) strong correlation between image-ability ratings (obtained in Experiment 1 and, independently, in Experiment 2) and both recognition speed and accuracy, (2) superior performance with, and greater ease of imaging, two-dimensional as opposed to three-dimensional depictions, despite equivalence in rated line complexity, and (3) a significant correlation between the general ability of the observer to image and obtained imageability ratings of the stimulus depictions. That congenitally blind observers performed the same task even more poorly, while their performance did not differ for two- versus three-dimensional depictions (Experiment 3), provides further evidence that visual translation was used by the sighted. Such limited performance is contrasted with the considerable skill with which real common objects are processed and recognized haptically. The reasons for the general difference in the haptic performance of two- versus three-dimensional tasks are considered. Implications for the presentation of spatial information in the form of tangible graphics displays for the blind are also discussed.