An MHD Fluid Flow over a Porous Stretching/Shrinking Sheet with Slips and Mass Transpiration

In the present paper, an MHD three-dimensional non-Newtonian fluid flow over a porous stretching/shrinking sheet in the presence of mass transpiration and thermal radiation is examined. This problem mainly focusses on an analytical solution; graphene water is immersed in the flow of a fluid to enhance the thermal efficiency. The given non-linear PDEs are mapped into ODEs via suitable transformations, then the solution is obtained in terms of incomplete gamma function. The momentum equation is analyzed, and to derive the mass transpiration analytically, this mass transpiration is used in the heat transfer analysis and to find the analytical results with a Biot number. Physical significance parameters, including volume fraction, skin friction, mass transpiration, and thermal radiation, can be analyzed with the help of graphical representations. We indicate the unique solution at stretching sheet and multiple solution at shrinking sheet. The physical scenario can be understood with the help of different physical parameters, namely a Biot number, magnetic parameter, inverse Darcy number, Prandtl number, and thermal radiation; these physical parameters control the analytical results. Graphene nanoparticles are used to analyze the present study, and the value of the Prandtl number is fixed to 6.2. The graphical representations help to discuss the results of the present work. This problem is used in many industrial applications such as Polymer extrusion, paper production, metal cooling, glass blowing, etc. At the end of this work, we found that the velocity and temperature profile increases with the increasing values of the viscoelastic parameter and solid volume fraction; additionally, efficiency is increased for higher values of thermal radiation.

Visualization of Archimedian and Platonic polyhedra using a web environment in Augmented Reality and Virtual Reality

This paper shows the development of a web environment for the construction of Archimedes and Plato polyhedra in Augmented Reality (AR) and Virtual Reality (VR). In this environment we used the geometric transformations of translation and rotation with the structure of hierarchies of HTML pages, without the use of the coordinates of each polyhedra vertex. The developed environment can be used in classroom to visualize the polyhedra in Augmented Reality, with the possibility of manipulations of the graphical representations by students in the environment created in Virtual Reality. Other studies that can be developed with the polyhedra modeled are areas, volumes and the relation of Euler. Another important content that can be developed is truncation, because seven Archimedes polyhedra are obtained by using truncation of Plato's polyhedrons. With this work, it becomes possible to develop didactic materials with a simple technology, free and with great contribution to improvement of the teaching of Geometry and other areas that use representation of 3D objects.

Examining data visualization pitfalls in scientific publications

Data visualization blends art and science to convey stories from data via graphical representations. Considering different problems, applications, requirements, and design goals, it is challenging to combine these two components at their full force. While the art component involves creating visually appealing and easily interpreted graphics for users, the science component requires accurate representations of a large amount of input data. With a lack of the science component, visualization cannot serve its role of creating correct representations of the actual data, thus leading to wrong perception, interpretation, and decision. It might be even worse if incorrect visual representations were intentionally produced to deceive the viewers. To address common pitfalls in graphical representations, this paper focuses on identifying and understanding the root causes of misinformation in graphical representations. We reviewed the misleading data visualization examples in the scientific publications collected from indexing databases and then projected them onto the fundamental units of visual communication such as color, shape, size, and spatial orientation. Moreover, a text mining technique was applied to extract practical insights from common visualization pitfalls. Cochran’s Q test and McNemar’s test were conducted to examine if there is any difference in the proportions of common errors among color, shape, size, and spatial orientation. The findings showed that the pie chart is the most misused graphical representation, and size is the most critical issue. It was also observed that there were statistically significant differences in the proportion of errors among color, shape, size, and spatial orientation.

Fractal Calculus on Fractal Interpolation Functions

In this paper, fractal calculus, which is called Fα-calculus, is reviewed. Fractal calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non-differentiable and non-integrable in the sense of ordinary calculus. Graphical representations of fractal calculus of fractal interpolation functions and Weierstrass functions are presented.

Co-Designers Not Troublemakers

Players in Massively Multiplayer Online Role-Playing Games (MMORPGs) generate long-standing histories with their characters, but cannot express or see traces of their adventures in the game worlds. We are interested in designing game systems where players shape and contribute their own narratives as game content. Study one designed and playtested three Virtual Tabletop Role-Playing Game (VTTRPG) prototypes where we found that structured, graphical representations of players' traces support co-design and narrative analysis. We also identified four categories of traces: environment, build, memory and object. We introduce Play Traces, a novel analysis method for representing and co-designing with players and their narratives. A structured observation including Play Traces studied 17 players over 16 four-hour sessions in the third VTTRPG prototype. We found that players successfully (and enjoyably) co-designed novel narratives. We identified three themes for how traces can affect and support players in shaping new interactive narratives. We present four design implications describing how player-created narratives in MMORPGs should first Reveal & Pull Attention from other players, Invite & Push further exploration, Guide & Assist toward endings, and optionally Show & Hide traces. Finally, we discuss how treating players as co-designers offers a promising approach for developing the next generation of MMORPGs.

Discretization of Fractional Operators: Analysis by Means of Advanced Computational Techniques

This paper studies the discretization of fractional operators by means of advanced clustering methods. The Grünwald–Letnikov fractional operator is approximated by series generated by the Euler, Tustin and generalized mean. The series for different fractional orders form the objects to be assessed. For this purpose, the several distances associated with the hierarchical clustering and multidimensional scaling computational techniques are tested. The Arc-cosine distance and the 3-dim multidimensional scaling produce good results. The visualization of the graphical representations allows a better understanding of the properties embedded in each type of approximation of the fractional operators.

SOLUTION OF LOCAL FRACTIONAL GENERALIZED FOKKER–PLANCK EQUATION USING LOCAL FRACTIONAL MOHAND ADOMIAN DECOMPOSITION METHOD

In this paper, we solve the local fractional generalized Fokker–Planck equation. To solve the problem, local fractional Mohand transform with Adomian decomposition method is introduced due to its simple approach and less computational work. Furthermore, for the applicability of the technique, we illustrate some examples and their exact or approximate solutions with their graphical representations.