Graphical Simulation Research Articles

Abundant soliton solutions of the modified KdV-KP equation

The precise solutions of the (2+1)-dimensional modified KdV-KP equation are examined in this study. Three reliable methods, namely, the modified auxiliary equation scheme, extended rational sine–cosine methodology, and extended rational sinh–cosh technique, are utilized for the first time to extract multiple soliton solutions for the governing model. These types of solutions have applications in plasma, solid state, neuronal, biological production, and diffusion processes. Graphical simulations of the obtained solutions are included in the form of 3 dimensional surface plots to reveal their physical structure and dynamical features.

Physical scene understanding

AbstractCurrent AI systems still fail to match the flexibility, robustness, and generalizability of human intelligence: how even a young child can manipulate objects to achieve goals of their own invention or in cooperation, or can learn the essentials of a complex new task within minutes. We need AI with such embodied intelligence: transforming raw sensory inputs to rapidly build a rich understanding of the world for seeing, finding, and constructing things, achieving goals, and communicating with others. This problem of physical scene understanding is challenging because it requires a holistic interpretation of scenes, objects, and humans, including their geometry, physics, functionality, semantics, and modes of interaction, building upon studies across vision, learning, graphics, robotics, and AI. My research aims to address this problem by integrating bottom‐up recognition models, deep networks, and inference algorithms with top‐down structured graphical models, simulation engines, and probabilistic programs.

Designing a novel fractional order mathematical model for COVID-19 incorporating lockdown measures

This research focuses on the design of a novel fractional model for simulating the ongoing spread of the coronavirus (COVID-19). The model is composed of multiple categories named susceptible S(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S(t)$$\\end{document}, infected I(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$I(t)$$\\end{document}, treated T(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T(t)$$\\end{document}, and recovered R(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R(t)$$\\end{document} with the susceptible category further divided into two subcategories S1(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${S}_{1} (t)$$\\end{document} and S2(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${S}_{2} (t)$$\\end{document}. In light of the need for restrictive measures such as mandatory masks and social distancing to control the virus, the study of the dynamics and spread of the virus is an important topic. In addition, we investigate the positivity of the solution and its boundedness to ensure positive results. Furthermore, equilibrium points for the system are determined, and a stability analysis is conducted. Additionally, this study employs the analytical technique of the Laplace Adomian decomposition method (LADM) to simulate the different compartments of the model, taking into account various scenarios. The Laplace transform is used to convert the nonlinear resulting equations into an equivalent linear form, and the Adomian polynomials are utilized to treat the nonlinear terms. Solving this set of equations yields the solution for the state variables. To further assess the dynamics of the model, numerical simulations are conducted and compared with the results from LADM. Additionally, a comparison with real data from Italy is demonstrated, which shows a perfect agreement between the obtained data using the numerical and Laplace Adomian techniques. The graphical simulation is employed to investigate the effect of fractional-order terms, and an analysis of parameters is done to observe how quickly stabilization can be achieved with or without confinement rules. It is demonstrated that if no confinement rules are applied, it will take longer for stabilization after more people have been affected; however, if strict measures and a low contact rate are implemented, stabilization can be reached sooner.

Investigation of complex hyperbolic and periodic wave structures to a new form of the q-deformed sinh-Gordon equation with fractional temporal evolution

This paper presents the fractional generalized q-deformed sinh-Gordon equation. The fractional effects of the temporal derivative of the proposed model are studied using a conformable derivative. The analytical solutions of the governing model depend on the specified parameters. The resulting equation is studied with two integration architectures: the sine-Gordon expansion method and the modified auxiliary equation method. These strategies extract hyperbolic, trigonometric, and rational form solutions. For appropriate parametric values and different values of fractional parameter α, the acquired findings are displayed via 3D graphics, 2D line plots, and contour plots. The graphical simulations of the constricted solutions depict the existence of bright soliton, dark soliton, and periodic waves. The considered model is useful in describing physical mechanisms that possess broken symmetry and incorporate effects such as amplification or dissipation.

Seeing the piano sound Exploration on utilizing finite element analysis to visualize piano sound

The study aims to provide a way for impaired people to learn music better through music visualization. We established a relationship between piano key frequencies and Chladni patterns. Firstly, we performed modal analysis simulations using ANSYS, covering the full range of excitable modes in the frequency range of the piano keys. However, since the natural frequencies of the simulation results were slightly different from experimental results, we used the hammering method to validate the simulation results and to demonstrate that the finite element modal analysis was able to simulate the dynamic properties of the circular plate well. Subsequent studies have found that different excitation frequencies in the lower frequency range may also affect the generation of Chladni patterns. Using harmonic analysis in ANSYS, we confirmed that tones of similar frequency on the same plate can produce different Chladni patterns, thus greatly simplifying the previous problem of having to use multiple plates of different shapes and sizes in order to visualize most of the piano keys. Based on the graphical simulation of a single tone, we have successfully extended it to a melody. This result provides strong support for effectively helping the hearing impaired to learn to play musical instruments, makes it possible to present music in a visual form, and opens up new possibilities for the wider use of music education tools in the hearing-impaired community.

Computational neuroscience as atool for studying neurons.

Computational neuroscience uses aneuron model to investigate the behavior of aneuron under different stimuli e.g. magnetic field. The aim of the study is to investigate the effect of conductivity change of sodium (Na+) and potassium (K+) ion channels on the generation and course of action potential, excitability and firing rate of neuron. HHSim (Hodgkin-Huxley) graphical simulator was used for investigation of generation and firing rate of action potential (AP) and investigation of neuronal excitability. Na+ channel downregulation of conductance reveals adecrease of AP amplitude, and upregulation an increase of amplitude. Higher conductance of Na+ channel leads to higher firing rate from the value 53 HZ to 66 Hz. K+ channel downregulation of conductance reveals an increase of AP amplitude. Lower conductance of K+ channel leads to higher firing rate from the value 62 HZ to 68 Hz. K+ channel upregulation of conductance shows adecrease of AP amplitude. From the results it can be drawn that effect of conductivity change as aresult of magnetic field is significant and can leads to change of neurons. uman brain cultures, often termed "glia-like" cells (Tab. 4, Fig. 6, Ref. 21).

A generalized Gronwall inequality via $ \psi $-Hilfer proportional fractional operators and its applications to nonlocal Cauchy-type system

<p>This paper establishes a novel generalized Gronwall inequality concerning the $ \psi $-Hilfer proportional fractional operators. Before proving the main results, the solution of the linear nonlocal coupled $ \psi $-Hilfer proportional Cauchy-type system with constant coefficients under the Mittag-Leffler kernel is created. The uniqueness result for the proposed coupled system is established using Banach's contraction mapping principle. Furthermore, a variety of the Mittag-Leffler-Ulam-Hyers stability of the solutions for the proposed coupled system is investigated. Finally, a numerical example is given to show the effectiveness and applicability of the obtained results, and graphical simulations in the case of linear systems are shown.</p>

A mathematical model for fractal-fractional monkeypox disease and its application to real data

<abstract><p>In this paper, we developed a nonlinear mathematical model for the transmission of the monkeypox virus among populations of humans and rodents under the fractal-fractional operators in the context of Atangana-Baleanu. For the theoretical analysis, the renowned theorems of fixed points, like Banach's and Krasnoselskii's types, were used to prove the existence and uniqueness of the solutions. Additionally, some results regarding the stability of the equilibrium points and the basic reproduction number were provided. In addition, the numerical schemes of the considered model were established using the Adams-Bashforth method. Our analytical findings were supported by the numerical simulations to explain the effects of changing a few sets of fractional orders and fractal dimensions. Some graphic simulations were displayed with some parameters calculated from real data to understand the behavior of the model.</p></abstract>

A novel method to study time fractional coupled systems of shallow water equations arising in ocean engineering

<abstract><p>This study investigates solutions for the time-fractional coupled system of the shallow-water equations. The shallow-water equations are employed for the purpose of elucidating the dynamics of water motion in oceanic or sea environments. Also, the aforementioned system characterizes a thin fluid layer that maintains a hydrostatic equilibrium while exhibiting uniform density. Shallow water flows have a vertical dimension that is considerably smaller in magnitude than the typical horizontal dimension. In the current work, we employ an innovative and effective technique, known as the natural transform decomposition method, to obtain the solutions for these fractional systems. The present methodology entails the utilization of both singular and non-singular kernels for the purpose of handling fractional derivatives. The Banach fixed point theorem is employed to demonstrate the uniqueness and convergence of the obtained solution. The outcomes obtained from the application of the suggested methodology are compared to the exact solution and the results of other numerical methods found in the literature, including the modified homotopy analysis transform method, the residual power series method and the new iterative method. The results obtained from the proposed methodology are presented through the use of tabular and graphical simulations. The current framework effectively captures the behavior exhibited by different fractional orders. The findings illustrate the efficacy of the proposed method.</p></abstract>

Numerical and graphical simulation of the non-linear fractional dynamical system of bone mineralization.

The objective of the present study was to improve our understanding of the complex biological process of bone mineralization by performing mathematical modeling with the Caputo-Fabrizio fractional operator. To obtain a better understanding of Komarova's bone mineralization process, we have thoroughly examined the boundedness, existence, and uniqueness of solutions and stability analysis within this framework. To determine how model parameters affect the behavior of the system, sensitivity analysis was carried out. Furthermore, the fractional Adams-Bashforth method has been used to carry out numerical and graphical simulations. Our work is significant owing to its comparison of fractional- and integer-order models, which provides novel insight into the effectiveness of fractional operators in representing the complex dynamics of bone mineralization.

Optical Sensor-Based Image Texture Characterization for Image Simulation Applications in College Gymnastics Instruction

Abstract Gymnastics learning is characterized by imitation and reference, and a teaching model combining optical sensors and image simulation systems may have promising results in college gymnastics courses. Based on the introduction of the meaning of college gymnastics teaching, the article sorted out the value performance of the image teaching mode and also established an optical three-dimensional imaging system based on optical sensors for gymnastics movement to obtain gymnastic images. In the optical 3D imaging system, the acquisition error of gymnastics images is reduced by using the finite distance image measurement method, and the quality of gymnastics images is enhanced by adaptive bilateral filtering and adaptive threshold selection of the Canny operator by the OTSU method. The enhanced gymnastics images are then inputted into a panoramic graphic imaging simulation system, and a gymnastics image simulation teaching model is established for colleges and universities. The effectiveness of the gymnastics image simulation teaching model is analyzed through a teaching comparison test conducted during simulation verification for optical imaging. In the optical imaging system, when the measurement distance is about 150m, the measurement error range is between [15″and 30″], and the MSE value of the gymnastic enhanced image obtained by the improved Canny algorithm decreases by 46.97% compared with the MSE value before the improvement. The students’ handstand score against the wall improved by 22.63 points compared to before the experiment, and more than 90% of the students were satisfied with the gymnastics image simulation teaching method. The teaching mode is constructed with the optical sensor to obtain the image characteristics of gymnastics movement, and the simulation system is innovative, which effectively promotes students’ interest in learning gymnastics courses and enhances their gymnastics training level.

An Indigenous Computational Platform for Nowcasting and Forecasting Non-Linear Spread of COVID-19 across the Indian Sub-continent: A Geo-Temporal Visualization of Data

The rapid spread of the COVID-19 pandemic necessitated unprecedented collective action against coronavirus disease. In this light,we are proposing a novel online platform for the visualization of epidemiological data incorporating social determinants for understanding the patterns associated with the spread of COVID-19. The current AI computational platform combines modeling methodologies along with temporal geospatial visualization of COVID-19 data, providing real-time sharing of graphic analytical simulation of vulnerable hotspots of recurrent (nowcasting) and emergent (forecasting) infections visualized on a spatiotemporal scale on geoportals. The proposed study will be a secondary data analysis of primary data accessed from the national portal (Indian Council of Medical Research (ICMR)) incorporating 766 districts in India. Epidemiological data related to spatiotemporal visualization of the demographic spread of COVID-19 will be displayed using a compartmental socio-epidemiological model, reproduction number R, epi-curve diagrams as well as choropleth maps for different levels of administrative and development units at the district levels.

The new soliton solution types to the Myrzakulov-Lakshmanan-XXXII-equation

<abstract> <p>Our attention concenters on deriving diverse forms of the soliton arising from the Myrzakulov-Lakshmanan XXXII (M-XXXII) that describes the generalized Heisenberg ferromagnetic equation. This model has been solved numerically only using the N-fold Darboux Transformation method, not solved analytically before. We will derive new types of the analytical soliton solutions that will be constructed for the first time in the framework of three impressive schemas that are prepared for this target. These three techniques are the Generalized Kudryashov scheme (GKS), the (G'/G)-expansion scheme and the extended direct algebraic scheme (EDAS). Moreover, we will establish the 2D, 3D graphical simulations that clear the new dynamic properties of our achieved solutions.</p> </abstract>

Analyzing the dynamics of fractional spatio-temporal $ \mathrm{SEIR} $ epidemic model

<p>In this work, we present a comprehensive analysis of the spatio-temporal $ \mathrm{SEIR} $ epidemic model of fractional order. The infection dynamics in the proposed fractional order model (FOM) are described by a system of partial differential equations (PDEs) within a time-fractional order and diffusion operator in one-dimensional space, considering that the total population is split into four compartments: Susceptible, exposed, infected, and recovered individuals denoted as $ \mathrm{S} $, $ \mathrm{E} $, $ \mathrm{I} $ and $ \mathrm{R} $, respectively. Our contributions commence by establishing the existence and uniqueness of positively bounded solutions for the proposed FOM. Moreover, we determined all equilibrium points (EPs) and investigated their local stability based on the basic reproduction number (BRN) $ \mathcal{R}_{0} $, which is calculated by the next-generation matrix (NGM) method. Additionally, we demonstrated global stability using an appropriate Lyapunov function with fractional LaSalle's invariance principle (LIP). Sensitivity analysis of the FOM parameters was discussed to identify the most critical parameters by which the volume of disease propagation can be measured. The theoretical findings were corroborated by numerical simulations of solutions that are displayed in 3D and 2D graphs. Graphical simulations highlight the effect of vaccination on infection severity. Changing the fractional order $ \alpha $ in the proposed FOM has an influence on the speed of convergence to the steady state as a result of the memory effect. Furthermore, vaccination emerges as an effective strategy for disease control.</p>

Comparative analysis of electric motor drives employed for propulsion purpose of Battery Electric Vehicle (BEV) systems

This paper presents an analysis of electric motor drives for the propulsion system of a battery electric vehicle (BEV). It offers a comprehensive review and mathematical analysis of both AC and DC motor drives commonly used in electric vehicle (EV) applications. Various types of electric motor drives have been utilized for EV propulsion, and among them, the Permanent Magnet Synchronous Motor (PMSM) drive stands out as the optimal choice. The PMSM drive demonstrates superior performance and numerous advantages, including a robust structure, high efficiency, compact size, reduced maintenance costs, and minimal torque ripple. These characteristics make it a more suitable option for EV propulsion compared to other motors. This study investigates the performance of the PMSM drive in comparison to other competitive electric motor drives used in EV propulsion systems, namely the Brushless DC Motor (BLDCM), the Induction Motor (IM), and the Switched Reluctance Motor (SRM). The evaluation focuses on key criteria for electric motors—output power and torque densities, essential for effective application in EV propulsion systems. The paper introduces novel mathematical and analytical relationships between two prominent PM motor families: the PMSM and the BLDCM. Both motors are highly competitive in terms of power and torque output. The mathematical analysis and graphical plot simulation results demonstrate that the PMSM drive offers the highest power and torque densities among the three motor drives. Specifically, the PMSM drive exhibits 29.90% greater power and torque densities than the BLDCM drive, 88.68% greater than the SRM drive, and an impressive 200% greater than the IM drive, all under the same operating parameters such as power factor, size, rating, and efficiency. These findings highlight the significant advantages of the PMSM drive, positioning it as a superior choice for electric vehicle propulsion systems.

Exact solutions, symmetry groups and conservation laws for some (2+1)-dimensional nonlinear physical models

In this paper, the Bernoulli sub-equation function method is used to construct new exact travelling wave solutions for two important physical models: (2+1)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation and (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation. These solutions provide valuable insights into the behavior of these models, described in terms of exponential and hyperbolic tangent (tanh) functions. The study also involves an exploration of the infinitesimal generators and symmetry groups through the Lie symmetry method. In addition, by using multiplier approach, the conservation laws are established for these models. Graphical simulation of some solutions in the form of two-dimensional and three-dimensional are plotted to understanding of the underlying physical phenomena and mathematical properties of the (2+1)-dimensional HNLS and HFSC equations. The solutions and graphing are performed using Maple software.

Analysis of Joule heating and viscous dissipation on electromagnetohydrodynamic flow with electroosmotic effect in a porous microchannel: A heat transfer miniature enhancement

AbstractThis work investigates the effect of Joule heating and viscous dissipation due to electric double layer (EDL) and electroosmotic effect on steady fully developed electromagnetohydrodynamic flow in a porous microchannel. Dimensionless formulations of the Poisson–Boltzmann, momentum, and energy equations are derived for the electric potential, velocity profile, and temperature distribution in the microchannel. Exact solutions for the temperature distributions and velocity profiles were obtained using the method of undetermined coefficients. The Debye–Hückel linearization is used to get an exact solution for the electric potential. The results showed that the Brinkmann number , Joule heating parameter , Debye–Hückel parameter , Hartmann number , electric field , and suction/injection parameter have a substantial impact on flow formation and heat transfer. Using MATLAB software, graphical simulations are provided to deliver a greater understanding of the influence of relevant parameters on the results achieved.

Exact solutions of perturbed stochastic NLSE with generalized anti-cubic law nonlinearity and multiplicative white noise

The paper retrieves the perturbed stochastic nonlinear Schrödinger equation in magneto-optic waveguides with generalized anti-cubic law nonlinearity and multiplicative noise in the Itô sense. Exact solutions are obtained with the aid of the trial equation method and the complete discriminant system for a polynomial. Compared to previous solutions, this method has achieved a broader and more comprehensive set of exact solutions. The obtained exact solutions help explain light propagation, nonlinear effects, the impact of noise on the system, and various physical processes occurring within waveguides. Some graphical simulations have been provided to demonstrate the dynamical behavior of the solutions and the impact of noise term in Itô sense.

Dynamical behavior of perturbed Gerdjikov–Ivanov equation through different techniques

The objective of this work is to investigate the perturbed Gerdjikov–Ivanov (GI) equation along spatio-temporal dispersion which explains the dynamics of soliton dispersion and evolution of propagation distance in optical fibers, photonic crystal fibers (PCF), and metamaterials. The algorithms, namely hyperbolic extended function method and generalized Kudryashov’s method, are constructed to obtain the new soliton solutions. The dark, bright, periodic, and singular solitons are derived of the considered equation with the appropriate choice of parameters. These results are novel, confirm the stability of optical solitons, and have not been studied earlier. The explanation of evaluated results is given by sketching the various graphs in 3D, contour and 2D plots by using Maple 18. Graphical simulations divulge that varying the wave velocity affects the dynamical behaviors of the model. In summary, this research adds to our knowledge on how the perturbed GI equation with spatio-temporal dispersion behaves. The obtained soliton solutions and the methods offer computational tools for further analysis in this field. This work represents an advancement in our understanding of soliton dynamics and their applications in photonic systems.

Some problems of target approach for nonlinear control system at a fixed time moment

The game problem of target approach for nonlinear control system with a target set in a finite-dimensional phase space at a fixed time is studied. The problem is formulated and studied within the framework of concepts and constructions of the theory of positional differential games, created by N.N. Krasovskii and A.I. Subbotin in the second half of the 20th century. One of the central problems of the theory of positional differential games is the problem of calculating positional sets of uptake in convergence game problems. The paper investigates a key stability property in the theory of positional differential games, which is a characteristic of some closed sets in the space of positions of a controlled system that are convenient for the first player to conduct the game. It is important that this property is also characteristic for solvability sets in convergence problems: the inclusion of the concept of stability in research makes it possible to obtain analytical descriptions of solvability sets in some specific convergence problems and to develop algorithms for approximate calculation of the solution in a number of specific problems. Some modifications of the definition of a $u$-stable bridge in the considered convergence problem and a system of sets approximating the attainability set are given. Three specific problems on the convergence of mechanical systems are also presented, computer solutions are simulated, and graphical simulation results are presented.