Graphical Simulation Research Articles

Dynamical structures of optical solitons for highly dispersive perturbed NLSE with $$\beta $$-fractional derivatives and a sextic power-law refractive index using a novel approach

Dynamical structures of optical solitons for highly dispersive perturbed NLSE with $$\beta $$-fractional derivatives and a sextic power-law refractive index using a novel approach

Generative Portrait Shadow Removal

We introduce a high-fidelity portrait shadow removal model that can effectively enhance the image of a portrait by predicting its appearance under disturbing shadows and highlights. Portrait shadow removal is a highly ill-posed problem where multiple plausible solutions can be found based on a single image. For example, disentangling complex environmental lighting from original skin color is a non-trivial problem. While existing works have solved this problem by predicting the appearance residuals that can propagate local shadow distribution, such methods are often incomplete and lead to unnatural predictions, especially for portraits with hard shadows. We overcome the limitations of existing local propagation methods by formulating the removal problem as a generation task where a diffusion model learns to globally rebuild the human appearance from scratch as a condition of an input portrait image. For robust and natural shadow removal, we propose to train the diffusion model with a compositional repurposing framework: a pre-trained text-guided image generation model is first fine-tuned to harmonize the lighting and color of the foreground with a background scene by using a background harmonization dataset; and then the model is further fine-tuned to generate a shadow-free portrait image via a shadow-paired dataset. To overcome the limitation of losing fine details in the latent diffusion model, we propose a guided-upsampling network to restore the original high-frequency details (e.g. , wrinkles and dots) from the input image. To enable our compositional training framework, we construct a high-fidelity and large-scale dataset using a lightstage capturing system and synthetic graphics simulation. Our generative framework effectively removes shadows caused by both self and external occlusions while maintaining original lighting distribution and high-frequency details. Our method also demonstrates robustness to diverse subjects captured in real environments.

Mixed single, double, and triple poles solutions for the space-time shifted nonlocal DNLS equation with nonzero boundary conditions via Riemann–Hilbert approach

In this paper, we investigate the space-time shifted nonlocal derivative nonlinear Schrödinger (DNLS) equation under nonzero boundary conditions using the Riemann–Hilbert (RH) approach for the first time. To begin with, in the direct scattering problem, we analyze the analyticity, symmetries, and asymptotic behaviors of the Jost eigenfunctions and scattering matrix functions. Subsequently, we examine the coexistence of N-single, N-double, and N-triple poles in the inverse scattering problem. The corresponding residue conditions, trace formulae, θ condition, and symmetry relations of the norming constants are obtained. Moreover, we derive the exact expression for the mixed single, double, and triple poles solutions with the reflectionless potentials by solving the relevant RH problem associated with the space-time shifted nonlocal DNLS equation. Furthermore, to further explore the remarkable characteristics of soliton solutions, we graphically illustrate the dynamic behaviors of several representative solutions, such as three-soliton, two-breather, and soliton-breather solutions. Finally, we analyze the effects of shift parameters through graphical simulations.

Construction and analysis of symmetric Sprott B multi-attractors with electric implementation

Abstract In chaos theory, a number of systems and models which apparently contain simple ordinary differential equations (ODEs) turn out to show a dynamic characterized by complicated behaviors and complex trajectories. One of such systems is the Sprott B model. We construct some set of multi-attractors based on the Sprott B model where additional parameters and operators are considered. After summarizing important preliminaries relevant to simple chaotic differential systems, the model is firstly solved analytically and numerically, then graphical simulations are provided. The later show coexistence and evolution of two chaotic attractors in a symmetrical representation. Lastly, similar results and expected outcomes are recovered via an electrical circuit implementation, realized using the Field Programmable Gate Array (FPGA) board, the Digital-to-Analog Converter (DAC) and the Rigol Oscilloscope. They also show progressing sets of coexisting multi-attractors.

Interaction of lump, periodic, bright and kink soliton solutions of the (1+1)-dimensional Boussinesq equation using Hirota-bilinear approach

In this paper, we explore the characteristics of lump and interaction solutions for a (1+1) dimensional Boussinesq equation. By employing the Hirota bilinear method, we derive and analyze the exact solutions of this equation. Specifically, we achieve the lump with bright-bright soliton solution, 1-lump,2-lumps and 3-lumps with single bright soliton solution, lump with periodic, kink, and anti-kink soliton solutions. Alongside deriving these solutions, we also illustrate their dynamic properties through graphical simulations. The Boussinesq equation holds significant importance due to its applications in various domains, such as water wave modeling, coastal engineering, and the numerical simulation of water wave dynamics in harbors and shallow seas. Our research shows that the employed method is straightforward, easy to understand, and highly efficient, providing valuable insights into the equation’s nature and its practical applications.

A fractional-order improved FitzHugh-Nagumo neuron model

Abstract In this paper, we propose a fractional-order improved FitzHugh-Nagumo (FHN) neuron model in terms of a generalised Caputo fractional derivative. Following the existence of a unique solution for the proposed model, we derive the numerical solution using a recently proposed L1 predictor-corrector method. The given method is based on the L1-type discretization algorithm and the spline interpolation scheme. We perform the error and stability analyses for the given method. We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns, chaotic patterns, and quasi-periodic patterns. The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics, which are inherent to many biological systems.

On the singular-hybrid type of the Langevin fractional differential equation with a numerical approach

The nonlinear fractional Langevin equation is an important equation used in various areas of physics and mathematics. In this article, we focus on the singular-hybrid case of the generalized Langevin equations and prove the existence of a solution using fixed point theory. We also provide numerical and graphical simulations to demonstrate the convergence and existence of a solution for this singular problem. Finally, we present numerical examples in the form of tables and graphs to examine the accuracy of the method.

Intelligent computing framework to analyze the transmission risk of COVID-19: Meyer wavelet artificial neural networks

The optimum control methods for the epidemiology of the COVID-19 model are acknowledged using a novel advanced intelligent computing infrastructure that joins artificial neural networks with unsupervised learning-based optimizers i.e., Genetic Algorithms (GA) and sequential quadratic programming (SQP). Unsupervised learning strategy is provided which depends on the wavelet basis's sequential deconstruction of stochastic data. The weights or selection values of neural networks are utilizing cumulative algorithms of Meyer wavelet artificial neural networks (MWANNs) optimized with global search Genetic Algorithms (GAs) and Sequential Quadratic Programming (SQP), referred to as MWANNs-GA-SQP and the design technique is utilized to determine the COVID-19 model for five different scenarios employing different step sizes and input intervals. The findings of this research article examined that in order to minimize the total disease transmission at the lowest cost and complexity, safety, focused medical care, and exterior sterilization methods applicability. The provided data is validated through various graphical simulations, which surely authenticate the effectiveness and robustness of the proposed solver. The suggested solver, MWANNs-GA-SQP, is tested in a variety of circumstances to examine that how reliable, safe, and tolerant. Using the proposed MWANNs hubristic intelligent approach, an objective optimization function is created in feed forward neural networking to minimize the mean square error. An investigation of the hybrid GA-SQP is used to confirm the accuracy and dependability of the MWANNs model results. Mean absolute graphs have been constructed to assess the integrity and efficiency of the proposed methodology. The accuracy and reliability of the suggested method are demonstrated by constantly achieving maximum variables of analytical assessment criteria computed for a large appropriate variety of distinct trials.

Dynamics of Love-type wave propagation in composite transversely isotropic porous structures

The present study aims to analyze the propagation behavior of Love-type wave in a composite transversely isotropic porous structure. The structure comprises an inhomogeneous sandy porous layer lying between a non-homogeneous magneto-poroelastic layer and a heterogeneous fractured porous half-space. Analytic solutions of the field equations of the respective media involve the application of the variable separable method and Wentzel-Kramers-Brillouin (WKB) asymptotic approach for the conversion of partial differential equations into ordinary differential equations. Through careful imposition of boundary conditions and subsequent elimination of arbitrary constants, we derive a complex dispersion relation governing the propagation of Love-type waves. This dispersion equation yields both the phase velocity curve, corresponding to the real expression, and the damping velocity curve, derived from the imaginary expression. To represent our findings, we conduct extensive calculations and graphical simulations illustrating the influence of various material parameters such as heterogeneity, porosity, volume fraction of fractures, sandiness, magnet-oelastic coupling, angle at which wave crosses the magnetic field, and layer thickness on the dispersive nature of Love-type waves using MATHEMATICA software. Furthermore, we conduct case-specific analyses, revealing instances where the dispersion equation simplifies to the standard Love wave equation, thereby validating our mathematical framework. Our findings underscore the significant influence of the aforementioned material parameters on the phase and damping velocities of Love-type wave. This interdisciplinary investigation into different porous media opens new avenues for future research and has significant implications in various disciplines, ranging from engineering and geophysics to environmental science and beyond.

Tripartite evolutionary game analysis of government reward and punishment mechanisms and agricultural resilience under a dual carbon context

PurposeUnder the “dual carbon” framework, the article explores the equilibrium points among the government, agricultural enterprises and village committees, and uses sensitivity analysis to reveal the dynamic factors affecting these stakeholders, thereby proposing methods to enhance agricultural disaster resilience.Design/methodology/approachThe article uses MATLAB to construct a game model for the three parties with interests: agribusiness, government and village council. It examines the stability of strategies among these entities. Through graphical simulation, the paper analyzes the sensitivity of agricultural enterprises carbon emissions and village committees’ rent-seeking behaviors in the decision-making process, focusing on significant factors such as government carbon tax and regulatory policies.FindingsA single government reward and punishment mechanism is insufficient to influence the strategic choices of enterprises and village committees. The cost of rent-seeking does not affect the strategic choices of enterprises and village committees. A key factor influencing whether the village committee engages in rent-seeking is the level of labor income of the village committee as an “intermediary”.Originality/valueThis paper focuses on the dynamic game between three stakeholders (the government, agricultural enterprises and village committees), seeking dynamic equilibrium and conducting sensitivity analysis through visualization to provide the government with optimal policy recommendations.

Soliton solutions of nonlinear coupled Davey–Stewartson Fokas system using modified auxiliary equation method and extended (G′/G2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G'/G^{2})$$\\end{document}-expansion method

The captivating realm of the nonlinear coupled Davey–Stewartson Fokas system is explored in this research paper. As a powerful tool, the proposed system is utilized for the realistic representation of various non-linear dynamical mechanisms in different fields of sciences and engineering including non-linear optical fibers, plasma physics and water waves theory. Two distinct exact methods, namely the modified auxiliary equation method and the extended (G′/G2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G'/G^{2})$$\\end{document}-expansion method, are utilized to acquire the exact soliton solutions of the non-linear coupled Davey–Stewartson Fokas system. A plethora of novel soliton solutions containing anti-kink, kink, bright, dark, dark-bright, bright-dark and some other singular soliton solutions, have been obtained using the employed exact methods. The significance of proposed manuscript lies in the novelty of obtained solutions. Kink, dark and bright solitons have wide applications in optical fiber communications, plasma physics and water waves dynamics. The acquired nontrivial exact solutions contain exponential, trigonometric, rational and hyperbolic functions. Some obtained solutions are visually represented through graphical simulations of 3D, 2D-contour and 2D-line plots, providing a comprehensive visualization of the soliton dynamics.The modulation instability of the proposed nonlinear system has been investigated, which ensures the stability of the system.

Modelling Yeast Prion Dynamics: A Fractional Order Approach with Predictor–Corrector Algorithm

This work aims to comprehend the dynamics of neurodegenerative disease using a mathematical model of fractional-order yeast prions. In the context of the Caputo fractional derivative, we here study and examine the solution of this model using the Predictor–Corrector approach. An analysis has been conducted on the existence and uniqueness of the selected model. Also, we examined the model’s stability and the existence of equilibrium points. With the purpose of analyzing the dynamics of the Sup35 monomer and Sup35 prion population, we displayed the graphs to show the obtained solutions over time. Graphical simulations show that the behaviour of the populations can change based on fractional orders and threshold parameter values. This work may present a good example of how biological theories and data can be better understood via mathematical modelling.

Computation of integral transforms in terms of double hypergeometric series ψ2 with applications

The principal aim of the present paper is to evaluate a new integral transform involving the product of two Bessel Functions of the first kind expressed in terms of the Humbert function ψ2. We also derive some interesting special cases from the main result of this paper. The presented result will be applied to generate some new laser beams called as the Humbert beams of type-II and study there propagation behaviour. From graphical simulations this type of wave seems interesting and useful in optical trapping which is used in some applications for pushing and moving particles such as: biological cells, neutral atoms, fluorescent, DNA molecules and trapping productivity on nano-sized spheres.

A statistical Framework for a new two-parameter unit Bilal distribution with application to model Asymmetric Data

In the realm of statistical mechanics, unit models are commonly employed to elucidate tangible numerical values that fall within the range of 0–1, encompassing entities like proportions, percentages, and probabilities. Unit models are frequently created by adapting an existing model originally defined in a broader domain, while others are explicitly formulated independently. This study aims to develop a novel unit interval lifespan model with a small number of parameters that is capable of describing more complex failure patterns, such as growing and bathtub-shaped failure rates. The unit Bilal (UB) model, based on the inverse-exponential technique and the Bilal model, is explained in this research study. Different statistical features and aspects of reliability are investigated. The results have both theoretical and practical implications. We derive explicit expressions for primary functions from the UB distribution from a theoretical perspective. To evaluate parameter, estimate approaches, we demonstrate various numerical and graphical simulation findings. The applicability of the model to real-world data is also discussed.

A graphical simulation tool to estimate microalgae production capacity around the world

This paper presents a tool to simulate the biomass production capacity of microalgae-based processes as a function of the prevailing weather conditions at selected locations around the world. The tool is designed for the use of raceway reactors operated in turbidostat mode, allowing for the simulation of biomass production at whatever location for different strains as a function of reactor size, culture depth, and biomass concentration in the reactor. The tool integrates the solar radiation and temperature data available in existing databases for the selected location to determine the light availability and temperature impact in the culture, to finally provide the growth rate and biomass productivity. Hourly values are calculated to estimate a detailed overview of cultures performance, and finally, mean daily and annual values are calculated. The simulation tool developed is a very useful instrument for decision-making processes about the installation of microalgae-related facilities, and also allows the determination of the potential production capacity.

Exploring the Landscape of Fractional-Order Models in Epidemiology: A Comparative Simulation Study

Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many researchers have discussed various types of epidemiological models, including deterministic, stochastic, and fractional order models, for this purpose. This article presents a comprehensive review and comparative study of the transmission dynamics of fractional order in epidemiological modeling. A significant portion of the paper is dedicated to the graphical simulation of these models, providing a visual representation of their behavior and characteristics. The article further embarks on a comparative analysis of fractional-order models with their integer-order counterparts. This comparison sheds light on the nuances and subtleties that differentiate these models, thereby offering valuable insights into their respective strengths and limitations. The paper also explores time delay models, non-linear incidence rate models, and stochastic models, explaining their use and significance in epidemiology. It includes studies and models that focus on the transmission dynamics of diseases using fractional order models, as well as comparisons with integer-order models. The findings from this study contribute to the broader understanding of epidemiological modeling, paving the way for more accurate and effective strategies in disease control and prevention.

A study of time-fractional model for atmospheric internal waves with Caputo-Fabrizio derivative.

The internal atmospheric waves are gravity waves and occur in the inner part of the fluid system. In this study, a time-fractional model for internal atmospheric waves is investigated with the Caputo-Fabrizio time-fractional differential operator. The analytical solution of the considered model is retrieved by the Elzaki Adomian decomposition method. The variation in the solution is examined for increasing order of the fractional parameter α through numerical and graphical simulations. The accuracy of the obtained results is established by comparing the obtained solution of considered fractional model with the results available in the literature.

The role of Zakat and Fitrah in improving Community Welfare: A Case Study of Baznas Garut Regency

Zakat has great potential to improve the welfare of people in Indonesia, including in Garut Regency. The professional and accountable management of zakat by the National Zakat Agency (BAZNAS) of Garut Regency is expected to encourage an increase in the economic welfare of the community. However, the performance of BAZNAS Garut in this case is not optimal, so the impact on improving public welfare is also not optimal. This gives rise to a critical perspective in society. This study aims to analyze the governance, distribution system, and the impact of Zakat mal and Zakat fitrah distributed BAZNAS Garut in improving the economic welfare of the community. The method used is descriptive analysis with empirical juridical approach and graphic simulation. The results showed that: 1) conceptually and empirically, zakat can increase economic growth and welfare; 2) distribution of zakat Mal BAZNAS Garut consists of consumptive and productive programs; 3) zakat mal has a positive impact on improving economic welfare; and 4) zakat al-Fitr also has a positive impact on improving the economic welfare of the community. However, this study concludes that the management of zakat by BAZNAS Garut is not optimal, so it is necessary to improve performance to realize better welfare.

Exploring the solutions of Hilfer delayed Duffing problem on the positive real line

In this article, we focus on studying the Duffing problem with the time delay of pantograph type via the Hilfer fractional derivatives on the infinite interval (0,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(0,\\infty )$\\end{document}. An appropriate Banach space supported with the Bielecki norm in the Mittag–Leffler function sense is introduced for new and convenient analysis. The existence and uniqueness (E&U\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{E\\&U}$\\end{document}) of the solutions are proved by utilizing the classical fixed point theorems (FPTs). Moreover, the Hyers–Ulam (HU) stability is discussed for our Hilfer fractional Duffing pantograph system (HFDPS). Ultimately, our results are enhanced by providing numerical examples with graphics simulations to check the validity of the main outcomes.

Fractional Order and Numerical Solution Application of Modeling in the Management of Examination Misconducts

The fractional order model that represents the spread of Examination misconduct using compartments of the population of honest students (susceptible), those lightly involved in misconduct (exposed), seriously involved ones (infected), and quitters (removed) is provided. The fractional order derivative is considered in the Caputo sense. To determine the epidemic forecast and persistence, we calculate the reproduction number. Analyzing the stability of this scheme ensures a non-negative and unique solution within the defined domain (0,1). Employing the Laplace-Adomian Decomposition Method aids in estimating the solution for the nonlinear fractional differential equations. Utilizing infinite series helps derive solutions for these equations, ensuring convergence to their precise values. The results obtained align with outcomes from the traditional Differential Transformed Method. Finally, numerical results and an outstanding graphic simulation are presented.