Novel techniques to analyze dynamical properties of quantum chaos with peculiar evidence of hybrid systems confinement.

Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields.

Appraisal of reservoir quality for hydrocarbon-bearing deep-water Miocene sandstones incised valley, south-east Asian offshore Indus: An application of seismic attributes and instantaneous spectral porosity quantitative reservoir simulations.

Incised marine valleys (IVS) are hot topics in exploring the stratigraphic oil and gas-bearing plays. Multiple channelized sandstone lenses at varying depths [m], thicknesses [m], and porosities [%] constrain seismic impedance. The presence of hydrocarbon-bearing resources affects the seismic impedance (density (g/cc) and velocity (m/s)). Therefore, a quantitative prediction has been carried out for determining the thickness [m], porosity [%], and depths [m] of laterally distributed channelized sandstone lenses (SLS) for IVS, Indus offshore Basin (IOB), Pakistan, using 2-D instantaneous spectral porosity quantitative modelling (2DSSM), continuous wavelet transforms-based (CWT) 2-D instantaneous spectral density modelling (2DSSDM), and spectral decomposition tools. The 2DSSM remained limited in predicting the number of channelized sandstone lenses and their quantitative stratigraphic attributes. The 45-Hz-based processing of conventional 2DSSM has resolved the two channelized sandstone lenses of the stratigraphic trap. The deepest channelized sandstone lens has attained 1-6 m thickness with a lateral extent of 3 km, within the porosity range of 18-33 %. The highest confidence level for predicted petrophysical attributes such as 13 m-thick pay zones, -0.08, -0.067, and -0.07 acoustic impedances [g/c.c.*m/s], and 28 % porosities with R2 > 0.85 have validated interpretations. The response of 45-Hz CWT waveform-based inverted density and thickness simulations has predicted the highest thicknesses and lowest densities of reservoir sandstones within the meandering channel belt of the deepwater depositional system. The predicted densities and thicknesses for the coarse-grained sandstone lenses of point bars were 1.8-1.9 g/cc and 15 m, respectively. In the same way, the quantitative estimates of predicted density and simulated thickness have shown a strong coefficient correlation (R2 > 0.80), which confirms the presence of gas-bearing prospects within the IVS. The facies-controlled migration is thought to be the movement of the reservoir facies of the point bars and channelled sandstone-filled lenses to the side.

Novel design and performance evaluation of an indirectly forced convection desiccant integrated solar dryer for drying tomatoes in Pakistan.

The process of drying agricultural products for food preservation is a difficult task that requires a significant amount of energy. The increasing cost and depletion of fossil fuels have led to the development of a food dryer that utilizes renewable energy sources. This research paper proposes the design and performance evaluation of an indirectly forced convection desiccant integrated solar dryer (IFCDISD) at the Solar Energy Research Lab at USPCAS-E, NUST Pakistan. Tomatoes were chosen as the test product due to their importance and widespread consumption. The drying process involves slicing the tomatoes and placing them on the IFCDISD rack, where a desiccant called calcium chloride (CaCl2) is integrated into the dryer. The experiments were conducted during both sunshine (SS) hours and Off-sunshine (OSS) hours. The IFCDISD operates using sunlight during SS hours and utilizes the absorbed heat of CaCl2 in OSS hours via a forced DC brushless fan powered by battery charged thro solar panel. The tomatoes were weighed before and after each drying mode, and the moisture removal was calculated. The results show that the dryer efficiency was 50.14 % on day 1, 66 % on day 2, and an overall efficiency of 58.07 %. The moisture content removal was 42.858 % on day 1, 22.9979 % on day 2, and an overall moisture content removal of 58.07 %. Moreover, the payback period is 5.1396 and the carbon mitigation was recorded as 2.0335, and the earned carbon credit was recorded as 11559.6.

Computation and convergence of fixed-point with an RLC-electric circuit model in an extended b-suprametric space.

This article establishes various fixed-point results and introduces the idea of an extended b-suprametric space. We also give several applications pertaining to the existence and uniqueness of the solution to the equations concerning RLC electric circuits. At the end of the article, a few open questions are posed concerning the distortion of Chua's circuit and the formulation of the Lagrangian for Chua's circuit.

Real-time navigation of mecanum wheel-based mobile robot in a dynamic environment.

Path planning and control of a mobile robot, in a dynamic environment, has been an important research topic for many years. In this paper an algorithm for autonomous motion of a mobile robot is proposed, with mecanum wheels, to reach a goal while avoiding obstacles through the shortest path in a dynamic environment. The proposed method uses a hybrid A⁎ and a velocity obstacle algorithms for path planning and obstacle avoidance. The A⁎ algorithm is implemented to explore the shortest path from starting position to the goal while avoiding all the static obstacles. However, in real time applications the dynamic obstacles need to be avoided, therefore, for such a case velocity obstacle algorithm is unified with the A⁎ algorithm. Initially, the proposed algorithm is verified through simulations. Then it is implemented using experimental setup in real time environment using single and multiple static obstacles as well as on a dynamic obstacle. It can be observed that the robot reaches the goal, effectively by avoiding static and dynamic obstacles. Moreover, the performance of the proposed work is evaluated through qualitative comparison between proposed method and recently published work, showing that the proposed algorithm is gives better features than existing work. In the end, the possible application of mobile robot having mecanum wheels with proposed path planning method is also given in the paper.

Existence of common fuzzy fixed points via fuzzy F-contractions in b-metric spaces.

The main goal of this study is to establish common fuzzy fixed points in the context of complete b-metric spaces for a pair of fuzzy mappings that satisfy F-contractions. To strengthen the validity of the derived results, non-trivial examples are provided to substantiate the conclusions. Moreover, prior discoveries have been drawn as logical extensions from pertinent literature. Our findings are further reinforced and integrated by the numerous implications that this technique has in the literature. Using fixed point techniques to approximate the solutions of differential and integral equations is very useful. Specifically, in order to enhance the validity of our findings, the existence result of the system of non-linear Fredholm integral equations of second-kind is incorporated as an application.

Fractional epidemic model of coronavirus disease with vaccination and crowding effects.

Most of the countries in the world are affected by the coronavirus epidemic that put people in danger, with many infected cases and deaths. The crowding factor plays a significant role in the transmission of coronavirus disease. On the other hand, the vaccines of the covid-19 played a decisive role in the control of coronavirus infection. In this paper, a fractional order epidemic model (SIVR) of coronavirus disease is proposed by considering the effects of crowding and vaccination because the transmission of this infection is highly influenced by these two factors. The nonlinear incidence rate with the inclusion of these effects is a better approach to understand and analyse the dynamics of the model. The positivity and boundedness of the fractional order model is ensured by applying some standard results of Mittag Leffler function and Laplace transformation. The equilibrium points are described analytically. The existence and uniqueness of the non-integer order model is also confirmed by using results of the fixed-point theory. Stability analysis is carried out for the system at both the steady states by using Jacobian matrix theory, Routh-Hurwitz criterion and Volterra-type Lyapunov functions. Basic reproductive number is calculated by using next generation matrix. It is verified that disease-free equilibrium is locally asymptotically stable if R 0 < 1 and endemic equilibrium is locally asymptotically stable if R 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable if R 0 < 1 and endemic equilibrium is globally asymptotically stable if R 0 > 1 . The non-standard finite difference (NSFD) scheme is developed to approximate the solutions of the system. The simulated graphs are presented to show the key features of the NSFD approach. It is proved that non-standard finite difference approach preserves the positivity and boundedness properties of model. The simulated graphs show that the implementation of control strategies reduced the infected population and increase the recovered population. The impact of fractional order parameter α is described by the graphical templates. The future trends of the virus transmission are predicted under some control measures. The current work will be a value addition in the literature. The article is closed by some useful concluding remarks.

Multigrid simulations of non-Newtonian fluid flow and heat transfer in a ventilated square cavity with mixed convection and baffles.

The impact of baffles on a convective heat transfer of a non-Newtonian fluid is experimentally studied within a square cavity. The non-Newtonian fluid is pumped into the cavity through the inlet and subsequently departs from the cavity via the outlet. Given the inherent non-linearity of the model, a numerical technique has been selected as the method for obtaining the outcomes. Primarily, the governing equations within the two-dimensional domain have been discretized using the finite element method. For approximating velocity and pressure, we have employed the reliable P 2 - P 1 finite element pair, while for temperature, we have opted for the quadratic basis. To enhance convergence speed and accuracy, we employ the powerful multigrid approach. This study investigates how key parameters like Richardson number (Ri), Reynolds number (Re), and baffle gap b g influence heat transfer within a cavity comprising a non-Newtonian fluid. The baffle gap ( b g ) has been systematically altered within the range of 0.2-0.6, and for this research, three distinct power law indices have been selected namely: 0.5, 1.0, and 1.5. The primary outcomes of the investigation are illustrated through velocity profiles, streamlines, and isotherm visualizations. Furthermore, the study includes the computation of the Nu avg (average Nusselt number) across a range of parameter values. As the Richardson number (Ri) increases, Nu avg also rises, indicating that an increase in Ri results in augmented average heat transfer. Making the space between the baffles wider makes heat flow more intense. This, in turn, heats up more fluid within the cavity.

Enhancing automic and optimal control systems through graphical structures.

The concept of graphical structures of extended suprametric space is introduced in this study and applied to supra-graphical contractive mapping. A recursive algorithm in connection with graphical notions can be employed in adaptive systems to construct a desired output function iteratively after specific conditions are first defined to ensure the existence of the solution by use of supra-graphical contractive mapping. After analyzing the historical context and relevant outcomes, we discuss the usage of graphical structures and supra-graphical contractive mappings in the conceptual frameworks of adaptive control and optimal control systems.

Seismic attributes and spectral decomposition-based inverted porosity-constrained simulations for appraisal of shallow-marine lower-Cretaceous sequences of Miano gas field, Southern Pakistan.

Seismic attributes can play an important role in the exploration of hydrocarbon-bearing stratigraphic systems. Incised valley systems are developed during the falling sea, which causes the deposition of coarse-grained sandstone facies inside the low-standing tracts (LST). These regional phenomena constrain the quantitative attributes of ultra-thin-bedded stratigraphic petroleum traps, e.g., vertical and lateral variations in the thickness, accommodation space, lithology, and porosity. This study deals with the application of the continuous wavelet transform (CWT) of a spectral decomposition (SD) tool on a 3D post-stack seismic volume of the Miano gas Field, Lower Indus basin, Pakistan. The results show that the CWT accurately detected the regionally faulted/fractured system and distinguished the frequency-dependent amplitude anomalies. The wedge model resolved a 24-meter-thick gas-bearing resource. Quality control analysis was carried out using CWT-based broadband processing between the designed amplitude spectrum of 17 Hz and 70 Hz. The reservoirs with over 25% porosity that were located within the shale-dominated facies with less than 8% porosity were imaged through the processing of the instantaneous spectral porosity model at the 48-Hz tuning block. Moreover, 190 to 165-m-thick thin-bedded sandstone reservoirs at a 25% porosity zone were resolved using 22-Hz and 28-Hz, which implicates the sea standstill and medium-to-coarse-grained depositional reservoir facies. The ultra-thin-bedded traps inside the laterally continuous stratigraphic lens of 121 m and the prograding clinoform lens of 101-m within the incised valley petroleum system were resolved using 48-Hz, which implicates the falling sea and fine-scaled transgressed erosional facies. These implications suggest that the identified regional stratigraphic traps have development potential for this gas field. The treatment of the inverted model at the highest frequencies can be utilized to investigate the porous stratigraphically trapped facies of LST and can serve as an important analogue for the leading gas field of the Indus Basin and similar basins.

A comparative analysis of three distinct fractional derivatives for a second grade fluid with heat generation and chemical reaction.

This article provides a comparison among the generalized Second Grade fluid flow described by three recently proposed fractional derivatives i.e. Atangana Baleanu fractional derivative in Caputo sense (ABC), Caputo Fabrizio (CF) and Constant Proportional-Caputo hybrid (CPC) fractional derivative. The heat mass transfer is observed during the flow past a vertical porous plate that is accelerated exponentially under the effects of the Magneto hydro dynamics. The effects of the heat generation and exponential heating in the temperature boundary layer and chemical reaction at the concentration boundary layer are also analyzed in this article. The flow model is described by three partial differential equations and the set of non-dimensional PDE's is transformed into ODE's by utilization of the integral transform technique (Laplace transform). For the better understanding of the rheological properties of the Second Grade fluid we used the CF, ABC and CPC operators to describe the memory effects. The analytical exact solution of the problem is obtained in the form of G-functions and Mittag Leffler functions. For the physical significance of flow parameters, different parameters are graphed. From this analysis it is concluded that the CPC is the most suitable operator to describe the memory effects.

FEM simulations for double diffusive transport mechanism hybrid nano fluid flow in corrugated enclosure by installing uniformly heated and concentrated cylinder.

Generation of fluid flow due to simultaneous occurrence of heat and mass diffusions caused by buoyancy differences is termed as double diffusion. Pervasive applications of such diffusion arise in numerous natural and scientific systems. This article investigates double diffusion in naturally convective flow of water-based fluid saturated in corrugated enclosure and containing hybrid nano particles composed of Copper (Cu) and Alumina (Al2O3). Impact of uniformly applied magnetic field is also accounted. To produce thermosolutal convective potential circular cylinder of constant radius is also adjusted by providing uniform temperature and concentration distributions. Finite element approach is capitalized to provide solution of utilized governing equations by utilizing Multiphysics COMSOL software. Wide-range of physical parameters are incorporated to depict their influence on associated distributions (velocity, temperature and concentration). Interesting physical quantities like Nusselt number, Sherwood numbers are also calculated against involved sundry parameters. It is note worthily observed that maximum strength of stream lines [Formula: see text] is 3.3 at [Formula: see text] and drops to 1.2 when [Formula: see text] is increased to 0.04. Furthermore, in the hydrodynamic case (Ha = 0), it is observed that the velocity field exhibits an increasing trend compared to the hydromagnetic case [Formula: see text] which is proved from the attained values of stream-function i.e., [Formula: see text] (in the absence of a magnetic field) and [Formula: see text] (in the presence of a magnetic field). It is revealed from the statistics of Nusselt number that increase in volume fraction of nano particles from 0 to 0.4, heat flux coefficient upsurges up to 7% approximately. Since, present work includes novel physical aspects of thermosolutal diffusion generated due to induction of hybrid nanoparticles in water contained in corrugated enclosure, so this study will provide innovative thought to the researchers to conduct research in this direction.

Tubeimosides are pan-coronavirus and filovirus inhibitors that can block their fusion protein binding to Niemann-Pick C1.

SARS-CoV-2 and filovirus enter cells via the cell surface angiotensin-converting enzyme 2 (ACE2) or the late-endosome Niemann-Pick C1 (NPC1) as a receptor. Here, we screened 974 natural compounds and identified Tubeimosides I, II, and III as pan-coronavirus and filovirus entry inhibitors that target NPC1. Using in-silico, biochemical, and genomic approaches, we provide evidence that NPC1 also binds SARS-CoV-2 spike (S) protein on the receptor-binding domain (RBD), which is blocked by Tubeimosides. Importantly, NPC1 strongly promotes productive SARS-CoV-2 entry, which we propose is due to its influence on fusion in late endosomes. The Tubeimosides' antiviral activity and NPC1 function are further confirmed by infection with SARS-CoV-2 variants of concern (VOC), SARS-CoV, and MERS-CoV. Thus, NPC1 is a critical entry co-factor for highly pathogenic human coronaviruses (HCoVs) in the late endosomes, and Tubeimosides hold promise as a new countermeasure for these HCoVs and filoviruses.

Machine learning intelligent based hydromagnetic thermal transport under Soret and Dufour effects in convergent/divergent channels: a hybrid evolutionary numerical algorithm.

In this research, we analyze the complex dynamics of hydro-magnetic flow and heat transport under Sorent and Dofour effects within wedge-shaped converging and diverging channels emphasizing its critical role in conventional system design, high-performance thermal equipment. We utilized artificial neural networks (ANNs) to investigation the dynamics of the problem. Our study centers on unraveling the intricacies of energy transport and entropy production arising from the pressure-driven flow of a non-Newtonian fluid within both convergent and divergent channel. The weights of ANN based fitness function ranging from - 10 to 10. To optimize the weights and biases of artificial neural networks (ANNs), employ a hybridization of advanced evolutionary optimization algorithms, specifically the artificial bee colony (ABC) optimization integrated with neural network algorithms (NNA). This approach allows us to identify and fine-tune the optimal weights within the neural network, enabling accurate prediction. We compare our results against the established different analytical and numerical methods to assess the effectiveness of our approach. The methodology undergoes a rigorous evaluation, encompassing multiple independent runs to ensure the robustness and reliability of our findings. Additionally, we conduct a comprehensive analysis that includes metrics such as mean squared error, minimum values, maximum values, average values, and standard deviation over these multiple independent runs. The minimum fitness function value is 1.32 × 10-8 computed across these multiple runs. The absolute error, between the HAM and machine learning approach addressed ranging from 3.55 × 10-7 to 1.90 × 10-8. This multifaceted evaluation ensures a thorough understanding of the performance and variability of our proposed approach, ultimately contributing to our understanding of entropy management in non-uniform channel flows, with valuable implications for diverse engineering applications.

Heat generation/absorption effect on natural convective heat transfer in a wavy triangular cavity filled with nanofluid.

This study is numerically executed to investigate the influence of heat generation or absorption on free convective flow and temperature transport within a wavy triangular enclosure filled by the nanofluid taking the Brownian effect of nanoparticles. The water (H2O) is employed as base fluid and copper (Cu) as nanoparticles for making effective Cu-H2O nanofluids. The perpendicular sinusoidally wavy wall is cooled at low temperature while the horizontal bottom sidewall is heated non-uniformly (sinusoidal). The inclined wall of the enclosure is insulated. The governing dimensionless non-linear PDEs are executed numerically with the help of the Galerkin weighted residual type finite element technique. The numerically simulated results are displayed through average Nusselt number, isothermal contours, and streamlines for the various model parameters such as Hartmann number, Rayleigh number, heat generation or absorption parameter, nanoparticles volume fraction, and undulation parameter. The outcomes illustrate that the temperature transport rate augments significantly for the enhancement of Rayleigh number as well as nanoparticles volume fraction whereas reduces for the increment of Hartman number. The heat transfer is significantly influenced by the size, shape, and Brownian motion of the nanoparticles. The rate of heat transport increases by 20.43% considering the Brownian effect for 1% nanoparticle volume. The thermal performance increases by 8.66% for the blade shape instead of the spherical shape of nanoparticles. In addition, heat transfer is impacted by the small size of nanoparticles. The thermal transport rate increases by 35.87% when the size of the nanoparticles reduces from 100 to 10 nm. Moreover, the rate of heat transmission increases efficiently as the undulation parameter rises. It is also seen that a crucial factor in the flow of nanofluids and heat transmission is the heat generation/absorption parameter that influences temperature distribution, heat transfer rates, and overall thermal performance.

BMP9 is a potent inducer of chondrogenesis, volumetric expansion and collagen type II accumulation in bovine auricular cartilage chondroprogenitors.

Reconstruction of the outer ear currently requires harvesting of cartilage from the posterior of the auricle or ribs leading to pain and donor site morbidity. An alternative source for auricular reconstruction is in vitro tissue engineered cartilage using stem/progenitor cells. Several candidate cell-types have been studied with tissue-specific auricular cartilage progenitor cells (AuCPC) of particular interest. Whilst chondrogenic differentiation of competent stem cells using growth factor TGFß1 produces cartilage this tissue is frequently fibrocartilaginous and lacks the morphological features of hyaline cartilage. Recent work has shown that growth factor BMP9 is a potent chondrogenic and morphogenetic factor for articular cartilage progenitor cells, and we hypothesised that this property extends to cartilage-derived progenitors from other tissues. In this study we show monoclonal populations of AuCPCs from immature and mature bovine cartilage cultured with BMP9 produced cartilage pellets have 3-5-fold greater surface area in sections than those grown with TGFß1. Increased volumetric growth using BMP9 was due to greater sGAG deposition in immature pellets and significantly greater collagen accumulation in both immature and mature progenitor pellets. Polarised light microscopy and immunohistochemical analyses revealed that the organisation of collagen fibrils within pellets is an important factor in the growth of pellets. Additionally, chondrocytes in BMP9 stimulated cell pellets had larger lacunae and were more evenly dispersed throughout the extracellular matrix. Interestingly, BMP9 tended to normalise the response of immature AuCPC monoclonal cell lines to differentiation cues whereas cells exhibited more variation under TGFß1. In conclusion, BMP9 appears to be a potent inducer of chondrogenesis and volumetric growth for AuCPCs a property that can be exploited for tissue engineering strategies for reconstructive surgery though with the caveat of negligible elastin production following 21-day treatment with either growth factor.

Heat transfer analysis of generalized second-grade fluid with exponential heating and thermal heat flux.

The aim of present work is to apply the Caputo-Fabrizio fractional derivative in the constitutive equations of heat transfer. Natural convection flow of an unsteady second grade fluid over a vertical plate with exponential heating is discussed. The generalized Fourier law is substituted in temperature profile. A portion of the dimensionless factors are utilized to make the governing equations into dimensionless structures. The solutions for temperature and velocity profiles of Caputo-Fabrizio model are acquired through the Laplace transform method. These solutions are greatly affected through the variation of different dimensionless variables like Prandtl number, Grashof number, and second-grade fluid parameter. Finally, the influence of embedded parameters is shown by plotting graphs through Mathcad. From the graphical results it is concluded that, the temperature of the fluid decreases with the increasing values of the Prandtl number and Second grade fluid parameter and increases with the passage of time. The velocity of the fluid increases with increasing values of the Grashof number, second grade parameter and time while decreases with increasing values of fractional parameter and Prandtl number.

Time fractional Yang-Abdel-Cattani derivative in generalized MHD Casson fluid flow with heat source and chemical reaction.

This present research article investigates the exact analytical solution for the mathematical model of the generalized Casson fluid flow by using the new fractional operator with Rabotnov exponential kernel i.e. Yang-Abdel-Cattani operator. The impacts of heat source, magnetic hydrodynamics and chemical reactions on the flow of fractional Casson fluid through a vertical flat plate are studied in this article. For the sake of a better interpretation of the rheological behavior of Casson fluid we have used the new operator of fractional order with exponential kernel of Rabotnov known as Yang-Abdel-Cattani operator of fractional derivative. By making use of the technique of Laplace transform we have find the exact analytical solution of the problem in the Mittag-Leffler's form, for all the three governing equations i.e. Velocity, energy and concentration equation. It has been noticed from the literature that it is challenging to obtain analytical results from fractional fluid model derived by the various fractional operators. This article helps to address this issue by providing analytical solutions for fractionalized fluid models. To analyze the physical importance of different fluid parameters such as Schmidt number, Prandtl number, MHD and alpha on the heat, mass and momentum class are presented through graphs. The concentration of the fluid decreases with Schmidth number and temperature of the fluid decreases with the increasing Prandtl number. The velocity of the fluid decreases with increasing MHD effects and increases with increasing Alpha. The Yang-Abdel-Cattani operator of fractional order can describe the memory effects more suitably than the other fractional operators.

Magneto-bioconvection flow of Casson nanofluid configured by a rotating disk in the presence of gyrotatic microorganisms and Joule heating.

In this article, we investigate the bioconvection flow of Casson nanofluid by a rotating disk under the impacts of Joule heating, convective conditions, heat source/sink and gyrotactic microorganisms. When Brownian diffusion and thermophoretic effects exist, the Casson fluid is examined. The existing physical problem of Casson nanofluid flow with energy transports is demonstrated under the above considerations in the form of partial differential equations (PDEs). Using the appropriate transformations, the PDEs are converted into non-linear ordinary differential equations (ODEs). The mathematical results are calculated through MATLAB by using the function bvp4c. The problem's results are rigorously examined graphically and described with physical justifications. Velocity fields decrease as the bioconvection Rayleigh parameter rises. The thermal profile and soluteal field of species also magnify with an upsurge in thermophoresis number estimations. The microorganism's fields are decayed by larger microbes Biot number.

A reliable numerical investigation of an SEIR model of measles disease dynamics with fuzzy criteria.

The terms susceptibility, exposure, infectiousness, and recovered all have some inherent ambiguity because different population members have different susceptibility levels, exposure levels, infectiousness levels, and recovery patterns. This uncertainty becomes more pronounced when examining population subgroups characterized by distinct behaviors, cultural norms, and varying degrees of resilience across different age brackets, thereby introducing the possibility of fluctuations. There is a need for more accurate models that take into account the various levels of susceptibility, exposure, infectiousness, and recovery of the individuals. A fuzzy SEIR model of the dynamics of the measles disease is discussed in this article. The rates of disease transmission and recovery are treated as fuzzy sets. Three distinct numerical approaches, the forward Euler, fourth-order Runge-Kutta, and nonstandard finite difference (NSFD) are employed for the resolution of this fuzzy SEIR model. Next, the outcomes of the three methods are examined. The results of the simulation demonstrate that the NSFD method adeptly portrays convergent solutions across various time step sizes. Conversely, the conventional Euler and RK-4 methods only exhibit positivity and convergence solutions when handling smaller step sizes. Even when considering larger step sizes, the NSFD method maintains its consistency, showcasing its efficacy. This demonstrates the NSFD technique's superior reliability when compared to the other two methods, while maintaining all essential aspects of a continuous dynamical system. Additionally, the results from numerical and simulation studies offer solid proof that the suggested NSFD technique is a reliable and effective tool for controlling these kinds of dynamical systems.The convergence and consistency analysis of the NSFD method are also studied.