Pub Date : 2025-08-27DOI: 10.1016/j.padiff.2025.101277
Salena Akther , M.G. Hafez , Shahrina Akter
The time–space fractional modified Korteweg de-Vries (TSF-mKdV) equation is considered to investigate the nonlinear overtaking ion-acoustic multi-solitons around the critical values of any specific physical parameter in an unmagnetized collisionless plasma. To do so, various fractional derivative operators are considered. The TSF-mKdV equation is actually obtained by applying the Agrawal technique to the typical mKdV equation. The Hirota’s direct bilinear approach is used to obtain the proposed multi-soliton solutions to the TSF-mKdV model equation. In the framework under study, the effects of the space–time fractional parameters and plasma parameters on the overtaking collision of multi-soliton wave propagation are examined.
{"title":"A comparative study on overtaking collisional ion-acoustic multi-soliton around the critical values in the sense of fractal and fractional differential operators","authors":"Salena Akther , M.G. Hafez , Shahrina Akter","doi":"10.1016/j.padiff.2025.101277","DOIUrl":"10.1016/j.padiff.2025.101277","url":null,"abstract":"<div><div>The time–space fractional modified Korteweg de-Vries (TSF-mKdV) equation is considered to investigate the nonlinear overtaking ion-acoustic multi-solitons around the critical values of any specific physical parameter in an unmagnetized collisionless plasma. To do so, various fractional derivative operators are considered. The TSF-mKdV equation is actually obtained by applying the Agrawal technique to the typical mKdV equation. The Hirota’s direct bilinear approach is used to obtain the proposed multi-soliton solutions to the TSF-mKdV model equation. In the framework under study, the effects of the space–time fractional parameters and plasma parameters on the overtaking collision of multi-soliton wave propagation are examined.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101277"},"PeriodicalIF":0.0,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-27DOI: 10.1016/j.padiff.2025.101278
Ruchika Lochab , Luckshay Batra
The selection of suitable fuzzy logic control (FLC) systems for stabilizing hyperbolic conservation laws (HCLs) remains an open issue in computational fluid dynamics (CFD), particularly for shock-capturing schemes. This work addresses this gap by adopting a dual methodological strategy: (i) a systematic review of over 50 studies (2000–2025) on flux-limiting FLC approaches, and (ii) a comparative benchmark of Mamdani- and Sugeno-type FLCs applied to discontinuous solutions of HCLs. Our results demonstrate that, using weighted average defuzzification, Sugeno-type systems achieve approximately a 20% reduction in mean square error compared to the Mamdani centroid-based method in shock-dominated regimes. This performance gain aligns with adaptive CFD practices that prioritize rule-based, computationally inexpensive smoothing. By integrating theoretical analysis with experimental validation, this work strengthens the mathematical foundations of fuzzy control in PDE-driven modelling.
{"title":"Application of fuzzy logic controls on hyperbolic differential equations","authors":"Ruchika Lochab , Luckshay Batra","doi":"10.1016/j.padiff.2025.101278","DOIUrl":"10.1016/j.padiff.2025.101278","url":null,"abstract":"<div><div>The selection of suitable fuzzy logic control (FLC) systems for stabilizing hyperbolic conservation laws (HCLs) remains an open issue in computational fluid dynamics (CFD), particularly for shock-capturing schemes. This work addresses this gap by adopting a dual methodological strategy: (i) a systematic review of over 50 studies (2000–2025) on flux-limiting FLC approaches, and (ii) a comparative benchmark of Mamdani- and Sugeno-type FLCs applied to discontinuous solutions of HCLs. Our results demonstrate that, using weighted average defuzzification, Sugeno-type systems achieve approximately a 20% reduction in mean square error compared to the Mamdani centroid-based method in shock-dominated regimes. This performance gain aligns with adaptive CFD practices that prioritize rule-based, computationally inexpensive smoothing. By integrating theoretical analysis with experimental validation, this work strengthens the mathematical foundations of fuzzy control in PDE-driven modelling.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101278"},"PeriodicalIF":0.0,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-26DOI: 10.1016/j.padiff.2025.101297
Rezaul Karim , M. A. Bkar Pk , M. Ali Akbar , Pinakee Dey
Leukemia is the name for a blood cancer that develops in the bone marrow. Leukemia is a global public health issue caused by the uncontrolled growth of immature white blood cells in the bloodstream. In this study, we consider a fractional-order five-compartment mathematical model (MM) of leukemia, which includes susceptible blood cells, infected blood cells , cancer cells , immune blood cells , cytokine cells , and we analyze the dynamics of transmission of the disease. We developed a model to examine the spread of the leukemia virus and analyze the effects of adoptive T-cell therapy. This study presents a model of the well-known leukemia virus utilizing Caputo fractional order (CFO) and Beta derivatives. In this, the extended system characterizing the virus spread is addressed using two analytical methods: the Laplace perturbation method (LPM) and the Homotopy decomposition method (HDM). Iterative schemes were employed to obtain specific solutions of the extended system, and numerical simulations were conducted based on selected theoretical parameters. Moreover, the concerned analytical solutions that have been found using the methods are compared. The corresponding plots against various orders of the differentiations are plotted using specific values for the model’s parameters. We emphasize the significance of fractional-order (FO) modeling in understanding the spread of leukemia and highlight the critical need for global access to this immunotherapy.
{"title":"A study on fractional-order mathematical analysis for inspecting the spread of the leukemia virus","authors":"Rezaul Karim , M. A. Bkar Pk , M. Ali Akbar , Pinakee Dey","doi":"10.1016/j.padiff.2025.101297","DOIUrl":"10.1016/j.padiff.2025.101297","url":null,"abstract":"<div><div>Leukemia is the name for a blood cancer that develops in the bone marrow. Leukemia is a global public health issue caused by the uncontrolled growth of immature white blood cells in the bloodstream. In this study, we consider a fractional-order five-compartment mathematical model (MM) of leukemia, which includes susceptible blood cells<span><math><mrow><mspace></mspace><msub><mi>S</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, infected blood cells <span><math><mrow><msub><mi>I</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, cancer cells <span><math><mrow><msub><mi>C</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, immune blood cells <span><math><mrow><msub><mi>W</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, cytokine cells <span><math><mrow><msub><mi>C</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, and we analyze the dynamics of transmission of the disease. We developed a model to examine the spread of the leukemia virus and analyze the effects of adoptive T-cell therapy. This study presents a model of the well-known leukemia virus utilizing Caputo fractional order (CFO) and Beta derivatives. In this, the extended system characterizing the virus spread is addressed using two analytical methods: the Laplace perturbation method (LPM) and the Homotopy decomposition method (HDM). Iterative schemes were employed to obtain specific solutions of the extended system, and numerical simulations were conducted based on selected theoretical parameters. Moreover, the concerned analytical solutions that have been found using the methods are compared. The corresponding plots against various orders of the differentiations are plotted using specific values for the model’s parameters. We emphasize the significance of fractional-order (FO) modeling in understanding the spread of leukemia and highlight the critical need for global access to this immunotherapy.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101297"},"PeriodicalIF":0.0,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-23DOI: 10.1016/j.padiff.2025.101294
Shilpa Choudhary , Ruchika Mehta , Tripti Mehta
This research presents a comparative analysis of Cross diffusion effect on 2D MHD chemical reactive Williamson hybrid nanofluid (MoS2 − GO/Methanol) on a moving thin needle with thermal radiation. The main aim of this study is to increase the thermal efficiency using two different categories of nanoparticles: MoS2 − GO, with Methanol serving as the original liquid is calculated. PDEs can be changed into ordinary differential equations with the help of similarity substitution. Which are nonlinear, and the bvp4c technique is used to numerically simplify it. The results of this investigation indicate that the velocity profile of GO/Methanol composite nanofluid increases more than that of MoS2 − GO/Methanol through the increasing amount of Grashof number and Weissenberg parameter, even as the magnetic parameter and porosity impact have the opposite effect. On other hand, the chemical reaction and Schmidt number increase the rate of mass transfer for both nanofluids. The larger values of thermal radiation and Dufour effect enhance the thermal profile.
{"title":"Numerical study of MHD Williamson hybrid nanofluid flow over incessantly moving thin needle in presence of Soret & Dufour effect","authors":"Shilpa Choudhary , Ruchika Mehta , Tripti Mehta","doi":"10.1016/j.padiff.2025.101294","DOIUrl":"10.1016/j.padiff.2025.101294","url":null,"abstract":"<div><div>This research presents a comparative analysis of Cross diffusion effect on 2D MHD chemical reactive Williamson hybrid nanofluid (<em>MoS</em><sub>2</sub> − <em>GO</em>/<em>Methanol</em>) on a moving thin needle with thermal radiation. The main aim of this study is to increase the thermal efficiency using two different categories of nanoparticles: <em>MoS</em><sub>2</sub> − <em>GO</em>, with <em>Methanol</em> serving as the original liquid is calculated. PDEs can be changed into ordinary differential equations with the help of similarity substitution. Which are nonlinear, and the bvp4c technique is used to numerically simplify it. The results of this investigation indicate that the velocity profile of <em>GO</em>/<em>Methanol</em> composite nanofluid increases more than that of <em>MoS</em><sub>2</sub> − <em>GO</em>/<em>Methanol</em> through the increasing amount of Grashof number and Weissenberg parameter, even as the magnetic parameter and porosity impact have the opposite effect. On other hand, the chemical reaction and Schmidt number increase the rate of mass transfer for both nanofluids. The larger values of thermal radiation and Dufour effect enhance the thermal profile.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101294"},"PeriodicalIF":0.0,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Benjamin-Bhona-Mahony equation is a non-linear partial differential equation arising in the study of waves, oceanography, Plasma physics, and shallow water theory. In the present work, we looked at the approximate solution of non-linear Benjamin-Bona-Mahony (BBM) problem by the Optimal Homotopy Asymptotic Method with Daftardar Jeffery Polynomials (OHAM-DJ). The BBM result is compared to analytic evaluation, the Homotopy Perturbation Technique (HPM), the Adomian Decomposition Method (ADM), and the Optimal Homotopy Asymptotic Method (OHAM-DJ). Figures of precise versus approximate solutions are also created, and it is established that OHAM-DJ's solution is substantially closer to the approximative than the precise. Additionally, the outcome demonstrates the effectiveness, simplicity, ease of use, and explicitness of OAM-DJ and provides a good means of controlling the convergence of approximations.
{"title":"Application of optimal homotopy asymptotic method with use of Daftardar Jeffery Polynomials to Benjamin-Bona-Mahony equation","authors":"Showkat Ahmad Lone , Rawan Bossly , M.M. Seada , Anwar Saeed","doi":"10.1016/j.padiff.2025.101282","DOIUrl":"10.1016/j.padiff.2025.101282","url":null,"abstract":"<div><div>The Benjamin-Bhona-Mahony equation is a non-linear partial differential equation arising in the study of waves, oceanography, Plasma physics, and shallow water theory. In the present work, we looked at the approximate solution of non-linear Benjamin-Bona-Mahony (BBM) problem by the Optimal Homotopy Asymptotic Method with Daftardar Jeffery Polynomials (OHAM-DJ). The BBM result is compared to analytic evaluation, the Homotopy Perturbation Technique (HPM), the Adomian Decomposition Method (ADM), and the Optimal Homotopy Asymptotic Method (OHAM-DJ). Figures of precise versus approximate solutions are also created, and it is established that OHAM-DJ's solution is substantially closer to the approximative than the precise. Additionally, the outcome demonstrates the effectiveness, simplicity, ease of use, and explicitness of OAM-DJ and provides a good means of controlling the convergence of approximations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101282"},"PeriodicalIF":0.0,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-22DOI: 10.1016/j.padiff.2025.101291
Pramod S , Sujatha N , Sreekala C. K , Hanumagowda B. N , Kiran S , Jagadish V. Tawade , Manish Gupta , Barno Abdullaeva , M. Ijaz Khan
This research paper comprehensively investigates magnetohydrodynamic free convection in a ferrofluid-filled rectangular cavity. The researchers designed a rectangular cavity where the left vertical wall maintains a warmer temperature than the right, while the horizontal walls (top and bottom) are adiabatic. A uniform magnetic field is imposed horizontally along the positive x-axis. The main objective is to analyse the impacts of various parameters, such as Hartmann number (0 ≤ Ha ≤ 60), Rayleigh number (103 ≤ Ra ≤ 106), and volume fraction (0 ≤ ϕ ≤ 0.04), on the heat transfer characteristics and fluid flow behavior within the enclosure. The governing equations are rigorously solved using the Galerkin finite element method. Quality plots like streamlines and isotherms and quantity plots like average Nusselt number (Nua) are presented to elucidate the underlying physics. The findings indicate that increasing Rayleigh numbers increases the convective flow, whereas increasing Hartmann numbers decreases the convective flow, promoting conduction as the primary mode of heat transfer. It is also notable that the inclusion of a magnetic field significantly alters the flow and temperature distributions, leading to a notable reduction in average Nusselt number. Furthermore, the incorporation of nanoparticles is found to intensify the heat transfer rates, with higher volume fractions yielding greater thermal performance. These findings offer significant implications for advancing thermal management, material processing techniques, and magnetohydrodynamic power generation, thereby providing innovative heat transfer solutions across diverse engineering applications.
{"title":"Magnetically driven free convection of nanofluids in rectangular cavities: A FEM approach","authors":"Pramod S , Sujatha N , Sreekala C. K , Hanumagowda B. N , Kiran S , Jagadish V. Tawade , Manish Gupta , Barno Abdullaeva , M. Ijaz Khan","doi":"10.1016/j.padiff.2025.101291","DOIUrl":"10.1016/j.padiff.2025.101291","url":null,"abstract":"<div><div>This research paper comprehensively investigates magnetohydrodynamic free convection in a ferrofluid-filled rectangular cavity. The researchers designed a rectangular cavity where the left vertical wall maintains a warmer temperature than the right, while the horizontal walls (top and bottom) are adiabatic. A uniform magnetic field is imposed horizontally along the positive <em>x-</em>axis. The main objective is to analyse the impacts of various parameters, such as Hartmann number (0 ≤ <em>Ha</em> ≤ 60), Rayleigh number (10<sup>3</sup> ≤ <em>Ra</em> ≤ 10<sup>6</sup>), and volume fraction (0 ≤ ϕ ≤ 0.04), on the heat transfer characteristics and fluid flow behavior within the enclosure. The governing equations are rigorously solved using the Galerkin finite element method. Quality plots like streamlines and isotherms and quantity plots like average Nusselt number (<em>Nu<sub>a</sub></em>) are presented to elucidate the underlying physics. The findings indicate that increasing Rayleigh numbers increases the convective flow, whereas increasing Hartmann numbers decreases the convective flow, promoting conduction as the primary mode of heat transfer. It is also notable that the inclusion of a magnetic field significantly alters the flow and temperature distributions, leading to a notable reduction in average Nusselt number. Furthermore, the incorporation of nanoparticles is found to intensify the heat transfer rates, with higher volume fractions yielding greater thermal performance. These findings offer significant implications for advancing thermal management, material processing techniques, and magnetohydrodynamic power generation, thereby providing innovative heat transfer solutions across diverse engineering applications.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101291"},"PeriodicalIF":0.0,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-21DOI: 10.1016/j.padiff.2025.101274
Sharanayya Swami , Ali B M Ali , Suresh Biradar , Jagadish V Tawade , M. Ijaz Khan , Nitiraj Kulkarni , Dilsora Abduvalieva , M. Waqas
This study investigates mixed convection magnetohydrodynamic (MHD) flow and heat transfer of a /water hybrid nanofluid over stretching and shrinking surfaces embedded in a porous medium, incorporating the simultaneous effects of suction/injection, thermal slip, viscous dissipation, Joule heating, and thermal radiation. The governing boundary layer equations were transformed using similarity variables and solved numerically with the MATLAB bvp4c solver, employing experimentally validated thermophysical property correlations. Parametric analysis reveals that suction enhances heat transfer by thinning the momentum and thermal boundary layers, while injection reduces it. Magnetic fields and higher nanoparticle loadings increase fluid temperature but reduce the Nusselt number. Thermal slip improves wall heat transfer, whereas viscous dissipation, Joule heating, and radiation diminish it by thickening the thermal layer. Higher Prandtl numbers yield thinner thermal boundary layers and greater heat transfer efficiency. The findings provide useful design insights for thermal systems employing hybrid nanofluids in porous and magnetically influenced environments.
{"title":"Thermal and flow characteristics of hybrid nanofluids in free-forced convection under suction/blowing effects","authors":"Sharanayya Swami , Ali B M Ali , Suresh Biradar , Jagadish V Tawade , M. Ijaz Khan , Nitiraj Kulkarni , Dilsora Abduvalieva , M. Waqas","doi":"10.1016/j.padiff.2025.101274","DOIUrl":"10.1016/j.padiff.2025.101274","url":null,"abstract":"<div><div>This study investigates mixed convection magnetohydrodynamic (MHD) flow and heat transfer of a <span><math><mrow><mi>A</mi><msub><mi>l</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub><mo>−</mo><mo>−</mo><mi>C</mi><mi>u</mi></mrow></math></span>/water hybrid nanofluid over stretching and shrinking surfaces embedded in a porous medium, incorporating the simultaneous effects of suction/injection, thermal slip, viscous dissipation, Joule heating, and thermal radiation. The governing boundary layer equations were transformed using similarity variables and solved numerically with the MATLAB <em>bvp4c</em> solver, employing experimentally validated thermophysical property correlations. Parametric analysis reveals that suction enhances heat transfer by thinning the momentum and thermal boundary layers, while injection reduces it. Magnetic fields and higher nanoparticle loadings increase fluid temperature but reduce the Nusselt number. Thermal slip improves wall heat transfer, whereas viscous dissipation, Joule heating, and radiation diminish it by thickening the thermal layer. Higher Prandtl numbers yield thinner thermal boundary layers and greater heat transfer efficiency. The findings provide useful design insights for thermal systems employing hybrid nanofluids in porous and magnetically influenced environments.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101274"},"PeriodicalIF":0.0,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-21DOI: 10.1016/j.padiff.2025.101279
S.R. Mishra , Rupa Baithalu , P.K. Pattnaik , Subhajit Panda
The present analysis pursuit of optimizing heat transfer rate by employing a Box-Behnken machine learning design of aluminium alloy aqueous hybrid nanomaterial over a Riga Wedge surface. The interaction of alloy nanoparticles AA7072 and AA7075 are taking part in pursuing the heat flow rate of the hybrid nanomaterial in association with the radiating heat and substantial heat supplier/absorption. The heightened thermal conductivity and stability of the hybrid nanomaterial offered by the inclusion of both alloy nanoparticles address the limitations of conventional fluid. The proposed mathematical framework is converted into dimensionless form by the adequate similarity function and a computational technique is adopted for the solution of the problem. Further, a robust statistical approach such as Box-Behnken design is utilized to evaluate systematically the influence of various factors such as particle concentrations, and radiating heat. By the use of machine learning techniques, it predicts the optimal conditions for heat transfer rate. Sensitivity evaluation is conducted to assess the influence of each of the terms on the thermal performance. This ongoing investigation is utilized in several applications spanning industries for efficient thermal management including aerospace, electronics, etc. However, the important outcomes of the study are; the thinner in momentum bounding surface is observed for the enhanced Hartmann number which enhances the profile in magnitude. Further, the inclusion of heat source overshoots the heat transport properties.
{"title":"Box-Behnken design for the machine learning prediction of heat flow rate on the flow of Aluminium alloy aqueous hybrid nanomaterial over wedged Riga surface: Sensitivity analysis","authors":"S.R. Mishra , Rupa Baithalu , P.K. Pattnaik , Subhajit Panda","doi":"10.1016/j.padiff.2025.101279","DOIUrl":"10.1016/j.padiff.2025.101279","url":null,"abstract":"<div><div>The present analysis pursuit of optimizing heat transfer rate by employing a Box-Behnken machine learning design of aluminium alloy aqueous hybrid nanomaterial over a Riga Wedge surface. The interaction of alloy nanoparticles <em>AA7072</em> and <em>AA7075</em> are taking part in pursuing the heat flow rate of the hybrid nanomaterial in association with the radiating heat and substantial heat supplier/absorption. The heightened thermal conductivity and stability of the hybrid nanomaterial offered by the inclusion of both alloy nanoparticles address the limitations of conventional fluid. The proposed mathematical framework is converted into dimensionless form by the adequate similarity function and a computational technique is adopted for the solution of the problem. Further, a robust statistical approach such as Box-Behnken design is utilized to evaluate systematically the influence of various factors such as particle concentrations, and radiating heat. By the use of machine learning techniques, it predicts the optimal conditions for heat transfer rate. Sensitivity evaluation is conducted to assess the influence of each of the terms on the thermal performance. This ongoing investigation is utilized in several applications spanning industries for efficient thermal management including aerospace, electronics, etc. However, the important outcomes of the study are; the thinner in momentum bounding surface is observed for the enhanced Hartmann number which enhances the profile in magnitude. Further, the inclusion of heat source overshoots the heat transport properties.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101279"},"PeriodicalIF":0.0,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144914035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-11DOI: 10.1016/j.padiff.2025.101270
Youness Saoudi , Khalid Jeaab , Hanaa Hachimi
This paper examines and applies the Monte Carlo approach to the two-dimensional Black–Scholes partial differential equation, including the Cholesky decomposition to generate correlated Brownian motions to evaluate options on two underlying assets. This study focuses on assessing the performance and risk management of investment portfolios that include these two assets, which are part of the NASDAQ 100 stock index and two active stocks of the S&P500 stock index, namely NVIDIA Corp, Tesla Inc, Apple Inc, and Microsoft Corp over one year from November 30, 2023, to November 30, 2024. The two-dimensional Black–Scholes model is chosen for its ability to capture complex market dynamics involving correlated assets. To optimize the valuation of the basket option (Call - Put), variance minimization techniques, namely control variate and stratified sampling methods, were used. The results highlight how these techniques accurately filter Brownian paths and clarify the impact of as set correlations on market behavior.
{"title":"Pricing basket options using Monte Carlo simulation employing Cholesky decomposition and variance reduction techniques under the 2D stochastic Black–Scholes equation","authors":"Youness Saoudi , Khalid Jeaab , Hanaa Hachimi","doi":"10.1016/j.padiff.2025.101270","DOIUrl":"10.1016/j.padiff.2025.101270","url":null,"abstract":"<div><div>This paper examines and applies the Monte Carlo approach to the two-dimensional Black–Scholes partial differential equation, including the Cholesky decomposition to generate correlated Brownian motions to evaluate options on two underlying assets. This study focuses on assessing the performance and risk management of investment portfolios that include these two assets, which are part of the NASDAQ 100 stock index and two active stocks of the S&P500 stock index, namely NVIDIA Corp, Tesla Inc, Apple Inc, and Microsoft Corp over one year from November 30, 2023, to November 30, 2024. The two-dimensional Black–Scholes model is chosen for its ability to capture complex market dynamics involving correlated assets. To optimize the valuation of the basket option (Call - Put), variance minimization techniques, namely control variate and stratified sampling methods, were used. The results highlight how these techniques accurately filter Brownian paths and clarify the impact of as set correlations on market behavior.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101270"},"PeriodicalIF":0.0,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144826864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study presents a comprehensive theoretical investigation into the influence of surface roughness, magnetohydrodynamics (MHD), and micropolar fluid dynamics on the squeeze film behavior between two wide, parallel rectangular plates. A modified Reynolds equation is derived by incorporating Eringen’s microcontinuum theory, Christensen’s stochastic surface roughness model, and classical hydrodynamic principles. The model accounts for the effects of a perpendicular magnetic field and longitudinal surface irregularities. Key performance parameters—namely pressure distribution, load-carrying capacity, and squeeze film duration—are obtained analytically and evaluated using dimensionless groups such as the Hartmann number, coupling number, fluid gap interaction number, and surface roughness parameter. The results demonstrate that incorporating micropolar fluid properties and MHD effects significantly enhances squeeze film performance compared to the Newtonian fluid case. Surface roughness is also found to play a beneficial role in improving load support and film retention. The findings offer valuable insights for designing advanced lubrication systems in engineering applications where microstructural effects and magnetic fields are present.
{"title":"Stochastic reynolds equation for magnetohydrodynamics micropolar fluid and surface roughness in squeeze-film lubrication characteristics of rough parallel rectangular plates","authors":"B.S. Asha , H.M. Shivakumar , B.N. Hanumagowda , Jagadish V. Tawade , Barno Abdullaeva , Manish Gupta , Murali Gundagani , Taoufik Saidani , Nadia Batool","doi":"10.1016/j.padiff.2025.101269","DOIUrl":"10.1016/j.padiff.2025.101269","url":null,"abstract":"<div><div>This study presents a comprehensive theoretical investigation into the influence of surface roughness, magnetohydrodynamics (MHD), and micropolar fluid dynamics on the squeeze film behavior between two wide, parallel rectangular plates. A modified Reynolds equation is derived by incorporating Eringen’s microcontinuum theory, Christensen’s stochastic surface roughness model, and classical hydrodynamic principles. The model accounts for the effects of a perpendicular magnetic field and longitudinal surface irregularities. Key performance parameters—namely pressure distribution, load-carrying capacity, and squeeze film duration—are obtained analytically and evaluated using dimensionless groups such as the Hartmann number, coupling number, fluid gap interaction number, and surface roughness parameter. The results demonstrate that incorporating micropolar fluid properties and MHD effects significantly enhances squeeze film performance compared to the Newtonian fluid case. Surface roughness is also found to play a beneficial role in improving load support and film retention. The findings offer valuable insights for designing advanced lubrication systems in engineering applications where microstructural effects and magnetic fields are present.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101269"},"PeriodicalIF":0.0,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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