Journal of Applied Mathematical Models in Engineering

Fractional-Order Mathematical Models for Vibration Analysis in Smart Structural Systems

T M Sathish Kumar, Shaik Sadulla — Tue, 02 Dec 2025 00:00:00 +0300

Adaptive intelligent and sensing structures are novel architecture of structures that comprise new breath in structural engineering and permit better performance, greater durability and a superior security in the transforming working conditions of the structure. Nonlocal, hereditary and memory-dependent behavior such as that observed when viscoelastic damping occurs, adaptive actuation and nonlinear stiffness responses are usually difficult to capture with standard vibration analysis using integer-order models alone. In order to defeat these inadequacies, the paper theorizes a holistic conceit of fractional-order mathematical modeling that will examine vibration of smart structural systems. It can be recognized that the methodology can extend the classical theory that investigated viscoelastic damping and energy dissipation to the level of the fractional-order by the application of the Caputo operator in the determination of governing equations. Beam-like structures are solved analytically, with beam-excitation under harmonic excitation, and computer codes under numerical simulation and employing finite element formulations which are combined with a fractional operator. A systematic comparison to the classical model reveals that the fractional-order model better captures resonance frequencies changes, amplitude decay and dynamical stability, over an excitation space. Two are provided, one piezoelectric embedded smart beam and an actuator system made of shape memory alloy(SMA). The model suggested in this paper suits the experimental modal data in both cases and can also predict the vibration response behavior which would be underestimated by integer-order models. Additionally, parametric study shows how the fractional order can influence the damping characteristics of the systems that can be incorporated in optimization problems of the design and active vibration suppression. The paper concludes that not only is the concept of the fractional-order modeling mathematically well-founded, but also practically significant to the development of applications in structural health-monitoring, aerospace engineering, and robotics/civil infrastructure. This contribution connects theoretical fractional calculus to the practice of engineering, such that fractional-order models become a potentially radical instrument to next-generation smart structural design and vibration control.

Advanced Numerical Techniques for Solving High-Dimensional Integral Equations in Environmental Engineering Applications

Charpe Prasanjeet Prabhakar, Gaurav Tamrakar — Tue, 02 Dec 2025 00:00:00 +0300

Applications in environmental engineering include pollutant dispersion, groundwater contamination and atmospheric transport which use high-dimensional integral equations. Their solutions are nonlinear, stochastic in variability, and the curse of dimensionality frequently makes their analysis solutions intractable. This paper explores modern numerical methods that are aimed at effectively solving such equations at both accuracy and scalability. Deterministic (such as Galerkin formulations, spectral decomposition, and quadrature-based discretization) are compared with stochastic (such as Monte Carlo (MC), quasi-Monte Carlo (QMC), and sparse grid methods). Hybrid machine learning-assisted solvers are also proposed to further improve performance to surrogate model and accelerate convergence. Case studies are concentrated on two important areas; the transport of groundwater contaminants and prediction of urban air quality. Findings indicate that the sparse grid and QMC techniques are much more efficient and accurate than conventional MC simulations with a potential to reduce the cost of computation by as much as 40 percent. Spectral techniques allow extremely high accuracy with smooth deterministic models at increased computational cost, and hybrid ML-assisted solvers can scale to dimensions of tens of thousands or more (that is, comparable limits) hence are applicable to real-time environmental monitoring. The results endorse the idea that the combination of the deterministic, stochastic, and hybrid strategies produces a powerful computational system to tackle the complicate environmental processes. The stated findings demonstrate the promise of complex numerical integration models in improving predictive performance, resource utilization, and real-time decision-making in environmental engineering problems.

Data-Driven Reduced-Order Modeling of Turbulent Flows: A Case Study in Aerospace Engineering

Moti Ranjan Tandi, Nisha Milind Shrirao — Tue, 02 Dec 2025 00:00:00 +0300

Turbulent flows have high dimensions of turbulence, nonlinearity and multiscale nature are some of the most challenging to model accurately in aerospace engineering. Conventional computational fluid dynamics (CFD) solutions, which are highly accurate, require many computational resources and, therefore, cannot be used in real time prediction, optimization, and control. Reduced-order modeling (ROM) is an attractive option because it attempts to evaluate the required flow physics in a smaller-dimensional subspace, and hence can provide significant economies of scale in computing without significant loss in predictive performance. In the current case study, different data-based ROM approaches are to be used to investigate the turbulent flow around a NACA 0012 airfoil at Reynolds number of 1 x 106 and subsonic Mach number. Three have been explored: (i) Proper Orthogonal Decomposition (POD) which is a leading energy bearing mode; (ii) Dynamic Mode Decomposition (DMD) which captures time-spatial flow dynamics and coherent structures; (iii) an autoencer-based neural ROM which utilizes deep learning to identify nonlinear latent representations of the flow field. Moreover, a hybrid architecture was constructed between POD mode extraction and autoencoder-based regression to trade-off between physics interpretability and machine learning adaptability. The results indicate that the hybrid model provided an optimal computation of 90 percent less than the conventional CFD with an error margin of less than 5 percent variation of the lift and drag coefficient. Compared analysis showed that POD and DMD are useful at coherent structure captivity of large scale but less effective at replication of broader turbulence, whilst the autoencoder-based model was more efficient in reconstruction of finer-scale details. The findings indicate the possible practical utility of data-driven ROMs in aerospace industry that may involve the optimization of aerodynamic design, digital twins, real-time flow regulation, and quantification of uncertainty. The present work proves that physics-based and machine learning methods are a promising route to effective and accurate modeling of the complex turbulent flows associated with aerospace systems.

Mathematical Modeling of Drug Diffusion in Bioengineered Scaffolds for Tissue Regeneration

K. Geetha, M. Karpagam — Tue, 02 Dec 2025 00:00:00 +0300

Localized and targeted controlled drug delivery using bioengineered scaffolds offers a promising concept in tissue engineering and regenerative medicine, in that, therapeutic molecules, including growth factors, proteins, and small-molecule drugs, can be released at the tissue-repair site on-command. The key to designing scaffolds is a clear comprehension of the processes underlying drug release, which can depend on the complicated relationship between scaffold porosity, degradation dynamics and drug-matrix binding phenomena. To overcome this issue, the current study constructs a detailed mathematical modeling framework that combines multi-scale diffusion equations, multi-scale porosity evolution driven by degradation, and nonlinear binding kinetics to determine reliably drug release of polymeric scaffolds. The governing equations are Fickian with time-dependent effective diffusivity to include effects due to the scaffold microarchitecture and degradation and binding terms modeling reversible polymer-drug interactions. Finite element methods (FEM) were applied to numerical simulations in COMSOL Multiphysics, and geometry of scaffolds were computed as porous cylindrical structures with sink boundary conditions which are physiologically relevant. The parametric analysis examined the effect of scaffold porosity, degradation rate, tortuosity, and binding constants on cumulative drug release during a 30-day cumulative drug release. Findings have revealed that increasing porosity contributes to a faster release rate with increase in effective diffusivity but the over-increase in porosity results in early burst release which causes loss of scaffold integrity. On the other hand, controlled degradation increased release time by progressively opening porosity without disrupting mechanical stability and nonlinear binding interaction dramatically decreased release time, allowing persistent therapeutic residence. Experimental datasets of literature on PLGA-based scaffolds were compared against model predictions and found to match well with a deviation of not more than 10 percent. Here, it is pointed out that mathematical modeling is an effective predictive method to design scaffolds with specific drug release kinetics, easier therapeutic approaches in tissue regeneration and future scaffold development in clinical translation.

Machine Learning-Augmented Partial Differential Equation Solvers for High-Fidelity Engineering Design Optimization

Haitham M. Snousi, Fateh A. Aleej — Tue, 02 Dec 2025 00:00:00 +0300

Solution of multiphysics problems in aerospace, energy and manufacturing systems involve engineering design optimization, where partial differential equations (PDEs) prevail. Nevertheless, the dimensionality of parameter spaces and repetitive calculations in optimization loops mean that the traditional solvers: finite element, finite difference, and spectral methods are computationally expensive. This paper presents a machine learning (ML)-enhanced solver of PDEs that can be used to optimize the design of engineering applications at high-fidelity. The framework is a combination of neural operator architecture, surrogate modeling, and physics-informed learning to improve solution efficiency without compromising accuracy. The algorithm combines PDE solvers at baseline to generate data with ML surrogates, which model solution operators and objective functions. Physics-informed loss is used to satisfy governing equations and adaptive sampling plans are used to improve performance of surrogates in important design regions. The approach is seen to be effective in benchmark case studies in structural mechanics, thermal conduction, and fluid dynamics. In all these domains, the ML-enhanced framework can reduce up to 65 percent of the computational time in comparison to traditional approaches, and the error rate always remains less than 2 percent. These findings indicate a promise of ML-augmented PDE solvers to greatly decrease design cycle times without fidelity loss. The proposed framework provides a way of next-generation automation in the design of engineering models; this is because it can provide scalable, multi-objective optimization to computationally intensive computational programs. Future developments will cover quantification of uncertainty, multi-scale modeling and large scale implementation in the distributed high-performance computing infrastructure.

Coupled Thermo-Fluid Models for Heat Transfer Optimization in Microelectronic Cooling Systems

O.J.M. Smith, K.N. Kantor — Tue, 02 Dec 2025 00:00:00 +0300

The ever-increasing miniaturization and scaling of performance of micro-electronic devices have resulted in unprecedented levels of heat flux, requiring innovative and dependable thermal management solutions. The traditional single-domain thermal models lack the ability to explain the intense interaction between fluid convection and solid conduction, and hence is not predictive of the next-generation cooling systems. This paper constructs a unified thermo-fluid modeling platform incorporating incompressible Navier Stokes equations, the transient heat conduction and heat transfer equations to represent the multi-physics interactions between solid and fluid interfaces. The discretized coupled system is solved with a hybrid finite element / finite volume method that allows both the complex geometry and nonlinear interactions between thermal and fluid forces to be effectively addressed. The framework is used on representative representative microelectronic cooling systems, such as, microchannel heat sinks, nanofluid-imbued channels, and phase-change-aided hybrid systems. Multi-objective optimization scheme is used to reduce maximum device temperature, thermal resistance and temperature non-uniformity and balance hydraulic performance. The simulation findings indicate that coupled modeling is more effective in the prediction of temperatures by greater than 12 percent relative to decoupled modeling models, whereas optimized designs will lead to a decrease in peak temperature of up to 15 percent and temperature evenness of as much as 22 percent. Moreover, phase-change-aided cooling is shown to be better at transient thermal control with time-varying loads, and nanofluid-enhanced channels provide a higher steady-state heat transfer rate. The suggested hybrid framework does not only promote mathematical modeling of thermo-fluid systems, but offers useful design guidelines to optimized cooling structures in high-power-density microelectronics, which is within the journal focus on mathematical modeling, computational methods and engineering applications.