Underground coal mines are widely distributed across China, and underground mining is highly concealed. The rapid and accurate identification of the spatial distribution of coal mining subsidence over large areas is of significant importance for the reuse of land resources in mining areas and the detection of illegal mining activities. The traditional method of monitoring subsidence basins has limitations in terms of monitoring range and timeliness. The development of synthetic aperture radar (InSAR) technology has provided a valuable tool for monitoring mining subsidence areas. However, this method faces challenges in quickly and effectively monitoring subsidence basins using wide-swath SAR images. With the rapid development of deep learning and computer vision technologies, leveraging advanced deep learning models in combination with InSAR technology has become a crucial research direction to enhance the monitoring efficiency of surface subsidence in mining areas. Therefore, this paper proposes a new method for the rapid identification of mining subsidence basins in mining areas, which integrates Deformable Detection Transformer (Deformable DETR) and InSAR technology. First, the real deformation sample set of the mining area, obtained through interference processing, is combined with simulated deformation samples generated using the dynamic probability integral method, elastic transformation, and various noise synthesis techniques to construct a mixed InSAR sample set. This mixed sample set is then used to train the Deformable DETR model and compared with common deep learning methods. The experimental results show that the monitoring accuracy is significantly improved, with the model achieving a Precision of 0.926, Recall of 0.886, F1-score of 0.905, and mean Intersection over Union (mIoU) of 0.828. The detection model was applied to monitor the dynamically updated mining subsidence in the Huainan mining area from 2023 to 2024, detecting 402 subsidence basins. Further training demonstrates that the model exhibits strong robustness. Therefore, this method reduces the construction cost of the target detection training set and holds significant application potential for monitoring geological disasters in large-scale mining areas.

This work introduces a modern computational approach that blends classical integral transforms with artificial intelligence (AI) to solve nonlinear differential equations commonly seen in engineering.Traditional transforms-such as Laplace, Fourier, and Mellin-are powerful, but they often struggle with nonlinear or irregular systems.To address these limitations, we propose an AI-enhanced transform method that automatically learns and adjusts transformation parameters, improving accuracy and stability.Using MATLAB and Python simulations, the method is tested on heat transfer, structural vibration, and nonlinear fluid flow problems.Results show faster convergence, reduced numerical error, and broader applicability when compared to conventional transform techniques.

Analysis of binding kinetics and mass transport in SPR-based biosensor using the Generalized Integral Transform Technique and the Markov Chain Monte Carlo Method.

This study introduces a novel hyperbolic thermoelastic model tailored for elastic semiconducting materials, marking a significant leap in the analysis of thermal and mechanical behavior under photothermal excitation. The model’s novelty arises from its incorporation of nonsimple characteristics, where heat sources are defined as a linear function of temperature within the semiconductor medium. By employing the dual-phase lag (DPL) theory, the model emphasizes the temperature-disparity parameter, delivering a more precise depiction of transient heat conduction behavior at the microscale. This approach addresses gaps in existing models and sheds light on intricate heat transfer dynamics. A key contribution is the application of integral transformation techniques to solve equations based on the two-temperature theory. Analytical solutions are derived for displacement, carrier density, thermal stress, and temperature fields in a thin, two-dimensional, circular semiconductor plate subjected to ramp-type sectional heating. These physical fields, influenced by mechanical forces and thermal loads on the plate’s free surface, underscore the coupled interaction between photothermal and mechanical effects. The study also introduces a methodological innovation by utilizing numerical approximation techniques for the inverse Laplace transform, enabling seamless analysis in the time space domain. The results, presented graphically, reveal the intricate coupling of physical phenomena and provide profound insights into thermo-photoelastic systems. This work has substantial implications for optoelectronics, material science, and nanoscale systems. It not only advances our understanding of semiconducting materials but also lays the groundwork for innovations in thermal management, device optimization, and multiphysics simulations, bridging theoretical models with real-world applications.

This article introduces a novel nonsimple hygrothermal model incorporating two-phase delays, higher-order time derivatives, and two distinct temperatures – thermodynamic and conductive – through the unification of multi-kernel fractional operators. Specifically, the study employs the Rabotnov fractional-exponential function and the two-parameter Goufo-Caputo fractional operator to analyze thermal conduction and moisture diffusion in materials. The model examines the effects of microscopic structures on a two-temperature (2TT) hygrothermoelastic cylinder subjected to heat and moisture sources, which are generated based on the linear functions of temperature and moisture. By applying modified Fourier and Fick’s laws, and considering the energy-balance equation and rate of moisture generation, the study derives partial differential equations (PDEs) with linear coupling and higher-order time derivatives. An exact solution for the modified system of linearly coupled equations, subjected to sectional hygrothermal loads, is obtained using the integral transformation technique. The transition from the Laplace domain back to the time domain is performed using Zakian’s technique algorithm. This hygrothermal model with multi-kernel derivatives and two-phase lags has wide applications in microelectronics, nanotechnology, aerospace, biomedical engineering, civil engineering, energy systems, and the textile industry. It provides critical insights into heat and moisture transport behavior in various materials and devices. The research aims to offer future researchers a comprehensive understanding of three-phase lags hygrothermoelasticity, including a detailed investigation of higher-order phase delays.

Abstract This work presents an explicit methodology for estimating source terms in the diffusion equation based on the classical integral transform technique (CITT), employing eigenfunction expansions. This work extends the application of a recently developed methodology to more general three-dimensional cases. Given the high computational costs associated with these calculations, the study introduces essential enhancements for solving the related inverse problems more efficiently and proposes an automatic criterion for selecting the truncation order in the inverse problem solution, aiming at regularization based on the discrepancy principle. The results, based on simulated measurements for transient three-dimensional diffusion problems, demonstrate the effective improvements achieved, yielding consistently good results across the tested scenarios, including varying noise levels and different functional forms of the sought source terms. Accurate source term detection via an explicit computationally fast approach. Three-dimensional transient source terms are successfully handled. Selection of expansion truncation order for regularization is handled automatically. Computational efficiency is achieved through automatic truncation.

In this paper, the frictionless contact problem of layers on a Pasternak foundation is addressed using various methods, such as the analytical method, finite element method (FEM), and multilayer perceptron (MLP). The problem consists of two layers: The upper layer is homogeneous (HOM), while the lower layer is functionally graded (FG). The upper layer is loaded by a circular rigid block that applies a concentrated force, and Poisson’s ratios of the layers are kept constant. In the solution, the weights of both layers are neglected, and stress due to pressure is considered. First, the problem is solved analytically using the theory of elasticity and integral transformation techniques. In this method, the equations governing the stress and displacement components of the layers are transformed into a system of two singular integral equations involving unknown contact pressures and contact lengths using Fourier transform techniques and boundary conditions. The integral equations are solved numerically using the Gauss–Chebyshev integration formula. Then, the finite element solution of the problem was performed using the ANSYS package program, which is based on the finite element method. Finally, the problem was solved with a multilayer perceptron (MLP), an artificial neural network for different problem parameters. The results obtained with all three methods were compared and interpreted. It is clear from the results that the contact pressure and contact length vary depending on various parameters such as block radius, stiffness parameter, shear modulus ratios, and Pasternak soil parameters.

With the advent of the next generation of astrophysics experiments, the volume of data available to researchers will be greater than ever. As these projects will significantly drive down statistical uncertainties in measurements, it is crucial to develop novel tools to assess the ability of our models to fit these data within the specified errors. We introduce to astronomy the Leave One Out-Probability Integral Transform (LOO-PIT) technique. This first estimates the LOO posterior predictive distributions based on the model and likelihood distribution specified, then evaluates the quality of the match between the model and data by applying the PIT to each estimated distribution and data point, outputting a LOO-PIT distribution. Deviations between this output distribution and that expected can be characterised visually and with a standard Kolmogorov-Smirnov distribution test. We compare LOO-PIT and the more common χ 2 test using both a simplified model and a more realistic astrophysics problem, where we consider fitting Baryon Acoustic Oscillations in galaxy survey data with contamination from emission line interlopers. LOO-PIT and χ 2 tend to find different signals from the contaminants, and using these tests in conjunction increases the statistical power compared to using either test alone. We also show that LOO-PIT outperforms χ 2 in certain realistic test cases.

Nonlinear diffusion equations (NDEs) are fundamental mathematical models describing a vast array of phenomena across science, engineering, and biology. Due to their inherent nonlinearities, obtaining exact or even approximate solutions for these equations poses significant challenges. This paper provides a comprehensive review of various established and emerging methodologies employed to solve NDEs, drawing insights from both analytical and numerical approaches. We explore methods such as the Differential Transform Method (DTM), Generalized Integral Transform Technique (GITT), Lie Symmetry Method, and Residual Power Series Method (RPSM) for analytical and semi-analytical solutions. For numerical approaches, we delve into the Differential Quadrature Method (DQM), Finite Difference Method (FDM), Finite Element Method (FEM), Collocation Methods, and the Method of Lines. The review highlights the applicability of these methods to diverse NDE types, including those with reaction terms, convection, and delays, emphasizing their strengths, limitations, and the critical importance of error analysis and stability considerations.

The process of aquifer remediation extends with the growing dependence on groundwater.Mathematical model of solute transport in porous media is important tool used to characterise the extent of approximating the shape, size and position of a contaminant.In the present study, an unsteady solute transport model advection-diffusion equation (ADE) is taken and analytical solutions were obtained by using Laplace integral transformation technique (LITT).The concentration is predicted in presence and absence of source, i.e., firstly initially medium (aquifer/air) is not supposed to be solute free, i.e., initially domain is already polluted/contaminated and secondly the medium is clean, taking decay type exponential input at origin.The dependence of velocity on space variable is of linear non-homogeneous nature due to heterogeneity of the semi-infinite horizontal dispersion medium.The dispersivity is considered square of the velocity which represents the seasonal variation of the year in tropical regions.

This paper aims to derive the mathematical model of modified heat conduction by utilizing the Goufo-Caputo fractional operator in an infinite-length cylinder subjected to various time-dependent sectional heat supplies. As a limiting case, the two-parameter Goufo-Caputo fractional derivative can be converted into a fractional Atangana-Baleanu derivative. For the application of the derived model, the study material considered for investigation is presumed to be homogenous and isotropic, with surface pressure assumed to be uniform over the boundaries. An exact solution of the modified nonsimple heat conduction subjected to different sectional heat loads is considered, and a solution is obtained utilizing the integral transformation technique. The inverse transformation from the Laplace domain to the time domain is achieved by employing the Gaver-Stehfest algorithm. In this paper, the effects of temperature distribution play an essential role in predicting the behavior of nonlocal thermoelastic displacement and stress functions using the two-parameter Goufo-Caputo fractional operator. The stress theory model is derived from Eringen’s nonlocal continuum theory. The results have been computed numerically and illustrated graphically. The solution considers a special case where various sectional heat supplies affect the inner curved surface, examining their non-Fourier thermal behavior and the influence of nonlocal parameters. The parameters significantly impact transient thermoelastic responses, the result crucial for accurately predicting them in micro- and nanostructure design and processing.

When seawater streams around risers, it causes vortex-induced vibrations (VIV), which occur in two forms: in-line (IL) and cross-flow (CF). Accurate prediction of coupled IL and CF VIV behaviors is essential for designing risers. To investigate the VIV of marine risers used in deep-sea oil and gas transportation, this study analyzed the coupled CF and IL VIV characteristics of the riser with axially time-varying tension under the combined effects of internal flow and oceanic linear shear flow. The work established the vibration control equation for the riser considering internal flow velocity, axial top tension, and bending stiffness, which is based on Euler-Bernoulli beam theory. The double Van der Pol diffusion wake oscillator model was used to simulate the vortex-induced forces from the ocean currents, and the internal fluid was considered as a single-phase incompressible liquid. Using the Generalized Integral Transform Technique (GITT), the coupled system of nonlinear partial differential equations was further transformed into a system of nonlinear ordinary differential equations for numerical solution. A parametric study was conducted to analyze the impact of current velocity, internal flow velocity, and diffusion term on the VIV responses, including structural displacement, structural frequency, displacement envelope, and displacement evolution. Numerical results indicate that the vibration modes of the riser are influenced by both CF and IL directions, and the effect of IL can not be ignored. The diffusion term has a significant impact on the vibrations of the riser. The number of vibration modes of the riser is mainly influenced by the increasing current velocity, and for a given current velocity, the vibration of the riser becomes chaotic when the dimensionless internal fluid velocity increased within a certain range.

Comprehensive two-dimensional analytical modeling of groundwater levels in bi-directional sloping heterogeneous aquifers under variable recharge conditions

Three-dimensional solute transport in finite and curved porous media with surface input sources

Channel flow dynamics of fractional viscoelastic nanofluids in molybdenum disulphide grease: A case study

In this study, frictionless receding contact problem of two elastic layers which one is functionally graded material (FGM) resting on a Pasternak foundation is considered. The external load is applied to the homogeneous elastic layer by means of a circular rigid block and the functionally graded layer rests on a Pasternak foundation. The effect of gravity forces is neglected, and only compressive normal tractions can be transmitted through the interfaces. Displacement and stress expressions for the layers are obtained using the theory of elasticity and integral transformation technique. By applying the boundary conditions for the problem, reduced to two integral equations in which the contact stresses and contact lengths are unknown. The system of integral equations is numerically solved by making use of appropriate Gauss Chebyshev integration formulas. The equilibrium conditions are satisfied in the solution and the contact stresses and contact distances related to the problem are obtained for various dimensionless quantities.

The miniaturization of electronics, electrical, thermal, mechanical and optical devices and systems calls for increasing demand for efficient cooling systems with higher thermal efficiency. The use of passive mode of cooling using fins has provided unprecedented results. However, the previous transient analyses of the extended surfaces have been done without proper considerations of the imperfect contact between the fin base and the prime surface. Also, the tip of the passive device has been assumed to be adiabatic. However, the present article explores the significances of thermal contact resistance and diabatic tip on the transient thermal response of straight fin with temperature-dependent thermal conductivity and magnetic field under radiative-convective conditions. The nonlinear model is analyzed numerically using generalized Integral Transform Techniques and the numerical results are verified by the exact solution for the linear thermal model. The parametric explorations reveal that the adimensional local temperature in the conductive-radiative fin increases when the conductive-convective, conductive-radiative and magnetic field parameters increase. However, under the assumption of perfect thermal contact between the prime surface and the base of the fin, the adimensional temperature in the fin will decrease as the conductive-convective, conductive-radiative and magnetic field parameters increase. The fin temperature is significantly affected by the Biot numbers under the comparably low values of the conductive-convective, conductive-radiative, magnetic field and thermal conductivity parameters. The effects of the fin thermal conductivity parameter along the fin length depend on the respective values of thermal contact Biot number at the base of the fin and the end cooling Biot number at the tip of the fin. When the thermal conductivity parameter is amplified, the fin adimensional temperature increases when thermal contact Biot number at the base of the fin is zero and the end cooling Biot number at the tip of the fin is very large. This study will help in accurate analysis and design of heat sinks and passive devices for heat transfer enhancement for thermal and electronic systems.

The study investigates thermal interactions in a two-dimensional time fractional-order thermoelastic problem in a homogeneous, isotropic, and perfectly conducting thick annular disc subjected to a point impulsive sectional heat source. We utilize unconventional integral transformation techniques to study the thermoelastic response of a disc, in which an internal heat source is generated according to the linear function of the temperature and radiation-type boundary conditions. The time fractional-order thermoelastic theory is used to determine temperature, displacement, and stresses through a series of Bessel functions. Numerical calculations analyze fractional-order parameters on aluminum discs, incorporating time-based fractional derivatives into field equations for practical engineering scenarios, enhancing thermal properties analysis.

Thermal contact conductance (TCC) is a critical factor in various engineering applications involving heat transfer between solid surfaces. Accurate knowledge of TCC enables a more precise thermal system analysis, leading to improved efficiency, reduced energy consumption, and prevention of thermal damages. Moreover, TCC estimation can help to identify material discontinuities or failures. A recent tool for TCC estimation is the Reciprocity Functional Method (RFM) coupled with the Classical Integral Transform Technique (CITT). This method allows the solution of inverse boundary value problems without the need of iterative methods or intrusive measurements, making it valuable for nondestructive testing of interfacial flaws between solid materials. Furthermore, it enables the computation of TCCs using analytical expressions, resulting in a computationally fast procedure. The technique involves the solution of two auxiliary problems: one for the temperature discontinuity estimation, and the other for the interfacial heat flux estimation, both at the inaccessible interface between the two contacting materials. In this study, we applied the RFM and the CITT to estimate different types of TCCs, using a three-dimensional double-layer hollow cylinder geometry as a representative model, like double-layer pipelines used in the oil industry. Temperature measurements for solving the inverse problem were considered available on the outer surface of the pipe which, in the case of a real experiment, could be obtained via an infrared camera. The results demonstrated a good estimate for various analyzed test-cases, even when the measurements were contaminated with Gaussian noises.

The stabilization of groundwater resources in excellent quality is crucial for both the environment and human societies. To examine the contaminant concentration pattern of infinite and semi-infinite aquifers, mathematical models provide accurate descriptions. The two-dimensional model for a semi-infinite heterogeneous porous medium with temporally dependent and space-dependent (degenerate form) dispersion coefficients for longitudinal and transverse directions is derived in this study. The Laplace Integral Transform Techniques (LITT) is used to find analytical solutions. The dispersion coefficient is considered the square of the velocity which represents the seasonal variation of the year in coastal/tropical regions. To demonstrate the solutions, the findings are presented graphically. Figures are drawn for different times for a function and discussed in the result and discussion section. It is also concluded that a two-dimensional model is more useful than a one-dimensional model for assessing aquifer contamination.