Search Results (528)

High-stress soft rock roadways in deep underground engineering often exhibit significant time-dependent deformation due to strong rheological behavior of surrounding rock. To investigate the deformation characteristics and support effect, a composite viscoelastic constitutive model considering anchored and unanchored rock zones is established based on the Maxwell rheological framework. The equivalent stiffness contribution of rock bolts is incorporated to characterize the interaction between support and surrounding rock. Analytical solutions of radial displacement and creep rate are derived using viscoelastic theory and Laplace transform methods. The effects of bolt spacing, bolt length, and burial depth on the rheological response are analyzed. Numerical simulations based on FLAC3D creep analysis and field monitoring data are used to verify the proposed model. Results show that decreasing bolt spacing effectively reduces long-term deformation, while bolt length has a diminishing effect beyond a critical anchorage length. Increasing burial depth significantly increases creep rate and total deformation. The numerical results agree well with theoretical predictions (R² ≈ 0.985), and field measurements show a relative error within 10%. The proposed model effectively describes the long-term deformation trend of high-stress soft rock roadways and provides a theoretical reference for support design under similar conditions. Full article

This paper develops a parameterized generalized transform framework for nonlinear differential models. The method combines a generalized Laplace-type transform, Adomian decomposition, Chebyshev–Padé rational reconstruction, and a $\mu$-scaled generalized transform to construct admissible semi-analytical approximations. The framework treats the transform geometry as part of the approximation process, allowing the transformed domain to be adjusted while preserving an explicit analytical structure. The theoretical analysis establishes admissibility conditions, existence of admissible minimizers, characterization of the admissible region for the parametric kernel, interior optimality conditions, inverse and residue inversion formulas, and fixed-point consistency with a first-order truncation estimate. The method is illustrated on a logistic–Allee tumor-growth model using experimental data. The resulting compact representations remain real-valued and admissible on the full data interval and produce errors comparable to standard numerical reference solutions. Full article

To address the complex pressure-response mechanisms and difficulties in quantitatively characterizing dynamic reservoir properties during CO₂ geological storage in tight oil reservoirs, this work develops a dual-region composite seepage model coupling reservoir heterogeneity and CO₂-induced fluid property variation. The reservoir is divided into a near-well CO₂-stimulated zone and a far-field unstimulated zone. Combining the Laplace transform and the Stehfest368 numerical inversion method, we derive the analytical solutions of the bottom-hole pressure (BHP) and its derivative, and we establish a complete transient BHP monitoring and parameter inversion framework. The pressure-derivative curves are divided into five typical flow stages: wellbore storage, skin transition, inner-region radial flow, inter-region transition and outer-region radial flow. The key parameters, including wellbore storage coefficient, skin factor, mobility ratio, storativity ratio and CO₂ swept radius, can be accurately inverted via the BHP data analysis, which quantitatively characterizes flow capacity evolution, stimulated region scale and fluid flow patterns after CO₂ injection. The field application on two production wells in H138 block verifies the reliability of the proposed method. Further numerical simulation validation, measurement error sensitivity analysis and cross-verification of reservoir parameters are supplemented to prove the robustness and the applicability of the model. This study provides solid theoretical and technical support for on-site pressure monitoring, storage performance evaluation and operation optimization of CO₂ geological storage in tight reservoirs, and it also offers a reference for long-term storage security and storage capacity assessment. Full article

Leakage-induced transients in natural gas transmission pipelines can significantly affect operational safety and emergency response. This study develops a physics-based analytical framework for predicting transient pressure evolution, leakage dynamics, and emergency valve response in high-pressure gas pipelines while deriving a closed-form criterion for optimal valve spacing. The governing equations of compressible gas flow are reduced to a diffusion-type model incorporating acoustic wave propagation and frictional attenuation. A dynamic Robin-type boundary condition is introduced to describe valve–pipeline interactions, and closed-form analytical solutions are obtained using the Laplace transform method. An analytical leakage function and an explicit valve spacing criterion are derived directly from the governing equations and boundary conditions. Parametric investigations under representative transmission pipeline operating conditions demonstrate that the optimal valve spacing depends systematically on attenuation characteristics, activation thresholds, and allowable response times. The analytical solution further predicts a narrow quasi-invariant valve activation interval of approximately 112–116 s, which is theoretically explained through the dominant acoustic–diffusive balance of the proposed model. Verification against an independent finite difference solution shows excellent agreement, with the maximum relative deviation remaining below 1%, thereby confirming the accuracy and numerical consistency of the analytical formulation. The proposed framework provides a physically interpretable and computationally efficient tool for leakage assessment, emergency valve design, and safety-oriented analysis of conventional natural gas transmission pipelines. Full article

This study develops a mathematical model for non-Darcian flow toward a fully penetrating pumping well in a confined aquifer, explicitly incorporating both well skin effects and non-Darcian flow behavior, which are conventionally neglected in classical models. A two-zone radial flow model consisting of a skin zone and a background region is established to account for hydraulic property differences caused by well construction. The Izbash equation is adopted to describe the nonlinear velocity-gradient relationship, and the transformed differential quadrature method (TDQM) is employed for the efficient solution. By combining the Laplace transform, differential quadrature discretization, and Stehfest numerical inversion, transient drawdown responses are obtained. The model is verified against benchmark solutions and field pumping-test data, showing good agreement. Parametric analyses reveal that (1) increasing the non-Darcian parameter intensifies near-well flow resistance, producing a steeper and more localized drawdown cone; (2) a larger skin factor (improved near-well hydraulic conductivity) significantly reduces drawdown and enhances well efficiency; and (3) increasing skin thickness primarily improves near-field hydraulic response with limited far-field influence. The proposed framework provides an effective tool for analyzing nonlinear pumping behavior in radially heterogeneous aquifers. Full article

The manuscript contains the new scientific results of theoretical modeling of longitudinal flow dynamics (creeping) of a viscoelastic fluid governed by a fractional-type rheological Maxwell model material within a pipe of variable cross-section. Structurally, the paper utilizes a fractional-order differential operator defined on the interval 0 < α ≤ 1 to form a differential constitutive relationship between normal stress and axial dilatation, which is subsequently combined with D’Alembert’s dynamic equilibrium principles to form a governing fractional-order partial differential equation (PDE). Then the Bernoulli method of particular integrals for the separation of variables is applied to decompose the continuous field model into spatial eigen-amplitude ordinary differential equations (ODEs) and temporal fractional-order evolutionary ODEs, which are then solved analytically using series expansions of Laplace transforms and inverse Laplace transforms to yield three-dimensional parametric surfaces representing normal stress relaxation. The scientific findings indicate that normal stress asymptotically relaxes to zero under constant axial dilatation over time, showing a highly nonlinear dependence on the fractional order α. Full article

This paper is devoted to the construction and analysis of solution operators for a broad class of fractional-order systems. Both coupled systems with a memory-decoupled structure and fully coupled systems are considered. Using Laplace transform techniques and matrix-valued operator methods, explicit representations of the associated operator families are derived. The developed framework extends classical fractional resolvent theory to distributed-order and fully coupled systems, highlighting the role of coupling in shaping the structure of solution operators. These operators provide a natural setting for the fractional Duhamel principle and thus play a central role in the analysis of nonhomogeneous problems. Finally, several examples are presented to illustrate the theory and demonstrate the construction of solution operators for representative distributed-order and fully coupled systems. Full article

This study presents an analytical model for the long-term bending behavior of simply supported laminated glass (LG) plates with temperature-dependent viscoelastic interlayers. The glass layers are described based on three-dimensional elasticity theory, and the governing stress and displacement equations are formulated using the state-space method. The polymer interlayer is characterized by the generalized Maxwell model and the Williams–Landel–Ferry equation, while its time-dependent response is described through the Boltzmann convolution principle. By combining double Fourier series expansions with the Laplace-transform technique, analytical solutions for the stresses and displacements of multilayer LG plates are derived. The comparison shows that Kirchhoff–Love plate theory gives results close to the present solution for relatively thin LG plates, whereas the discrepancy becomes increasingly pronounced as the plate thickness increases. The finite element results agree well with those obtained from the proposed model; however, for the representative benchmark case, the present solution is approximately 1.13 × 10³ times faster than the FE simulation, and its memory usage is only about 10.88% of that required by the FE model. Parametric studies further reveal the effects of temperature, interlayer thickness, interlayer material, number of glass layers, and aspect ratio on the stress redistribution and deflection development of LG plates. Full article

In this work, we solve fractional Burgers equations by using the new natural generalized Laplace transform (NGLT) and double natural generalized Laplace transform (DNGLT) methods with the variation iteration method. First, we present the basic definitions of natural transforms, the generalized Laplace transform, and Caputo fractional derivatives, which provide the theoretical basis of this work. This work is mainly concerned with the natural generalized Laplace variational iteration method (NGLTVIM), which is a new approach for the solution of conventional problems. The stability and convergence of the proposed method are discussed in detail to prove its reliability and effectiveness. The efficiency of the method for finding solutions to one-dimensional and singular fractional coupled Burgers equations is illustrated by several numerical examples. The results demonstrate that NGLTVIM can be successfully applied to solving various problems of mathematical physics. Full article

This paper adapts a semi-analytical framework the Laplace-Residual Power Series Method (LRPSM) to solve the time-fractional Allen–Cahn equation under the Caputo derivative. While the classical Allen–Cahn model successfully describes phase separation, its fractional counterpart is essential for capturing sub-diffusive memory effects in complex heterogeneous materials. However, the interplay between the non-local fractional temporal operator and the cubic nonlinearity of the bistable double-well potential creates significant computational bottlenecks for conventional time-domain series solvers. The proposed approach projects the governing fractional partial differential equation into the Laplace domain, systematically replacing the computation of iterative fractional derivatives with the algebraic evaluation of asymptotic limits at infinity. Furthermore, the nonlinear cubic interactions are managed through Laplace-space convolution theorems. The structural convergence of this approach is evaluated against multi-scenario one-dimensional phase transitions. Graphical analyses, featuring 2D profile trajectories and 3D spatiotemporal surface mappings, visually illustrate the retarded interfacial propagation driven by fractional memory. Ultimately, this study presents the LRPSM as an applicable, continuous mathematical tool for approximating anomalous diffusion in the specific phase-field dynamics evaluated herein. Full article

In this study, a comprehensive stochastic and fractional-order modeling framework is developed to investigate the dynamic behavior of a shunt DC motor under random disturbances and memory effects. The motor dynamics are formulated as a system of stochastic differential equations incorporating Gaussian noise to represent uncertainties in the electrical and mechanical subsystems. The existence, stochastic ultimate boundedness, stationary distribution, and ergodic properties of the proposed model are established. To further enhance modeling capabilities, a modified Atangana–Baleanu–Caputo (mABC) fractional operator is introduced, enabling the incorporation of nonlocal memory effects inherent in electromechanical systems. The series solution is derived using the Laplace transform and the Adomian decomposition method to handle nonlinearities. Qualitative analysis of the solution is performed through fixed-point theory, while stability assessments utilize the T-Picard method. The results of the numerical simulation indicate that the stochastic model exhibits limited variability around the operating regimes, whereas the fractional-order representation is more effective at smoothing transient responses and limiting oscillatory behavior. The study proposes a realistic and adaptable method to analyze the dynamics of shunt DC motors with uncertainty and also presents useful information for the design and control of electromechanical systems. Full article

Aircraft targets in SAR imagery often exhibit discrete scattering characteristics, significant variations in pose and scale, strong speckle noise in background clutter, and complex background interference, which jointly hinder stable structural feature extraction and accurate target localization. Existing detectors for SAR aircraft recognition primarily rely on bounding-box regression and classification; they do not completely exploit target structural cues, spatial attention, and frequency-domain information. To address these limitations, we propose a collaborative detection framework that integrates an uncertainty-aware keypoint-driven module (UAKM) with a fractional Fourier convolution backbone (S-FRConv). UAKM introduces a center-keypoint regression branch that jointly predicts keypoint coordinates and Laplacian scale parameters and employs a 2D Laplace negative log-likelihood loss to estimate uncertainty. The derived dense uncertainty heatmap is then used as spatial attention weights to guide distribution-based regression and multi-scale feature re-weighting, without requiring any additional annotations. S-FRConv embeds the Fractional Fourier Transform into shallow backbone layers and C2f modules, enabling joint spatial–spectral feature modeling that suppresses speckle noise and enhances edge and orientation representations. Experiments on the public SAR-AIRcraft-1.0 dataset demonstrate that the proposed method systematically improves the detection performance. For the Nano model, the overall mAP50 increases from 0.810 to 0.867, and the mAP 50:95 improves from 0.637 to 0.655 compared with the baseline, corresponding to gains of 5.7 and 1.8 percentage points, respectively. These results validate the effectiveness and generalization potential of combining uncertainty-driven spatial attention with fractional spectral feature enhancement for SAR aircraft target detection. Full article

This study investigates a 2D fractional order generalized thermoelastic problem in a homogeneous and isotropic thermoelastic hollow sphere. The sphere is exposed to a decaying heat source, and the governing equations are derived using a refined fractional-order Lord–Shulman (LS) model of generalized thermoelasticity. The Laplace transform technique is used to convert time-dependent PDEs into simpler ODEs in the Laplace domain. Its numerical inversion method is used to revert to the time domain. Numerical simulations are carried out to investigate the distributions of temperature, displacement, and stress fields within the hollow sphere. The obtained results reveal that both the fractional-order parameter and the variable thermal conductivity strongly affect the thermoelastic response, particularly the propagation characteristics of thermal waves, stress intensity, and relaxation behavior. In addition, the curvature of the hollow geometry plays an important role in modifying the radial and circumferential stress distributions and their attenuation throughout the medium. Full article

One of the interesting properties of the two-dimensional potential problem is that solutions of the Laplace equation remain solutions of the Laplace equation when subjected to a conformal transformation. While this result was established long ago, the consequences within computational mechanics have not been fully explored. Here, we demonstrate for the first time that in a finite element formulation of the potential problem, the stiffness matrix remains invariant under a conformal mapping. This holds even when the mapped domain extends to infinity. Furthermore, by introducing the local flux in a finite element method, we find that the fundamental boundary eigensolutions also are invariant under a conformal mapping transformation by using a special weight function related to the Jacobian of the transformation. A series of computational examples is presented to emphasize the most important characteristics of conformal mappings within the finite element method and to demonstrate convergence of the computational results. Included are two exterior problems, the latter of which permits determination of the tearing stress intensity factor for a crack in an infinite plate. Full article

We develop a closed-form analysis of the joint distribution for cumulative shock reliability systems with phase-type inter-shock times. The analytical literature on shock-driven reliability has hitherto been split into two largely separate traditions: scalar fluctuation theory, which delivers closed-form joint distributions of pre-failure and failure-time observables but cannot accommodate matrix phase structure; and matrix-analytic methods, which handle phase-type dynamics naturally but focus on stationary indicators rather than first-passage distributions. We bridge these traditions by introducing a matrix-valued reliability functional ${\mathbf{\Phi }}_{\nu }(\xi ,u,v,\vartheta ,\theta )$ that encodes the joint distribution of the failure index, pre-failure damage and time, failure-time damage and time, and the operational phase at the moment of failure. We derive ${\mathbf{\Phi }}_{\nu }$ in closed form via Sherman–Morrison reduction of the matrix Laplace–Stieltjes transform together with the Dshalalow $\mathfrak{D}$-operator, and establish a span-reduction theorem showing that ${\mathbf{\Phi }}_{\nu }$ lies in a three-dimensional matrix subspace generated by the identity and two matrix LSTs. The functional simultaneously generalizes the scalar fluctuation functional of Dshalalow and White and the phase-tagged first excess functional of Tadj, recovering both as projections. We extract twelve closed-form reliability indices, including the reliability function, mean time to failure, mean overshoot, joint pre-failure and failure transforms, and, new to the cumulative shock literature, the phase distribution at failure and the phase-resolved failure-time distribution. Two structural identities of Wald type emerge as corollaries. The framework reduces to elementary arithmetic for rational model primitives and is verified against $2\times {10}^5$ Monte Carlo trajectories in a worked example. Full article