Search Results (2,334)

The existence of fault zones in high-intensity earthquake areas has a serious impact on engineering structures, and the longitudinal response of tunnels crossing faults needs further in-depth research. To analyze the tangential contact effect between the surrounding rock and the tunnel lining, and the axial deformation characteristics of the tunnel structure, tangential foundation springs were introduced and a theoretical model for the longitudinal response of the tunnel under fault dislocation was established. Firstly, the tunnel was simplified as a finite-length beam. The normal and tangential springs were taken to represent the interaction between the soil and the lining. The fault’s free-field displacement was applied at the end of the normal foundation spring to simulate fault dislocation, and the differential equation for the longitudinal response of the tunnel structure was obtained. The analytical solution of the structural response was obtained using the Green’s function method. Then, the three-dimensional finite difference method was used to verify the effectiveness of the analytical model in this paper. The results show that the tangential contact effect between the surrounding rock and the lining has a significant impact on the longitudinal response of the tunnel structure. Ignoring this effect leads to an error of up to 35.33% in the peak value of the structural bending moment. Finally, the influences of the width of the fault zone, the soil stiffness of the fault zone, and the stiffness of the tunnel lining on the longitudinal response of the tunnel were explored. As the fault width increases, the internal force of the tunnel structure decreases. Increasing the lining concrete grade leads to an increase in the internal force of the structure. The increase in the elastic modulus of the surrounding rock in the fault area reduces the bending moment and shear force of the structure and increases the axial force. The research results can provide a theoretical basis for the anti-dislocation design of tunnels crossing faults. Full article

A rotating imperfect ring resonator of the gyroscope is modeled by a rotating thin ring with evenly distributed point masses. The free response of the rotating ring structure at constant speed is investigated, including the steady elastic deformation and wave response. The dynamic equations are formulated by using Hamilton’s principle in the ground-fixed coordinates. The coordinate transformation is applied to facilitate the solution of the steady deformation, and the displacements and tangential tension for the deformation are calculated by the perturbation method. Employing Galerkin’s method, the governing equation of the free vibration is casted in matrix differential operator form after the separation of the real and imaginary parts with the inextensional assumption. The natural frequencies are calculated through the eigenvalue analysis, and the numerical results are obtained. The effects of the point masses on the natural frequencies of the forward and backward traveling wave curves of different orders are discussed, especially on the measurement accuracy of gyroscopes for different cases. In the ground-fixed coordinates, the frequency splitting results in a crosspoint of the natural frequencies of the forward and backward traveling waves. The finite element method is applied to demonstrate the validity and accuracy of the model. Full article

Consider a class of coupled discrete-time Riccati equations arising from jump systems. To compute their solutions when systems reach a steady state, we propose an operator Newton method and correspondingly establish its quadratic convergence under suitable assumptions. The advantage of the proposed method lies in the fact that its subproblems are solved using the operator Smith method, which allows it to maintain quadratic convergence in both the inner and outer iterations. Moreover, it does not require the constant term matrix of the equation to be invertible, making it more broadly applicable than existing inverse-free iterative methods. For large-scale problems, we develop a low-rank variant by incorporating truncation and compression techniques into the operator Newton framework. A complexity analysis is also provided to assess its scalability. Numerical experiments demonstrate that the presented low-rank operator Newton method is highly effective in approximating solutions to large-scale structured coupled Riccati equations. Full article

The present paper proposes a three-dimensional (3D) spherical shell model for the magneto-electro-elastic (MEE) free vibration analysis of simply supported multilayered smart shells. A mixed curvilinear orthogonal reference system is used to write the unified 3D governing equations for cylinders, cylindrical panels and spherical shells. The closed-form solution of the problem is performed considering Navier harmonic forms in the in-plane directions and the exponential matrix method in the thickness direction. A layerwise approach is possible, considering the interlaminar continuity conditions for displacements, electric and magnetic potentials, transverse shear/normal stresses, transverse normal magnetic induction and transverse normal electric displacement. Some preliminary cases are proposed to validate the present 3D MEE free vibration model for several curvatures, materials, thickness values and vibration modes. Then, new benchmarks are proposed in order to discuss possible effects in multilayered MEE curved smart structures. In the new benchmarks, first, three circular frequencies for several half-wave number couples and for different thickness ratios are proposed. Thickness vibration modes are shown in terms of displacements, stresses, electric displacement and magnetic induction along the thickness direction. These new benchmarks are useful to understand the free vibration behavior of MEE curved smart structures, and they can be used as reference for researchers interested in the development of of 2D/3D MEE models. Full article

The equivalent source method (ESM) is a core algorithm in integrated radiation-propagation acoustic field modeling. However, in challenging marine environments, including deep-sea and polar regions, where sound speed profiles exhibit strong vertical gradients, the ESM must increase waveguide stratification to maintain accuracy. This causes computational costs to scale exponentially with the number of layers, compromising efficiency and limiting applicability. To address this, this paper proposes a modal equivalent source (MES) model employing normal modes as basis functions instead of free-field Green’s functions. This model constructs a set of normal mode bases using full-depth hydroacoustic parameters, incorporating water column characteristics into the basis functions to eliminate waveguide stratification. This significantly reduces the computational matrix size of the ESM and computes acoustic fields in range-dependent waveguides using a single set of normal modes, resolving the dual limitations of inadequate precision and low efficiency in such environments. Concurrently, for the construction of basis functions, this paper also proposes a fast computation method for eigenvalues and eigenmodes in waveguide contexts based on phase functions and difference equations. Furthermore, coupling the MES method with the Finite Element Method (FEM) enables integrated computation of underwater target radiation and propagation fields. Multiple simulations demonstrate close agreement between the proposed model and reference results (errors < 4 dB). Under equivalent accuracy requirements, the proposed model reduces computation time to less than 1/25 of traditional ESM, achieving significant efficiency gains. Additionally, sea trial verification confirms model effectiveness, with mean correlation coefficients exceeding 0.9 and mean errors below 5 dB against experimental data. Full article

This paper presents a three-dimensional (3D) free surface model to predict incompressible flow around a spur dike in a meandering channel bend, which is highly 3D due to the presence of curvature effects. The model solves the Reynolds-averaged Navier–Stokes (RANS) equations using an explicit projection method. The 3D grid system is built from a two-dimensional grid by adding dozens of horizontal layers in the vertical direction. Numerical simulations consider four test cases with different spur dike locations in the same meandering channel bend with the same Froude numbers as 0.22. Four turbulence models, the standard k-ε model, the k-ω model, the RNG k-ε model and a nonlinear k-ε model, are implemented in our three-dimensional free surface model. The performance of these turbulence models within the RANS framework is assessed. Comparisons between the model results and experimental data show that the nonlinear k-ε model behaves better than the three other models in general. Based on the results obtained by the nonlinear k-ε model, the highly 3D flow field downstream of the spur dike was revealed by presenting velocity vectors at representative cross-sections and streamlines at the surface and bottom layers. Meanwhile, the 3D characteristics of the downstream separation zone were also investigated. In addition, to highlight the advantage of the nonlinear turbulence model, comparisons of velocity vectors at representative cross-sections between the results obtained by the linear and nonlinear $k$-$\epsilon$ models are also presented. Full article

This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fiber optic communications, nonlinear optics, optical signal processing, and laser–tissue interactions in medical science. The nonlinear effects exhibited by the model—such as self-focusing, self-phase modulation, and wave mixing—are influenced by the combined impact of the cubic and quintic nonlinear terms. To explore the dynamics of this model, we apply a robust analytical technique known as the sub-ODE method, which reveals a diverse range of soliton structures and offers deep insight into laser pulse interactions. The investigation yields a rich set of explicit soliton solutions, including hyperbolic, rational, singular, bright, Jacobian elliptic, Weierstrass elliptic, and periodic solutions. These waveforms have significant real-world relevance: bright solitons are employed in fiber optic communications for distortion-free long-distance data transmission, while both bright and dark solitons are used in nonlinear optics to study light behavior in media with intensity-dependent refractive indices. Solitons also contribute to advancements in quantum technologies, precision measurement, and fiber laser systems, where hyperbolic and periodic solitons facilitate stable, high-intensity pulse generation. Additionally, in nonlinear acoustics, solitons describe wave propagation in media where amplitude influences wave speed. Overall, this work highlights the theoretical depth and practical utility of soliton dynamics in fractional nonlinear systems. Full article

We present a thermodynamically consistent energetic variational model for active nematics driven by ATP hydrolysis. Extending the classical Toner–Tu framework, we introduce a chemo-mechanical coupling mechanism in which the self-advection and polarization dynamics are modulated by the ATP hydrolysis rate. The model is derived using an energetic variational approach that integrates both chemical free energy and mechanical energy into a unified energy dissipation law. The reaction rate equation explicitly incorporates mechanical feedback, revealing how active transport and alignment interactions influence chemical fluxes and vice versa. This formulation not only preserves consistency with non-equilibrium thermodynamics but also provides a transparent pathway for modeling energy transduction in active systems. We also present numerical simulations demonstrating the positive energy transduction under a specific choice of model parameters. The new modeling framework offers new insights into energy transduction and regulation mechanisms in biologically related active systems. Full article

The time-domain electromagnetic method has been widely applied in mineral exploration, oil, and gas fields in recent years. However, its response characteristics remain unclear, and there is an urgent need to study the response characteristics of the borehole-surface transient electromagnetic(BSTEM) field. This study starts from the time-domain electric field diffusion equation and discretizes the calculation area in space using tetrahedral meshes. The Galerkin method is used to derive the finite element equation of the electric field, and the vector interpolation basis function is used to approximate the electric field in any arbitrary tetrahedral mesh in the free space, thus achieving the three-dimensional forward simulation of the BSTEM field based on the finite element method. Following validation of the numerical simulation method, we further analyze the electromagnetic field response excited by vertical line sources.. Through comparison, it is concluded that measuring the radial electric field is the most intuitive and effective layout method for BSTEM, with a focus on the propagation characteristics of the electromagnetic field in both low-resistance and high-resistance anomalies at different positions. Numerical simulations reveal that BSTEM demonstrates superior resolution capability for low-resistivity anomalies, while showing limited detectability for high-resistivity anomalies Numerical simulation results of BSTEM with realistic orebody models, the correctness of this rule is further verified. This has important implications for our understanding of the propagation laws of BSTEM as well as for subsequent data processing and interpretation. Full article

Functionally graded carbon nanotube reinforced composites (FG-CNTRCs) are a novel breed of polymer nanocomposite, in which the nonuniform distribution of the carbon nanotube (CNT) reinforcement is adopted to maximize the macro-mechanical performance of the polymer with a lower content of CNTs. Composite conical–cylindrical combined shells (CCCSs) are widely utilized as loading-bearing components in various engineering applications, and a comprehensive understanding of the vibration characteristics of these shells under different external excitations and boundary conditions is crucial for engineering applications. In this study, the free vibration behaviors of FG-CNTRC CCCSs supported by an elastic foundation are examined using the Haar wavelet discretization method (HWDM). First, by means of the HWDM, the equations of motion of each shell segment, the continuity and boundary conditions are converted into a system of algebraic equations. Subsequently, the natural frequencies and modes of the CCCSs are achieved by calculating the resultant algebraic equations. The convergence and accuracy are evaluated, and the results demonstrate that the proposed method has stable convergence, high efficiency, and excellent accuracy. Furthermore, an exhaustive parametric investigation is conducted to reveal the effects of foundation stiffnesses, boundary conditions, material mechanical properties, and geometric parameters on the vibration characteristics of the FG-CNTRC CCCS. Full article

In order to explore the essence of the anticoccidiosis of anticoccidial drugs under bioelectric currents, the intermolecular double-proton transfer and conformational transformation of 4-pyridone-3-carboxylic acid were investigated by quantum chemistry calculations (at the M06-2X/6-311++G**, M06-2X/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels) and finite temperature string (FTS) under external electric fields. The solvent effect of H₂O on the double-proton transfer was evaluated by the integral equation formalism polarized continuum model. The results indicate that the influences of the external electric fields along the direction of the dipole moment on double-proton transfer are significant. The corresponding products are controlled by the direction of the external electric field. Due to the first-order Stark effect, some good linear relationships form between the changes of the structures, atoms in molecules (AIMs) results, surface electrostatic potentials, barriers of the transition state, and the external electric field strengths. From the gas to solvent phase, the barrier heights increased. The spatial order parameters (ϕ, ψ) of the conformational transformation could be quickly converged through the umbrella sampling and parameter averaging, and thus the free-energy landscape for the conformational transformation was obtained. Under the external electric field, there is competition between the double-proton transfer and conformational transformation. The external electric field greatly affects the cooperativity transfer, while it has little effect on the conformational transformation. This study is helpful in the selection and updating of anticoccidial drugs. Full article

This paper is focused on developing a Galerkin finite element framework for the fractional Allen–Cahn equation with regularized logarithmic potential over the ${\mathbb{R}}^d$ ($d=1,2,3$) domain, where the regularization of the singular potential extends beyond the classical double-well formulation. A fully discrete finite element scheme is developed using a k-th-order finite element space for spatial approximation and a backward Euler scheme for the temporal discretization of a regularized system. The existence and uniqueness of numerical solutions are rigorously established by applying Brouwer’s fixed-point theorem. Moreover, the proposed numerical framework is shown to preserve the discrete energy dissipation law analytically, while a priori error estimates are derived. Finally, numerical experiments are conducted to verify the theoretical results and the inherent physical property, such as phase separation phenomenon and coarsening processes. The results show that the fractional Allen–Cahn model provides enhanced capability in capturing phase transition characteristics compared to its classical equation. Full article

The transport of intensity equation enables quantitative phase imaging from only two axially displaced intensity images, facilitating the characterization of low-contrast samples like cells and microorganisms. However, the rapid selection of the correct defocused planes, crucial for real-time phase imaging of dynamic events, remains challenging. Additionally, the different images are normally acquired sequentially, further limiting phase-reconstruction speed. Here, we report on a system that addresses these issues and enables user-tuned defocusing with snapshot phase retrieval. Our approach is based on combining multi-color pulsed illumination with acousto-optic defocusing for microsecond-scale chromatic aberration control. By illuminating each plane with a different color and using a color camera, the information to reconstruct a phase map can be gathered in a single acquisition. We detail the fundamentals of our method, characterize its performance, and demonstrate live phase imaging of a freely moving microorganism at speeds of 150 phase reconstructions per second, limited only by the camera’s frame rate. Full article

This study presents an analysis of the electromagnetic noise and vibration in a surface-mounted permanent magnet synchronous machine (SPMSM), focusing on their excitation sources. To investigate this, the excitation sources were identified through an analytical approach, and their effects on electromagnetic noise and vibration were evaluated using a finite element method (FEM)-based analysis approach. Additionally, an equivalent curved-beam model based on three-dimensional shell theory was applied to determine the deflection forces on the stator yoke, accounting for the tooth-modulation effect. The stator’s natural frequencies were derived through the characteristic equation in free vibration analysis. Modal analysis was performed to validate the analytically derived natural frequencies and to investigate stator deformation under the tooth-modulation effect across various vibration modes. Furthermore, noise, vibration, and harshness (NVH) analysis via FEM reveals that major harmonic components align closely with the natural frequencies, identifying them as primary sources of elevated vibrations. A comparative study between 8-pole–9-slot and 8-pole–12-slot SPMSMs highlights the impact of force variations on the stator teeth in relation to vibration and noise characteristics, with FEM verification. The proposed method provides a valuable tool for early-stage motor design, enabling the rapid identification of resonance operating points that may induce severe vibrations. This facilitates proactive mitigation strategies to enhance motor performance and reliability. Full article

A four-vector potential of an external test electromagnetic field in a Schwarzschild background is described in terms of a combination of dipole and quadrupole magnetic fields. This combination is an interior solution of the source-free Maxwell equations. Such external test magnetic fields cause the dynamics of charged particles around the black hole to be nonintegrable, and are mainly responsible for chaotic dynamics of charged particles. In addition to the external magnetic fields, some circumstances should be required for the onset of chaos. The effect of the magnetic fields on chaos is shown clearly through an explicit symplectic integrator and a fast Lyapunov indicator. The inclusion of the quadrupole magnetic fields easily induces chaos, compared with that of the dipole magnetic fields. This result is because the Lorentz forces from the quadrupole magnetic fields are larger than those from the dipole magnetic fields. In addition, the Lorentz forces act as attractive forces, which are helpful for bringing the occurrence of chaos in the nonintegrable case. Full article