Article
Engineering, Multidisciplinary
Lin Chen, Hanyan Huang
Summary: This study proposes a generalized hybrid metamodel using radial basis function (RBF) and sparse polynomial chaos expansion (PCE) for covariance-based global sensitivity analysis (GSA) of multivariate outputs in engineering applications. An efficient sequential sampling method is introduced to improve the efficiency and performance of the RBF-PCE model in multivariate settings. Experimental results demonstrate that the proposed method outperforms existing methods in terms of accuracy and efficiency, with a significant reduction in sample demand compared to MCS-based Sobol' indices.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Kuan-Chung Lin, Cheng-Hung Hu, Kuo-Chou Wang
Summary: This work introduces a novel investigation into the use of the deep energy approach for addressing multi-physics issues often encountered in the field of piezoelectricity. The deep energy approach has become known as a robust numerical technique, demonstrating remarkable ability in handling complex nonlinearities and producing very precise results. The study comprehensively investigates the impact of various network characteristics on the accuracy of the approach, and the results show that the tanh activation function outperforms other solutions. Furthermore, the study expands the technique to examine piezoelectric composite plate actuators, demonstrating its flexibility and effectiveness.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Sanjeev Kumar
Summary: The local scaling symmetry of the Lagrange density is used to study the electro-mechanical coupling effects in elastic dielectrics. This approach not only explains the induced polarization and electric potential, but also considers the geometric foundations. By introducing minimal replacement and the concept of gauge compensating one form field, the gauge invariance of the Lagrange density is restored. Different components of the gauge invariant energy density are constructed using scale invariant gauge curvature. Numerical simulations and validation demonstrate the effectiveness of the theory. Explorations of this kind of coupling could have significant implications in various industrial and laboratory applications.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Huiling Zheng, Jun Yang, Wenda Kang, Yu Zhao
Summary: This paper develops a nonlinear accelerated model and inverse Gaussian process for depicting accelerated degradation data, considering the unit heterogeneity and nonlinear parameter-stress relationship. To address the challenge of parameter interval estimation, a novel two-step interval estimation method is proposed. The method derives generalized confidence intervals of random effect parameters and accelerated model parameters, as well as predictive reliability indexes, using the Cornish-Fisher expansion and generalized pivotal quantity procedure. Simulation studies and real examples demonstrate the effectiveness of the proposed method.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Mathematics, Applied
Damian Trofimowicz, Tomasz P. Stefanski, Jacek Gulgowski, Tomasz Talaska
Summary: This paper presents the application of control engineering methods in modeling and simulating signal propagation in time-fractional electrodynamics. By simulating signal propagation in electromagnetic media using Maxwell's equations with fractional-order constitutive relations in the time domain, the equations in time-fractional electrodynamics can be considered as a continuous-time system of state-space equations in control engineering. Analytical solutions are derived for electromagnetic-wave propagation in the time-fractional media based on state-transition matrices, and discrete time zero-order-hold equivalent models are developed and their analytical solutions are derived. The proposed models yield the same results as other reference methods, but are more flexible in terms of the number of simulation scenarios that can be tackled due to the application of the finite-difference scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yuhao Zhao, Fanhao Guo, Deshui Xu
Summary: This study develops a vibration analysis model of a nonlinear coupling-layered soft-core beam system and finds that nonlinear coupling layers are responsible for the nonlinear phenomena in the system. By using reasonable parameters for the nonlinear coupling layers, vibrations in the resonance regions can be reduced and effective control of the vibration energy of the soft-core beam system can be achieved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Engineering, Multidisciplinary
Bo Fan, Zhongmin Wang
Summary: A 3D rotating hyperelastic composite REF model was proposed to analyze the influence of tread structure and rotating angular speed on the vibration characteristics of radial tire. Nonlinear dynamic differential equations and modal equations were established to study the effects of internal pressure, tread pressure sharing ratio, belt structure, and rotating angular speed on the vibration characteristics.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Shanya Baghel, Shuvashree Mondal
Summary: This study focuses on the reliability analysis of one-shot devices and applies it to SEER gallbladder cancer data. The two-parameter logistic-exponential distribution is used as the lifetime distribution and weighted minimum density power divergence estimators and maximum likelihood estimators are used for parameter estimation. The performance of estimators is evaluated through simulation experiments and the search for optimum inspection times is performed using a population-based heuristic optimization method.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Mohamed Mehdaoui
Summary: This paper presents an extended class of epidemic models and proves their existence and uniqueness using mathematical methods. Numerical simulations are conducted to compare the new models with traditional models. These results lay the groundwork for further research on other problems associated with the new proposed class of epidemic models.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Ann Nwankwo, Daniel Okuonghae
Summary: This study investigates the impact of macrophages' uptake of hemozoin on the dynamics of malaria within a human host. The results reveal a backward bifurcation phenomenon induced by the suppression of macrophages' phagocytic function due to their interaction with hemozoin. Moreover, numerical simulations demonstrate that the model can undergo a Hopf bifurcation with periodic solutions appearing in all compartments when the suppression rate is sufficiently small.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Mathematics, Applied
Sun-Ho Choi, Hyowon Seo
Summary: In this paper, the asymptotic behavior of a macroscopic power grid system derived from energy conservation is studied. A sufficient condition for the existence of a special solution as well as the stability of the solution are provided.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Francois Mauger, Cristel Chandre, Mette B. Gaarde, Kenneth Lopata, Kenneth J. Schafer
Summary: This study revisits the equations of Kohn-Sham time-dependent density-functional theory (TDDFT) and demonstrates their derivation from a canonical Hamiltonian formalism. By using a geometric description, families of symplectic split-operator schemes are defined to accurately and efficiently simulate the time propagation for specific classes of DFT functionals. Numerical simulations are conducted to illustrate the approach, focusing on the far-from-equilibrium electronic dynamics of a one-dimensional carbon chain. The optimized 4th order scheme is found to provide a good compromise between numerical complexity and accuracy of the simulation.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Engineering, Multidisciplinary
Si-Li Liu, Qi-Zhi Zhu, Lun-Yang Zhao, Qiao-Juan Yu, Jin Zhang, Ya-Jun Cao
Summary: This paper presents a study on the transition from brittle to ductile behavior in a low-porosity sandstone under drained conditions. Experimental results show that the mechanical behavior changes from brittle faulting to dilatant ductile flow with increasing effective confining pressure. A micromechanics-based elastoplastic damage model is formulated to simulate this behavior, taking into account the coupling between plasticity, damage, and pore pressure. The model effectively reproduces the main features of the sandstone with a brittle-ductile transition, as shown by the comparison with experimental data.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Zhihao Zhai, Chengbiao Cai, Qinglai Zhang, Shengyang Zhu
Summary: This paper investigates the effect of localized cracks induced by environmental factors on the dynamic performance and service life of ballastless track in high-speed railways. A mathematical approach for forced vibrations of Mindlin plates with a side crack is derived and implemented into a train-track coupled dynamic system. The accuracy of this approach is verified by comparing with simulation and experimental results, and the dynamic behavior of the side crack under different conditions is analyzed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Computer Science, Interdisciplinary Applications
Ashish Bhole, Herve Guillard, Boniface Nkonga, Francesca Rapetti
Summary: Finite elements of class C-1 are used for computing magnetohydrodynamics instabilities in tokamak plasmas, and isoparametric approximations are employed to align the mesh with the magnetic field line. This numerical framework helps in understanding the operation of existing devices and predicting optimal strategies for the international ITER tokamak. However, a mesh-aligned isoparametric representation encounters issues near critical points of the magnetic field, which can be addressed by combining aligned and unaligned meshes.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
Article
Engineering, Multidisciplinary
Hao Wu, Jie Sun, Wen Peng, Lei Jin, Dianhua Zhang
Summary: This study establishes an analytical model for the coupling of temperature, deformation, and residual stress to explore the mechanism of residual stress formation in hot-rolled strip and how to control it. The accuracy of the model is verified by comparing it with a finite element model, and a method to calculate the critical exit crown ratio to maintain strip flatness is proposed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xiangyu Sha, Aizhong Lu, Ning Zhang
Summary: This paper investigates the stress and displacement of a layered soil with a fractional-order viscoelastic model under time-varying loads. The correctness of the solutions is validated using numerical methods and comparison with existing literature. The research findings are of significant importance for exploring soil behavior and its engineering applications under time-varying loads.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Shengwen Tu, Naoki Morita, Tsutomu Fukui, Kazuki Shibanuma
Summary: This study aimed to extend the finite element method to cope with elastic-plastic problems by introducing the s-version FEM. The s-version FEM, which overlays a set of local mesh with fine element size on the conventional FE mesh, simplifies domain discretisation and provides accurate numerical predictions. Previous applications of the s-version FEM were limited to elastic problems, lacking instructions for stress update in plasticity. This study presents detailed instructions and formulations for addressing plasticity problems with the s-version FEM and analyzes a stress concentration problem with linear/nonlinear material properties.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Computer Science, Interdisciplinary Applications
Federico Vismara, Tommaso Benacchio
Summary: This paper introduces a method for solving hyperbolic-parabolic problems on multidimensional semi-infinite domains. By dividing the computational domain into bounded and unbounded subdomains and coupling them using numerical fluxes at the interface, accurate numerical solutions are obtained. In addition, computational cost can be reduced by tuning the parameters of the basis functions.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
Article
Economics
John Rehbeck
Summary: This paper proposes a simple extension to analyze the impact of menu complexity on alternative choices and characterizes its mathematical properties. The research shows that, in some cases, people are more likely to choose the default option as the menu size increases. Furthermore, the study relates this model to the class of perturbed utility models.
JOURNAL OF MATHEMATICAL ECONOMICS
(2024)
