Applied Mathematical Modelling最新文献

Dynamic-spread assessment and kink detection in the early mpox outbreak

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-02-11 DOI: 10.1016/j.apm.2025.115996

Junyang Cai , Rui Xu , Jian Zhou , Haoran Gu

This paper proposes a varying coefficient Susceptible-Exposed-Infected-Removed (vSEIR) model to dynamically simulate the early mpox epidemic. We incorporate a time-varying infection rate and smallpox vaccination protection to capture real-time changes in transmission influenced by non-pharmaceutical interventions, setting our work apart from studies relying on fixed rates. To this end, we apply the recursive least squares algorithm with a forgetting factor for real-time identification of time-varying infection rate. The sparse Hodrick-Prescott (HP) filter, tuned with leave-one-out cross-validation, captures mpox epidemic kinks via the effective reproduction number

R_{t}

obtained from the discrete vSEIR model. This allows for accurate segmentation of epidemic phases, better evaluation of intervention effectiveness, and insights that can guide preparedness for future possible outbreaks. We analyze the mpox and COVID-19 outbreaks in four countries using the proposed kink-based framework. The results show that the mpox epidemic generally entered its decline phase earlier than COVID-19, despite weaker interventions. Additionally, the early mpox epidemic exhibited more inflection points compared to the early COVID-19 pandemic, reflecting stronger non-pharmacological controls during the latter. Sensitivity analyses further indicate that mpox infections would have increased by 12% without smallpox vaccination, and data uncertainty significantly impacts

R_{t}

estimates. Finally, our proposed systematic framework can also be extended to other early outbreaks of human-to-human epidemics, especially in the absence of reliable medical data on contact rates.

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引用次数: 0

Analytical springback modelling for thermal-mechanical bending of TA18 tube under non-isothermal loading

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-02-10 DOI: 10.1016/j.apm.2025.115964

Zili Wang , Le Wang , Shuyou Zhang , Xiaojian Liu , Yongzhe Xiang , Yaochen Lin , Jianrong Tan

The thermal-mechanical bending process is a promising forming method for high-strength hollow tubular structures, enabling the forming limit's extension, particularly for difficult-to-bend metal tubes such as TA18 tubes. However, this forming process complicates the springback characteristics due to the thermal-mechanical coupling effect under multi-die heating and constraint strategies. To further reveal the elastic release mechanism of TA18 thin-walled tubes post-unloading, we propose an analytical springback modeling method for the warm rotary draw bending (WRDB) process. A continuous steady-state heat transfer theoretical model across the tube cross-section is developed to model the thermal field and exactly capture the material flow behavior. Based on the experimental TA18 temperature softening behavior, the distribution of asymmetric strain and the nonlinear thermal field is introduced into the springback modeling, revealing the behavior of neutral layer shifting (NLS) and the evolution of yield surface across the cross-section under non-isothermal loading. Compared to finite element (FE) modeling, quantitative results show that the theoretical model can accurately predict tube springback behavior in experiments, achieving an average absolute relative error (AARE) below 1.4 % with low computational cost. The temperature effect on springback under different heating strategies is attributed to NLS and stress-strain redistribution induced by material temperature softening. The temperature difference of the local thermal field aggravates the NLS and contributes to the non-uniform tensile and compressive deformation, which is significant in the bending case with large diameter tubes and induces pronounced springback behavior.

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引用次数: 0

Dynamic response of a floating flexible plate to a localised time-periodic and moving load

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-02-07 DOI: 10.1016/j.apm.2025.115993

Susam Boral , Baoyu Ni

Flexural-gravity waves generated by a time-periodic and moving external load on a floating flexible plate are studied. The floating flexible plate, similar to an ice sheet, is modelled using the Kelvin-Voigt model. The external load is represented as a localised pressure load. A complex dispersion relation involving the plate viscosity and in-plane compressive force is derived and analysed to obtain the criteria for the occurrence of wave blocking. The study reveals that no real roots of the dispersion relation exist in the presence of viscous damping, and no wave blocking occurs. However, the dispersion relation possesses multiple complex roots with very small imaginary parts for given values of frequency, load speed and compressive force. The viscoelastic plate response is derived using the Fourier transform method, yielding an integral with no singularities in the presence of plate viscosity. Two different mathematical approaches, the principal value theorem and the method of residues, are employed, followed by numerical techniques to analyse the viscoelastic plate response for different parameters. The study demonstrates a damped and non-uniform oscillatory plate response for a range of external load frequencies within the limit of blocking points. Additionally, a significantly higher amplitude in the plate response is observed for low-frequency loads when the load speed exceeds minimum phase velocity.

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引用次数: 0

A game-theoretical analysis of route information cooperative update for road networks with mixed vehicles

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-02-06 DOI: 10.1016/j.apm.2025.115997

Yu Qian , Jian Zhang , Duxin Chen

With the development of vehicle-to-everything technologies, both RVs and CAVs coexist on urban road networks in the foreseeable future. In the mixed driving traffic flow scenario, although the mixed vehicles can obtain the same route information, the systems by which they obtain and process this information are independent. To improve the operation efficiency of urban road networks, this study proposes a cooperative route information update strategy for the mixed traffic flow. Dynamic traffic assignment of the mixed vehicles is taken into account based on the game theory, and a travel cost model for the mixed traffic flow scenario is established using the macroscopic fundamental diagram theory. Furthermore, a Stackelberg-cooperative strategy is proposed to optimize the information update mechanism by adjusting the route information update frequency and route guidance criteria, considering the mixed vehicles routing characteristics. Third, to ensure benefits for both travelers and managers, the study analyses the impact of Stackelberg-Cooperative strategy on the mixed driving traffic flow scenarios and proposes a Stackelberg-Evolutionary-Cooperative strategy to periodically revise the information update strategy. Finally, numerical experiments on Hefei road networks are conducted to validate the effectiveness of the proposed Stackelberg-Evolutionary-Cooperative strategy.

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引用次数: 0

Fluid-structure interaction approximation with embedded solid-shell finite elements using discontinuous shape functions

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-02-06 DOI: 10.1016/j.apm.2025.115994

A. Aguirre , R. Zorrilla , J. Baiges , R. Codina

This work introduces a numerical framework for addressing Fluid-Structure Interaction problems involving thin structures subject to finite strain deformations. The proposed approach utilizes an embedded mesh method to establish a coupling interface between the fluid and structural domains. The novelty of the work is the incorporation of a recently developed locking-free stabilized formulation of solid-shell elements to handle the structural domain. The framework employs established techniques to handle pressure jumps in the fluid domain across the embedding interface and enforce boundary conditions, such as discontinuous shape functions for the pressure unknowns designed to segregate nodal contributions of the cut elements, and Nitsche's method for the weak imposition of transmission conditions in the fluid. The present approach is validated through a series of benchmark cases in both 2D and 3D environments, progressively increasing in complexity. The results demonstrate good agreement with existing literature, establishing the presented framework as a viable method for addressing Fluid-Structure Interaction problems involving thin structures subject to large strains.

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引用次数: 0

Generalized mathematical electro-mechanical-yielding zone model for a non-centric semi-permeable anti-plane crack in arbitrary polarized piezoelectric strip

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-02-06 DOI: 10.1016/j.apm.2025.115995

Monika Meena , Pooja Raj Verma

In the paper, we propose a generalized mathematical electro-mechanical-yielding-zone model to address the presence of a mode-III, non-centric semi-permeable crack in an arbitrary polarized long and narrow piezoelectric (PE) strip. The electro-mechanical-yielding zone model is generalized by exploring three different scenarios on the rims of mechanical-yielding zone: Linear, quadratic and cubic interpolating polynomial times the distributed anti-plane yield point shear stress. It is assumed that the mechanical-yielding zones are smaller than the electrical-yielding zones. The solution to the problem has been achieved by utilizing the Fourier cosine transform and the integral equation techniques. The analytical expressions are derived for electrical-yielding zone, mechanical-yielding zone, electric crack condition parameter and various fracture parameters, such as crack-sliding displacement (CSD), crack-opening potential drop (COPD) and energy release rate (ERR) under all considered scenarios. Furthermore, numerical case study is conducted for investigating the effects of material properties, strip width, prescribed electro-mechanical loadings, crack-face boundary conditions and poling angle on numerous fracture parameters. The results obtained from the present study undergo rigorous analysis and a graphical comparison is employed to offer a clear and insightful representation of the findings.

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引用次数: 0

Dual-stage method with PINN for coupled strong-form diffusion and energy-based deformation analysis in lithium-ion batteries

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-02-05 DOI: 10.1016/j.apm.2025.115986

Yunhao Wu , Wei Feng , Yong Li , Kai Zhang , Fuqian Yang

Traditional numerical methods, such as finite element analysis, have been extensively used to solve lithiation-induced stress, while they are costly and computationally intensive in solving high-dimensional nonlinear problems. In this work, we combine an alternating iterative method with a deep energy method to study a nonlinear coupling problem associated with the deformation of electrode materials in lithium-ion battery, i.e., the coupling between stress and diffusion during electrochemical cycling. Physics-informed neural networks (PINNs) are established to solve the time-dependent diffusion equation, which captures the evolution of the concentration field under stress-limited diffusion. The concentration field at each specific time serves as a part of the loss function for the Deep Energy Method (DEM)-based model, which computes the corresponding stress field. An alternating iterative approach is used to solve the coupling between diffusion and stress, with the diffusion equation being solved by the trained PINN and the static stress computation by the DEM for the updated concentration field. This sequential and iterative process effectively addresses the interaction between the concentration field and the deformation field, ensuring accurate and efficient analysis of the coupled diffusion-deformation problem. Numerical experiments support the feasibility and robustness of the alternating-iterative method with de-coupled physics-informed neural networks to solve complex problems for various physical scenarios and demonstrate the superior performance of the proposed method. The proposed method offers a simple avenue to solve multi-physics coupling problems with significantly theoretical and practical potential. The code used in this work is available at https://github.com/Owen-Hugh/DEMs.git.

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引用次数: 0

Understanding instance hardness for optimisation algorithms: Methodologies, open challenges and post-quantum implications

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-02-05 DOI: 10.1016/j.apm.2025.115965

Kate Smith-Miles

This paper reviews efforts to characterise the hardness of optimisation problem instances, and to develop improved methodologies for empirical testing of the strengths and weaknesses of algorithms, based on comprehensive and unbiased sets of test instances whose hardness can be understood. Using the Travelling Salesperson Problem (TSP) as an illustrative example throughout the paper, efforts during the 20th century to solve optimisation problems with both exact and heuristic algorithms are briefly reviewed. From the early 21st century however, with a growing number of available algorithms (from nature-inspired to quantum), the focus has naturally shifted to exploring how the characteristics of particular problem instances impact algorithm performance, and whether empirical testing is rigorous, unbiased, conclusive and trustworthy based on the choice of test instances. Instance Space Analysis (ISA) was pioneered by the author as a methodology to visualize explainable strengths and weaknesses of algorithms across the broadest set of test instances, and to scrutinize the diversity and suitability of test instances chosen for empirical testing of algorithms. The ISA methodology is reviewed and illustrated using the TSP to show how insights into instance hardness for particular algorithms can be obtained. The paper then turns attention to quantum algorithms for optimisation, and argues that key lessons learned about testing optimisation algorithms over recent decades are highly relevant to current efforts to explore quantum advantage for optimisation. The implications of these lessons for quantum optimisation, including applications such as machine learning, are summarised. Given the difficulties faced by quantum algorithms for solving the TSP, the idea of designing extremely hard TSP instances as the basis for new post-quantum cryptography protocols is discussed. Finally, ten open research challenges are posed to provide fruitful directions for future research.

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引用次数: 0

New analytical solutions for stress and displacement in deeply buried noncircular tunnels incorporating the influence of seepage flow

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-02-01 DOI: 10.1016/j.apm.2025.115990

E.T. Wang , H.N. Wang , X.C. Jia

High water pressure is a common condition during the construction and operation of deeply buried tunnels, which is a significant factor in the stability analysis of underground structures. In this study, the complex variable theory is extended to analytically solve the hydro-mechanical coupled problems for tunnelling problems, which is the first time that fully considers the seepage field influence on the mechanical field, any tunnel shape and the actual steady-state pore pressure distribution. The detailed formulations of the extended complex variable theory are provided, by which specific analytical solutions are proposed for stress, displacement and pore pressure around tunnels with arbitrary shapes. The theory extension and solutions are verified by the good agreement between the analytical results and numerical predictions.

Based on an investigation of the mechanical mechanism using analytical solutions, it is found that the influence of the seepage field on the mechanical field can be divided into two parts, including the surface loading effect and the flow effect. The surface loading effect is more significant than the flow effect. We also investigate the influence of key parameters on stress and tunnel convergence, such as Biot coefficient and tunnel shape, providing normalized charts as a reference for engineering applications. The developed hydro-mechanical coupled solutions can be used for both external and internal high-pressure conditions. Furthermore, it is a tool with a high potential for application to several relevant case studies, such as nuclear waste disposals.

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引用次数: 0

Adjoint-based optimization for non-linear inverse problems with high-order discretization of the compressible RANS equations

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-31 DOI: 10.1016/j.apm.2025.115984

Bartolomeo Fanizza , Pedro Stefanin Volpiani , Florent Renac , Emeric Martin , Denis Sipp

This work presents an adjoint-based strategy to solve non-linear inverse problems discretized with high-order numerical methods. The inverse problem is defined here based on the optimization of a control parameter to minimize a cost-functional subject to the compressible RANS equations discretized with the modal discontinuous Galerkin (DG) method. The distributed control parameter is searched in the DG function space and the discrete adjoint approach, consistent with the formal problem, is used to compute the derivative of the cost function in the optimization process. The linearization of the cost-functional and of the governing equations, the expression of the gradient, as well as the numerical strategy to efficiently solve the adjoint system with flexible inner-outer GMRES solvers have been detailed. In the case of a strongly under-determined problem, regularization techniques based on the penalization of the norm of the control parameter have been introduced. The methodology is illustrated on the case of a data-assimilation (DA) problem, which aims at minimizing the discrepancy of (sparse) high-fidelity measurements with the solution of the RANS equations corrected by four different control parameters. The optimization strategy is tested progressively with measurements on the full computational domain (abundant measurements) and solid wall boundaries (sparse measurements). First, a laminar flow around a cylinder is used to validate the inverse problem resolution with a DG discretization of different approximation orders. Subsequently, results regarding a turbulent flow around a square cylinder allow to compare the optimization convergence of each corrective parameters with abundant measurements. Finally, a shock-wave/turbulent boundary-layer interaction configuration is considered. Great correction of the velocity field is obtained with one of the proposed corrective term. In the case of abundant measurements it is also possible to get accurate correction of wall variables such as the skin-friction and pressure coefficient. Regularization of the optimal space, in case of sparse measurements, is attempt through penalization techniques.

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引用次数: 0