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Surface mount technology (SMT) is widely used and plays an important role in electronic equipment. The purpose of this paper is to reveal the effects of interface cracks on the fatigue life of SMT solder joint under service load and to provide some valuable reference information for improving service reliability of SMT packages.

A 3D geometric model of SMT package is established. The mechanical properties of SMT solder joint under thermal cycling load and random vibration load were solved by 3D finite element analysis. The fatigue life of SMT solder joint under different loads can be calculated by using the modified Coffin–Manson model and high-cycle fatigue model.

The results revealed that cracks at different locations and propagation directions have different effect on the fatigue life of the SMT solder joint. From the location of the cracks, Crack 1 has the most significant impact on the thermal fatigue life of the solder joint. Under the same thermal cycling conditions, its life has decreased by 46.98%, followed by Crack 2, Crack 4 and Crack 3. On the other hand, under the same random vibration load, Crack 4 has the most significant impact on the solder joint fatigue life, reducing its life by 81.39%, followed by Crack 1, Crack 3 and Crack 2. From the crack propagation direction, with the increase of crack depth, the thermal fatigue life of the SMT solder joint decreases sharply at first and then continues to decline almost linearly. The random vibration fatigue life of the solder joint decreases continuously with the increase of crack depth. From the crack depth of 0.01 mm to 0.05 mm, the random vibration fatigue life decreases by 86.75%. When the crack width increases, the thermal and random vibration fatigue life of the solder joint decreases almost linearly.

This paper investigates the effects of interface cracks on the fatigue life and provides useful information on the reliability of SMT packages.

Physics-informed neural networks (PINNs) have become a new tendency in flow simulation, because of their self-advantage of integrating both physical and monitored information of fields in solving the Navier–Stokes equation and its variants. In view of the strengths of PINN, this study aims to investigate the impact of spatially embedded data distribution on the flow field results around the train in the crosswind environment reconstructed by PINN.

PINN can integrate data residuals with physical residuals into the loss function to train its parameters, allowing it to approximate the solution of the governing equations. In addition, with the aid of labelled training data, PINN can also incorporate the real site information of the flow field in model training. In light of this, the PINN model is adopted to reconstruct a two-dimensional time-averaged flow field around a train under crosswinds in the spatial domain with the aid of sparse flow field data, and the prediction results are compared with the reference results obtained from numerical modelling.

The prediction results from PINN results demonstrated a low discrepancy with those obtained from numerical simulations. The results of this study indicate that a threshold of the spatial embedded data density exists, in both the near wall and far wall areas on the train’s leeward side, as well as the near train surface area. In other words, a negative effect on the PINN reconstruction accuracy will emerge if the spatial embedded data density exceeds or slips below the threshold. Also, the optimum arrangement of the spatial embedded data in reconstructing the flow field of the train in crosswinds is obtained in this work.

In this work, a strategy of reconstructing the time-averaged flow field of the train under crosswind conditions is proposed based on the physics-informed data-driven method, which enhances the scope of neural network applications. In addition, for the flow field reconstruction, the effect of spatial embedded data arrangement in PINN is compared to improve its accuracy.

This study aims to explore the evolving field of physics-informed neural networks (PINNs) through an analysis of 996 records retrieved from the Web of Science (WoS) database from 2019 to 2022.

WoS database was analyzed for PINNs using an inhouse python code. The author’s collaborations, most contributing institutes, countries and journals were identified. The trends and application categories were also analyzed.

The papers were classified into seven key domains: Fluid Dynamics and computational fluid dynamics (CFD); Mechanics and Material Science; Electromagnetism and Wave Propagation; Biomedical Engineering and Biophysics; Quantum Mechanics and Physics; Renewable Energy and Power Systems; and Astrophysics and Cosmology. Fluid Dynamics and CFD emerged as the primary focus, accounting for 69.3% of total publications and witnessing exponential growth from 22 papers in 2019 to 366 in 2022. Mechanics and Material Science followed, with an impressive growth trajectory from 3 to 65 papers within the same period. The study also underscored the rising interest in PINNs across diverse fields such as Biomedical Engineering and Biophysics, and Renewable Energy and Power Systems. Furthermore, the focus of the most active countries within each application category was examined, revealing, for instance, the USA’s significant contribution to Fluid Dynamics and CFD with 319 papers and to Mechanics and Material Science with 66 papers.

This analysis illuminates the rapidly expanding role of PINNs in tackling complex scientific problems and highlights its potential for future research across diverse domains.

This study aims to explore the influence of Fourier-feature enhanced physics-informed neural networks (PINNs) on effectively solving two-dimensional local time-fractional anomalous diffusion equations with nonlinear thermal diffusivity. By tackling the shortcomings of conventional numerical methods in managing fractional derivatives and nonlinearities, this research addresses a significant gap in the literature regarding efficient solution strategies for complex diffusion processes.

This study uses a quantitative methodology featuring a feed-forward neural network architecture combined with a Fourier feature layer. Automatic differentiation is implemented to ensure precise gradient calculations for fractional derivatives. The effectiveness of the proposed approach is showcased through numerical simulations across various sub-diffusion and super-diffusion scenarios, with fractal space parameters adjusted to examine behavior. In addition, the training process is assessed using the Fisher information matrix to analyze the loss landscape.

The results demonstrate that the Fourier-feature enhanced PINNs effectively capture the dynamics of the anomalous diffusion equation, achieving greater solution accuracy than traditional methods. The analysis using the Fisher information matrix underscores the importance of hyperparameter tuning in optimizing network performance. These findings support the hypothesis that Fourier features improve the model’s capacity to represent complex solution behaviors, providing the relationship between model architecture and diffusion dynamics.

This research presents a novel approach to solving fractional anomalous diffusion equations through Fourier-feature enhanced PINNs. The results contribute to the advancement of computational methods in areas such as thermal engineering, materials science and biological diffusion modeling, while also providing a foundation for future investigations into training dynamics within neural networks.

Current methods for flow field reconstruction mainly rely on data-driven algorithms which require an immense amount of experimental or field-measured data. Physics-informed neural network (PINN), which was proposed to encode physical laws into neural networks, is a less data-demanding approach for flow field reconstruction. However, when the fluid physics is complex, it is tricky to obtain accurate solutions under the PINN framework. This study aims to propose a physics-based data-driven approach for time-averaged flow field reconstruction which can overcome the hurdles of the above methods.

A multifidelity strategy leveraging PINN and a nonlinear information fusion (NIF) algorithm is proposed. Plentiful low-fidelity data are generated from the predictions of a PINN which is constructed purely using Reynold-averaged Navier–Stokes equations, while sparse high-fidelity data are obtained by field or experimental measurements. The NIF algorithm is performed to elicit a multifidelity model, which blends the nonlinear cross-correlation information between low- and high-fidelity data.

Two experimental cases are used to verify the capability and efficacy of the proposed strategy through comparison with other widely used strategies. It is revealed that the missing flow information within the whole computational domain can be favorably recovered by the proposed multifidelity strategy with use of sparse measurement/experimental data. The elicited multifidelity model inherits the underlying physics inherent in low-fidelity PINN predictions and rectifies the low-fidelity predictions over the whole computational domain. The proposed strategy is much superior to other contrastive strategies in terms of the accuracy of reconstruction.

In this study, a physics-informed data-driven strategy for time-averaged flow field reconstruction is proposed which extends the applicability of the PINN framework. In addition, embedding physical laws when training the multifidelity model leads to less data demand for model development compared to purely data-driven methods for flow field reconstruction.

This study aims to analyze the relevance of the city spatial structure for smart city innovation from the perspective of agglomeration externalities, and discusses whether there is heterogeneity in innovation across different geographical areas and population scales of cities.

The authors construct the centralization and concentration indexes to conceptualize the city spatial structure of 286 cities (prefecture-level) in China based on the LandScan Global Population Dataset from 2001 to 2016. A fixed-effects panel data model is employed to analyze the relationship between the spatial structure and the innovation ability of smart cities; the results were validated through robustness tests and heterogeneity analyses.

The study found that the more concentrated and more evenly the distribution of urban population, namely the more city spatial structure tends to be weak-monocentricity, the higher the level of innovation in smart cities. The relevance of the weak-monocentricity structure and smart city innovation varies significantly depending on their geographical location and the size of the city. This result is more applicable to cities in the eastern and central regions, as well as to cities with smaller populations.

The adjustment and optimization of the city spatial structure is important for enhancing smart city construction. Unlike previous studies, which mostly use a single dimension of “the proportion of population in sub-centres to the population of all central areas” to measure city spatial structure, the authors employed the spatial centralization and spatial concentration. It is hoped that this study can guide smart city construction from the perspective of the development model of city spatial structure.

The purpose of this paper is to investigate a new and practical decision support model of the coordinated replenishment and delivery (CRD) problem with multi-warehouse (M-CRD) to improve the performance of a supply chain. Two algorithms, tabu search-RAND (TS-RAND) and adaptive hybrid different evolution (AHDE) algorithm, are developed and compared as to the performance of each in solving the M-CRD problem.

The proposed M-CRD is more complex and practical than classical CRDs, which are non-deterministic polynomial-time hard problems. According to the structure of the M-CRD, a hybrid algorithm, TS-RAND, and AHDE are designed to solve the M-CRD.

Results of M-CRDs with different scales show that TS-RAND and AHDE are good candidates for handling small-scale M-CRD. TS-RAND can also find satisfactory solutions for large-scale M-CRDs. The total cost (TC) of M-CRD is apparently lower than that of a CRD with a single warehouse. Moreover, the TC is lower for the M-CRD with a larger number of optional warehouses.

The proposed M-CRD is helpful for managers to select the suitable warehouse and to decide the delivery scheduling with a coordinated replenishment policy under complex operations management situations. TS-RAND can be easily used by practitioners because of its robustness, easy implementation, and quick convergence.

Compared with the traditional CRDs with one warehouse, a better policy with lower TC can be obtained by the new M-CRD. Moreover, the proposed TS-RAND is a good candidate for solving the M-CRD.

This research created a theoretical framework based on theory of consumption values (TCV) and theory of perceived risk (TPR) to investigate the determinant factors behind consumers' intention to use health and fitness apps during the COVID-19-related lockdown. In addition, based on selectivity hypothesis theory (SHT), this study also explored how gender differences moderate the relationships between the determinants and consumers' behavioral intention.

A total of 613 respondents completed a self-reported online questionnaire. Structural equation modeling was conducted to test the role of potential determinants in influencing consumers' behavioral intention. Hierarchical multiple regression was performed to examine the moderating effect of gender.

The findings of this research revealed that physical appearance, general health, enjoyment, affiliation and condition have positive influences on consumers' behavioral intention, while privacy risk and security risk exert negative impact on consumers' behavioral intention. More importantly, the moderating results indicated that only affiliation, privacy risk and security risk have stronger influences on female, while other predictors showed the same effects on both genders.

Fitness providers should embrace health and fitness apps as a new contactless tool to offer services during and after the COVID-19-related lockdown. Fitness providers and app developers need to focus more on the utility and quality of their health and fitness apps. In addition, they should add more gamification elements to health and fitness apps because these elements could increase consumers' hedonic experience especially during the lockdown. Third, the security systems in health and fitness apps should be continuously updated to decline privacy risk during and after the COVID-19-related lockdown. Lastly, when female consumers are targeted during the lockdown, fitness providers should make more efforts to imbue health and fitness apps with more social features and improve the level of security.

Although the importance of contactless technologies has been highlighted ever since the beginning of the COVID-19 pandemic, there has been very little research on the usage of health and fitness apps during the lockdown based on TCV and TPR. Meanwhile, the moderating role of gender differences in this context remains underexplored. This research is one of the early attempts to fill in these gaps. The findings of this study will enhance the theoretical framework regarding the acceptance and use of health and fitness apps; it also challenges the generalizability of SHT in the context of the COVID-19-related lockdown. Moreover, several important implications for the health and fitness industry during and after the COVID-19 pandemic were suggested.