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The propagation of flexural waves in advanced nanocomposites reinforced sandwich structures is a topic of paramount importance in the field of structural engineering and materials science. This study investigates the dynamic behavior of such structures, focusing on the wave propagation characteristics along with longitude and lateral directions and their influence on structural performance. Advanced nanocomposites, with their unique material properties and enhanced mechanical properties, offer promising opportunities for the development of lightweight and high-strength sandwich structures. For this important aim, first, a mathematical modeling using three-dimensional flexibility theory and an analytical solution procedure, the results are collected. After that using the datasets of the mathematical modeling section, the hybrid deep neural networks are trained, tested, and validated. Through comprehensive analytical simulations and machine network validations, this research elucidates the complex interplay between material composition, structural geometry, and wave propagation phenomena. Key parameters, such as wave velocity, dispersion, and geometry conditions are analyzed to gain insights into the dynamic response of the sandwich structure. The findings contribute to a deeper understanding of the underlying physics governing flexural wave propagation in nanocomposite-reinforced sandwich structures, thereby facilitating the design and optimization of lightweight and resilient structural systems for diverse engineering applications. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the nonlinear dynamic response and vibration characteristics of a car’s hood door, focusing on its energy capacity under various excitation frequencies. The hood door is modeled using a functionally graded triply periodic minimal surface (FG-TPMS) material, which offers superior mechanical properties and lightweight design. The analysis is conducted using a higher-order shear deformation theory (HSDT), which accounts for shear deformations more accurately than classical theories. The incorporation of von Karman nonlinear terms captures the geometric nonlinearity due to large deformations, providing a realistic simulation of the hood door’s behavior under dynamic loads. To solve the complex equations of motion derived from the HSDT and von Karman terms, a fourth-order Runge–Kutta method is employed. This numerical method ensures accurate time integration and stability of the solution. The dynamic response is further analyzed to determine the energy absorption capacity of the hood door material, crucial for safety and durability in automotive applications. Validation of the numerical model is performed using previous published articles and a hybrid machine learning algorithm, which combines data-driven approaches with traditional physics-based models. This hybrid validation enhances the accuracy and reliability of the predicted responses, ensuring that the proposed model can be effectively used in the design and optimization of car components. The results demonstrate the potential of FG-TPMS materials in automotive applications, offering improved energy absorption and vibration control, which are essential for enhancing vehicle safety and performance. [ABSTRACT FROM AUTHOR]

In order to develop an appropriate method for high-throughput detection of avian metapneumovirus, a quadruple real-time reverse-transcription polymerase chain reaction assay was established with four pairs of specific primers and four specific probes based on the G or M gene of aMPV-A, aMPV-B, aMPV-C and aMPV-D. Its specificity and sensitivity were evaluated, and clinical samples were tested by the method. The results showed that all the four subgroups of avian metapneumovirus can be detected in the quadruple real-time RT-PCR assay simultaneously, with a detection limit of 100–1000 cRNA copies/reaction. The other common poultry viruses were negative. In the avian clinical sample detection, 39 out of 1920 clinical samples collected from 8 provinces were positive. Compared with published RT-PCR assays, the κ value of the quadruple real-time RT-PCR assay in 1920 avian clinical samples was 1.000 (P < 0.001). The established method could be used for the rapid detection of the four subgroups of avian metapneumovirus with high specificity and high sensitivity. [ABSTRACT FROM AUTHOR]

Summary: In this article, a model reduction technique is presented to solve nonlinear multiscale parabolic problems using dynamic mode decomposition. The multiple scales and nonlinearity bring great challenges for simulating the problems. To overcome this difficulty, we develop a model reduction method for the nonlinear multiscale dynamic problems by integrating constraint energy minimizing generalized multiscale finite element method (CEM‐GMsFEM) with dynamic mode decomposition (DMD). CEM‐GMsFEM has shown great efficiency to solve linear multiscale problems in a coarse space. However, using CEM‐GMsFEM to directly solve multiscale nonlinear parabolic models involves dynamically computing the residual and the Jacobian on a fine grid. This may be very computationally expensive because the evaluation of the nonlinear term is implemented in a high‐dimensional fine scale space. As a data‐driven method, DMD can use observation data and give an explicit expression to accurately describe the underlying nonlinear dynamic system. To efficiently compute the multiscale nonlinear parabolic problems, we propose a CEM‐DMD model reduction by combing CEM‐GMsFEM and DMD. The CEM‐DMD reduced model is a coarsen linear model, which avoids the nonlinear solver in the fine space. It is crucial to judiciously choose observation in DMD. Only proper observation can render an accurate DMD model. In the context of CEM‐DMD, we introduce two different observations: fine scale observation and coarse scale observation. In the construction of DMD model, the coarse scale observation requires much less computation than the fine scale observation. The CEM‐DMD model using the coarse scale observation gives a complete coarse model for the nonlinear multiscale dynamic systems and significantly improves the computation efficiency. To show the performance of the CEM‐DMD using the different observations, we present a few numerical results for the nonlinear multiscale parabolic problems in heterogeneous porous media. [ABSTRACT FROM AUTHOR]

This article presents a semianalytical solution to a half-plane contact problem subjected to an arbitrarily distributed surface traction. The half-plane boundary is treated as a material surface of the Steigmann–Ogden type. Under the assumption of plane strain condition, the problem is formulated by coupling the methods of an Airy stress function and Fourier integral transforms. Stresses and displacements in the form of semi-infinite integrals are derived. A non-classical Flamant solution that is able to simultaneously account for the surface tension, membrane stiffness, and bending rigidity of the half-plane boundary is derived through limit analysis on the half-plane contact problem owing to a uniform surface traction. The fundamental Flamant solution is further integrated for tackling two half-plane contact problems owing to classical contact pressures corresponding to a rigid cylindrical roller and a rigid flat-ended punch. The resultant semi-infinite integrals are integrated by the joint use of the Gauss–Legendre numerical quadrature and the Euler transformation algorithm. Extensive parametric studies are conducted for comparing and contrasting the effects of Gurtin–Murdoch and Steigmann–Ogden surface mechanical models. The major observations and conclusions are two-fold. First, the introduction of either surface mechanical model results in size-dependent elastic fields. Second, the incorporation of the curvature-dependent nature of the half-plane boundary leads to bounded stresses and displacements in the fundamental Flamant solution. This is in contrast to the otherwise singular classical and Gurtin–Murdoch solutions. For all four case studies, the Steigmann–Ogden surface model also results in much smoother displacement and stress variations, indicating the significance of surface bending rigidity in nanoscale contact problems. [ABSTRACT FROM AUTHOR]

In this article, we present a data-driven method for parametric models with noisy observation data. Gaussian process regression based reduced order modeling (GPR-based ROM) can realize fast online predictions without using equations in the offline stage. However, GPR-based ROM does not perform well for complex systems since POD projection are naturally linear. Conditional variational autoencoder (CVAE) can address this issue via nonlinear neural networks but it has more model complexity, which poses challenges for training and tuning hyperparameters. To this end, we propose a framework of CVAE with Gaussian process regression recognition (CVAE-GPRR). The proposed method consists of a recognition model and a likelihood model. In the recognition model, we first extract low-dimensional features from data by POD to filter the redundant information with high frequency. And then a non-parametric model GPR is used to learn the map from parameters to POD latent variables, which can also alleviate the impact of noise. CVAE-GPRR can achieve the similar accuracy to CVAE but with fewer parameters. In the likelihood model, neural networks are used to reconstruct data. Besides the samples of POD latent variables and input parameters, physical variables are also added as the inputs to make predictions in the whole physical space. This cannot be achieved by either GPR-based ROM or CVAE. Moreover, the numerical results show that CVAE-GPRR may alleviate the overfitting issue in CVAE. [ABSTRACT FROM AUTHOR]

Summary: This work presents a new bi‐fidelity model reduction approach to the inverse problem under the framework of Bayesian inference. A low‐rank approximation is introduced to the solution of the corresponding forward problem and admits a variable‐separation form in terms of stochastic basis functions and physical basis functions. The calculation of stochastic basis functions is computationally predominant for the low‐rank expression. To significantly improve the efficiency of constructing the low‐rank approximation, we propose a bi‐fidelity model reduction based on a novel variable‐separation method, where a low‐fidelity model is used to compute the stochastic basis functions and a high‐fidelity model is used to compute the physical basis functions. The low‐fidelity model has lower accuracy but efficient to evaluate compared with the high‐fidelity model; it accelerates the derivative of recursive formulation for the stochastic basis functions. The high‐fidelity model is computed in parallel for a few samples scattered in the stochastic space when we construct the high‐fidelity physical basis functions. The required number of forward model simulations in constructing the basis functions is very limited. The bi‐fidelity model can be constructed efficiently while retaining good accuracy simultaneously. In the proposed approach, both the stochastic basis functions and physical basis functions are calculated using the model information. This implies that a few basis functions may accurately represent the model solution in high‐dimensional stochastic spaces. The bi‐fidelity model reduction is applied to Bayesian inverse problems to accelerate posterior exploration. A few numerical examples in time‐fractional derivative diffusion models are carried out to identify the smooth field and channel‐structured field in porous media in the framework of Bayesian inverse problems. [ABSTRACT FROM AUTHOR]

In this paper, we develop a reduced generalized multiscale basis method for efficiently solving the parametrized groundwater flow problems in heterogeneous porous media. Recently proposed generalized multiscale finite element (GMsFE) method is one of the accurate and efficient methods to solve the multiscale problems on a coarse grid. However, the GMsFE basis functions usually depend on the random parameters in the parametrized model, which substantially impacts on the computation efficiency when the parametrized equation needs to be solved many times for many instances of parameters. To enhance computation efficiency, we construct reduced generalized multiscale basis functions independent of parameters from the high‐dimensional GMsFE space and generate a reduced‐order multiscale model by projecting the parameterized flow governing equation onto the low‐dimensional reduced GMsFE space. Then, in order to improve the online computation of reduced‐order model, we apply a matrix discrete empirical interpolation method to affinely decompose the nonaffine parametrized systems arising from the discretization of governing equation. Finally, a few numerical experiments are carried out for the parametrized transient flow problems in heterogeneous porous media to illustrate the efficiency and accuracy of the proposed model reduction method. The results show that the proposed reduced generalized multiscale basis method can significantly improve computation efficiency while maintaining comparative accuracy for the groundwater flow problems by selecting a suitable coarse mesh size and an optimal number of reduced GMsFE basis functions at each of coarse nodes. Key Points: A reduced generalized multiscale basis method is developed for solving parametrized transient flow problems with multiscale inputsMethod is designed by incorporating reduced generalized multiscale bases and matrix discrete empirical interpolation into reduction modelThe proposed reduction method significantly enhance computation efficiency while maintaining accuracy for parametrized flow problems [ABSTRACT FROM AUTHOR]

A new bipolar material, (9H,9′H-[3,3′-bicarbazole]-9,9′-diylbis(benzene-5,1,3-triyl))tetrakis(diphenylphosphine oxide) (BCz-BPO), featuring 3,3′-bicarbazole and diphenylphosphine oxide groups has been designed and synthesized. BCz-BPO with a twisty and rigid configuration exhibited a high triplet energy, excellent thermal stability and bipolar charge carrier transport ability. Both DFT simulation and experimental results demonstrated that the increased electron-transporting ability endows the solution-processed devices based on BCz-BPO with a more balanced charge flux and a higher exciton recombination efficiency. As a result, the blue solution-processed electrophosphorescent device using BCz-BPO as the host showed a maximum luminance efficiency of 30.1 cd A−1, which was comparable to that of a (9H,9′H-[3,3′-bicarbazole]-9,9′-diylbis(4,1-phenylene))bis(diphenylphosphine oxide) (BCz-PO) based vacuum deposited device and was about three times higher when compared with that of the corresponding device based on BCz-PO. Our research put forward a guideline for the molecular design of bipolar host materials used in solution-processed PhOLEDs. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the approximation of elliptic eigenvalue problems using generalized multiscale finite element method (GMsFEM) and get error estimates for eigenfunctions and eigenvalues. For the case of simple eigenvalues, the approximation errors for eigenfunctions are considered in both energy error and L 2 error. The derived error estimates clearly give the relation between the errors and the coarse mesh size, local multiscale enrichment and the corresponding eigenvalues. The convergence analysis shows that the approximation of eigenvalue problems using GMsFEM does not depend on the contrastness of the coefficient when the diffusion coefficient is highly heterogeneous. A few numerical examples are presented to illustrate the performance of the GMsFEM approximation and the theoretic analysis for the eigenvalue problems. [ABSTRACT FROM AUTHOR]

This work presents a model reduction approach to the inverse problem in the application of subsurface flows. One such an application is to estimate model’s inputs and identify model’s parameters. This is often challenging because the complicated multiscale structures are inherent in the model and the estimated inputs are parameterized in a high-dimensional space. We often need to estimate the probabilistic distribution of the unknown inputs based on some observations. Bayesian inference is desirable for this situation and solving the inverse problem. For the Bayesian inverse problem, the forward model needs to be repeatedly computed for a large number of samplers to get a stationary chain. This requires large computational efforts. To significantly improve the computation efficiency, we use generalized multiscale finite element method and least-squares stochastic collocation method to construct a reduced computational model. To avoid the difficulty of choosing regularization parameter, hyperparameters are introduced to build a hierarchical model. We use truncated Karhunen–Loeve expansion (KLE) to reduce the dimension of the parameter spaces and decrease the mixed time of Markov chains. The techniques of hyperparameter and KLE are incorporated into the model reduction method. The reduced model is constructed offline. Then it is computed very efficiently in the online sampling stage. This strategy can significantly accelerate the evaluation of the Markov chain and the resultant posterior distribution converges fast. We analyze the convergence for the approximation between the posterior distribution by the reduced model and the reference posterior distribution by the full-order model. A few numerical examples in subsurface flows are carried out to demonstrate the performance of the presented model reduction method with application of the Bayesian inverse problem. [ABSTRACT FROM AUTHOR]

Elasticity is a fundamental model in mechanics and material sciences. In the article, we present an ensemble variable-separated multiscale method for elasticity problems in random media. A variable-separated method is utilized to provide a low-rank approximation for random fields. The variable-separated method is integrated with the Generalized Multiscale Finite Element Method (GMsFEM) to obtain an efficient reduced model. To this end, a few local problems are solved for snapshots to construct the multiscale basis functions in GMsFEM. An ensemble method is used to construct stochastic basis functions shared by a series of elasticity equations, and a residual decomposition is adopted to calculate the deterministic physical components for all ensemble members. The ensemble variable-separation is used to solve the local problems of the multiscale basis functions and achieves efficient online-computation for the basis. Then, under the Galerkin projection of the generalized finite element method, the solutions of stochastic elasticity problems are projected onto the low-dimensional space spanned by the online multiscale basis functions. This renders an effective coarse model. The ensemble variable-separated multiscale method is applied to steady-state elastic deformation and elastic wave propagation in random media. A few numerical results are carried out to demonstrate the accuracy and efficiency of the presented method. [ABSTRACT FROM AUTHOR]

In this paper, we present some reduced basis methods for elliptic PDEs with parameterized inputs. In the framework of Galerkin projection, dimension reduction techniques are used to construct a reduced order model. If the PDEs have multiscale structures, multiscale finite element method (MsFEM) is one of the efficient approaches to numerically solve the equations. When the inputs of the PDEs are parameterized by a few parameters, the MsFE basis functions usually depend on the parameters. This impacts on the computation efficiency. In order to get the multiscale basis functions independent of parameters, we can build multiscale basis functions based on a set of samples in the parameter space. This will result in a high dimensional MsFE space for approximation and bring great challenge for simulation. To treat this difficulty, we use some optimal strategies to identify a set of optimal reduced basis functions from the high dimensional MsFE space and obtain a reduced order multiscale model. We consider three optimal strategies for model reduction: cross-validation method, greedy algorithm and proper orthogonal decomposition. The dimension of the space spanned by the set of reduced basis functions is much smaller than the dimension of the original full order model. An offline–online computational decomposition is achieved in the reduced multiscale basis methods to significantly improve computation efficiency. Careful comparison is addressed for the reduced basis methods using different optimization strategies. A few numerical results are presented to illustrate the efficacy of the reduced basis methods. [ABSTRACT FROM AUTHOR]

In this article, we present a reduced order method for modeling and computing Allen–Cahn equations. A global basis method is used in the discretized system of the Allen–Cahn equations and Proper Orthogonal Decomposition (POD) method is utilized to reduce the global basis. To treat the difficulty of nonlinearity for Allen–Cahn equations, we apply Discrete Empirical Interpolation method (DEIM) to the nonlinear term from the discretization system. A reduced order method is developed by integrating POD and DEIM. It is well-known that the Allen–Cahn equations have a nonlinear stability property, i.e., the free-energy functional decreases with respect to time. The discretized Allen–Cahn system modeled by the POD–DEIM reduced order method can inherit the nonlinear stability of the continuous model. The computation efficiency is significantly enhanced by using the reduced order method. A few numerical results are presented to illustrate the performance of the reduced order method for deterministic Allen–Cahn equations and stochastic Allen–Cahn equations. [ABSTRACT FROM AUTHOR]

We consider a scalar wave equation with nonseparable spatial scales. If the solution of the wave equation smoothly depends on some global fields, then we can utilize the global fields to construct multiscale finite element basis functions. We present two finite element approaches using the global fields: partition of unity method and mixed multiscale finite element method. We derive a priori error estimates for the two approaches and theoretically investigate the relation between the smoothness of the global fields and convergence rates of the approximations for the wave equation. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011 [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. [Copyright &y& Elsevier]

In this article, we develop a residual-driven adaptive Gaussian mixture approximation (RD-AGMA) for Bayesian inverse problems. The posterior distribution is often non-Gaussian in practical Bayesian inference. To obtain a good approximation of the posterior, we provide the adaptive Gaussian mixture approximation (GMA) based on a residual. For GMA, the clustering of ensemble samples provides the predictor of means, covariances and weights by smoothed expectation–maximization (SmEM). SmEM can overcome the singularity of covariance matrix for small ensemble size. Then the parameters of GMA are updated by an iterative ensemble smoother (IES). To enhance clustering efficiency, the ensemble samples for the clustering are updated by IES as well. Since the goal of inverse problems is to minimize the residual between the observation data and the model response, the adaptive GMA of the posterior is constructed through a residual threshold. The mixture components with large residuals will be discarded in the adaptive procedure. When the prior is incorporated into the likelihood model, small residuals can drive the AGMA close to the true posterior. In the proposed method, a large number of samples can be efficiently drawn from the posterior distribution of GMA. A few numerical examples are presented to demonstrate the efficacy of RD-AGMA with applications in multimodal inversion and channel identification for subsurface flow problems in porous media. [ABSTRACT FROM AUTHOR]

This paper presents an implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is Markov chain Monte Carlo (MCMC). However, the samples generated by MCMC are usually strongly correlated, which may lead to a small size of effective samples. The implicit sampling method proposed in Chorin and Tu (2009) can generate independent samples and capture inherent non-Gaussian features of the posterior. In implicit sampling method, the posterior samples are generated by a map and distribution around the maximum a posterior (MAP) point. For practical applications, some parameters in prior density are often unknown and the hierarchical Bayesian formulation is used to estimate the MAP point effectively. It is applied to the Bayesian inverse problems of multi-term time fractional diffusion models in heterogeneous media. To effectively capture the heterogeneity effect, we present a mixed generalized multiscale finite element method (mixed GMsFEM) to substantially speed up the Bayesian inversion. Finally, we carry out a few numerical examples to effectively identify various unknown inputs. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with respect to the unknown parameter. Because the inverse problem is often ill-posed, regularization strategies are imposed on the least fit-to-data functional to overcome the stability issue. There may exist various kinds of functions to reconstruct. It is crucial to choose a suitable regularization method. We present a multi-parameter regularization L 2 + B V method for the inverse problem. This can extend the applicability for reconstructing the unknown functions. Rigorous analysis is carried out for the inverse problem. In particular, we analyze the existence and stability of regularized variational problem and the convergence. To reduce the dimension in the inversion for numerical simulation, the unknown coefficient is represented by a suitable set of basis functions based on a priori information. A few numerical examples are presented for the inverse problem in time fractional diffusion equations to confirm the theoretic analysis and the efficacy of the different regularization methods. [ABSTRACT FROM AUTHOR]