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The subharmonic resonances of an axially moving graphene-reinforced laminated composite plate are studied based on the Galerkin and multiscale methods. Graphene nanoplatelets (GPLs) are added into matrix material which acts as the basic layer of the plate, and a graphene-reinforced nanocomposite plate is thus obtained. Different GPL distribution patterns in the laminated plate are considered. The Halpin–Tsai model is selected to predict the physical properties of the nanocomposite. Hamilton's principle is utilized to conduct the dynamic modeling of the plate and the von Kármán deformation theory is used. The velocity is assumed to be a combination of constant and harmonically varied velocities. The natural frequencies of the linear system with constant velocity can be obtained using the eigenvalues of the coefficient matrix of the ordinary differential equations after the governing partial differential equations of motion are discretized through the Galerkin method. The instability regions of the linear system and the amplitude–frequency relations of the nonlinear system considering the harmonically varied velocity are obtained based on the multiscale analysis. The effect of GPL reinforcement on the subharmonic resonances of the linear and nonlinear systems is analyzed in detail. [ABSTRACT FROM AUTHOR]

Introduction: In this article, a quasi-zero stiffness energy harvesting system with an inertial amplifier is proposed. The device has adjustable performance and can adjust the intrinsic frequency of the system by varying the dynamic effective mass of the system. Materials and methods: The amplitude-frequency response equations and curves of the system when it is in the resonance state are obtained using the multi-scale method. In addition, the image of the system’s basin of attraction is plotted in terms of the system’s Lyapunov exponent, and the trajectory changes and energy harvesting changes of the system are investigated for different initial value states. Results: The results show that changes in the initial angle of the inertial amplification device will cause changes in the resonance frequency band of the system, and the energy collection efficiency of the system in the ultra-low frequency band can be improved by reasonably adjusting the initial angle of the inertial amplification device. Conclusion: The coexistence basins of attraction of the system can give a very good identification scheme, which can greatly improve the energy harvesting efficiency within a certain range. [ABSTRACT FROM AUTHOR]

In this work, we present a nonlinear variational multiscale finite element method for solving both stationary and transient incompressible Navier-Stokes equations. The method is founded on a two-level decomposition of the approximation space, where a nonlinear artificial viscosity operator is exclusively added to the unresolved scales. It can be regarded as a self-adaptive method, since the amount of subgrid viscosity is automatically introduced according to the residual of the equation, in its strong form, associated with the resolved scales. Two variants for the subgrid viscosity are presented: one considering only the residual of the momentum equation and the other also incorporating the residual of the conservation of mass. To alleviate the computational cost typical of two-scale methods, the microscale space is defined through polynomial functions that vanish on the boundary of the elements, known as bubble functions. We compared the numerical and computational performance of the method with the results obtained by the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation combined with the Pressure Stabilizing/Petrov-Galerkin (PSPG) method through a set of 2D reference problems. [ABSTRACT FROM AUTHOR]

The principal parameter resonance of a ferromagnetic functionally graded (FG) cylindrical shell under the action of axial time-varying tension in magnetic and temperature fields is investigated. The temperature dependence of physical parameters for functionally graded materials (FGMs) is considered. Meanwhile, the tension bending coupling effect is eliminated by introducing the physical neutral surface. The kinetic and strain energies are gained with the Kirchhoff–Love shell theory. Based on the nonlinear magnetization characteristics of ferromagnetic materials, the electromagnetic force acting on the shell is calculated. The nonlinear vibration equations are obtained through Hamilton’s principle. Afterward, the vibration equations are discretized and solved by Galerkin and multiscale methods, respectively. The stability criterion for steady-state motion is established utilizing Lyapunov stability theory. After example analysis, the effects of magnetic field intensity, temperature and power law index on the static deflection are elucidated. Subsequently, the impacts of these parameters, as well as axial tension, on the amplitude-frequency characteristics, resonance amplitude, and multiple solution regions are discussed explicitly. Results indicate that the stiffness can be enhanced due to the generation of static deflection. The amplitude decreases with increasing magnetic field intensity, temperature, and power law index. When the magnetic field intensity surpasses a threshold, the resonance phenomenon disappears. [ABSTRACT FROM AUTHOR]

Needled carbon/carbon composites contain complex microstructures such as irregular pores, anisotropic pyrolytic carbon, and interphases between fibers and pyrolytic carbon matrices. Additionally, these composites have hierarchical structures including weftless plies, short-cut fiber plies, and needled regions. To predict the effective elastic properties of needled carbon/carbon composites, this paper proposes a novel sequential multiscale method. At the microscale, representative volume element (RVE) models are established based on the microstructures of the weftless ply, short-cut fiber ply, and needled region, respectively. In the microscale RVE model, a modified Voronoi tessellation method is developed to characterize anisotropic pyrolytic carbon matrices. At the macroscale, an RVE model containing hierarchical structures is developed to predict the effective elastic properties of needled carbon/carbon composites. For the data interaction between scales, the homogenization results of microscale models are used as inputs for the macroscale model. By comparing these against the experimental results, the proposed multiscale model is validated. Furthermore, the effect of porosity on the effective elastic properties of needled carbon/carbon composites is investigated based on the multiscale model. The results show that the effective elastic properties of needled carbon/carbon composites decrease with the increase in porosity, but the extent of decrease is different in different directions. [ABSTRACT FROM AUTHOR]

Viscoelastic flows play an important role in numerous engineering fields, and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids. However, traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time, and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids. In this paper, a universal multiscale method coupling an improved smoothed particle hydrodynamics (SPH) and multiscale universal interface (MUI) library is presented for viscoelastic flows. The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain. We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows. In the first example, the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions. The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain. In the second example, the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics (DPD) method. The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain. Moreover, transferring different physical quantities has an important effect on the numerical results. [ABSTRACT FROM AUTHOR]

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for addressing time-harmonic scattering problems of Helmholtz type with high wavenumber k. This method operates on a coarse mesh of width HH and identifies local finite element source terms that produce rapidly decaying responses under the solution operator. These source terms can be constructed with high accuracy from independent local snapshot solutions on patches of width ℓH, and they are used as problem-adapted basis functions. Compared to classical LOD and other state-of-the-art multiscale methods, our approach demonstrates that the localization error decays super-exponentially as the oversampling parameter ℓ increases. This indicates that optimal convergence is achieved under a substantially relaxed oversampling condition of ℓ≳(log⁡κ/H)(d−1)/d, where d represents the spatial dimension. Numerical experiments highlight the significant improvements in both offline and online performance of the method, even in the presence of heterogeneous media and perfectly matched layers. [ABSTRACT FROM AUTHOR]

Phase‐field methods are attractive for simulating the mechanical failure of geometrically complex porous microstructures described by 2D/3D x‐ray μ$$ \mu $$CT images in subsurface (e.g., CO 2$$ {}_2 $$ storage) and manufacturing (e.g., Li‐ion battery) applications. They capture the nucleation, growth, and branching of fractures without prior knowledge of the propagation path or having to remesh the domain. Their drawback lies in the high computational cost for the typical domain sizes encountered in practice. We present a multiscale preconditioner that significantly accelerates the convergence of Krylov solvers in computing solutions of linear(ized) systems arising from the sequential discretization of the momentum and crack‐evolution equations in phase‐field methods. The preconditioner is an algebraic reformulation of a recent pore‐level multiscale method (PLMM) by the authors and consists of a global preconditioner MG$$ {\mathrm{M}}_{\mathrm{G}} $$ and a local smoother ML$$ {\mathrm{M}}_{\mathrm{L}} $$. Together, MG$$ {\mathrm{M}}_{\mathrm{G}} $$ and ML$$ {\mathrm{M}}_{\mathrm{L}} $$ attenuate low‐ and high‐frequency errors simultaneously. The proposed MG$$ {\mathrm{M}}_{\mathrm{G}} $$, used in the momentum equation only, is a simplification of a recent variant proposed by the authors that is much cheaper and easier to deploy in existing solvers. The smoother ML$$ {\mathrm{M}}_{\mathrm{L}} $$, used in both the momentum and crack‐evolution equations, is built such that it is compatible with MG$$ {\mathrm{M}}_{\mathrm{G}} $$ and more robust and efficient than black‐box smoothers like ILU(k$$ k $$). We test MG$$ {\mathrm{M}}_{\mathrm{G}} $$ and ML$$ {\mathrm{M}}_{\mathrm{L}} $$ systematically for static‐ and evolving‐crack problems on complex 2D/3D porous microstructures, and show that they outperform existing algebraic multigrid solvers. We also probe different strategies for updating MG$$ {\mathrm{M}}_{\mathrm{G}} $$ as cracks evolve and show the associated cost can be minimized if MG$$ {\mathrm{M}}_{\mathrm{G}} $$ is updated adaptively and infrequently. Both MG$$ {\mathrm{M}}_{\mathrm{G}} $$ and ML$$ {\mathrm{M}}_{\mathrm{L}} $$ are scalable on parallel machines and can be implemented non‐intrusively in existing codes. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel decomposition method using elastic-band transform (EBT), which mimics eye scanning and is utilized for multiscale analysis of signals. The proposed EBT-based method can efficiently extract the features of various signals with the following three advantages. First, it is a data-driven approach that extracts several important modes based solely on data without using predetermined basis functions. Second, it does not assume that the signal consists of (locally) sinusoidal intrinsic mode functions, which is a common assumption in existing methods. Therefore, the proposed method can handle a wide range of signals. Finally, it is robust to noise. A practical algorithm for decomposition is presented, along with some theoretical properties. Simulation examples and real data analysis results show promising empirical properties of the proposed method. • The proposed is a data-driven approach that extracts several important modes based solely on data. • The proposed method does not assume that the signal consists of (locally) sinusoidal intrinsic mode functions. • The proposed method is robust to noise. • The proposed method extends the scope of signals for decomposition significantly. • A practical algorithm for decomposition is presented along with some theoretical properties. [ABSTRACT FROM AUTHOR]

Single-layer molybdenum disulfide (MoS2) has been a research focus in recent years owing to its extensive potential applications. However, how to model the mechanical properties of MoS2 is an open question. In this study, we investigate the nonlinear static bending and forced vibrations of MoS2, subjected to boundary axial and thermal stresses using modified plate theory with independent in-plane and out-of-plane stiffnesses. First, two nonlinear ordinary differential equations are obtained using the Galerkin method to represent the nonlinear vibrations of the first two symmetrical modes. Second, we analyze nonlinear static bending by neglecting the inertial and damping terms of the two equations. Finally, we explore nonlinear forced vibrations using the method of multiple scales for the first- and third-order modes, and their 1:3 internal resonance. The main results are as follows: (1) The thermal stress and the axial compressive stress reduce the MoS2 stiffness significantly. (2) The bifurcation points of the load at the low-frequency primary resonance are much smaller than those at high frequency under single-mode vibrations. (3) Temperature has a more remarkable influence on the higher-order mode than the lower-order mode under the 1:3 internal resonance. [ABSTRACT FROM AUTHOR]

The parametric vibration and combined resonance of a turbine blade with a preset angle subjected to the combined effect of parametric and forced excitation were investigated. The blade was modeled as a rotating beam considering the effects of centrifugal, gyroscopic, and bending-torsion coupling. The instability region of the corresponding linear system with parametric excitation was analyzed using Floquet theory, and the effect of blade parameters on this region was discussed. Notably, the parametric vibration of the torsional degree-of-freedom (DOF) caused by parametric excitation of the bending degree-of-freedom has been found. The results show that the size and position of the parameter resonance region are affected by the blade aspect ratio and preset angle, respectively. Furthermore, the multiscale method was employed to solve the blade equation under the combined action of parametric and forced excitation to study the combined resonance caused by forced excitation and gyroscopic items. The effect of blade parameters and excitation characteristics on regions of combined resonance were investigated. The phenomenon of heteroclinic bifurcation was observed due to changes in the excitation frequency, and the harmonic components that accompanied the bifurcation changed. Specifically, a multiperiod response dominated by the excitation frequency and subharmonic components shifted to a single-period response dominated by subharmonic components. This study provides a theoretical explanation for the nonsynchronous resonance of blades and the subharmonic signals in blade vibration and guides blade parameter design, especially for wind turbines. [ABSTRACT FROM AUTHOR]

This paper presents a method of transforming from the three-dimensional piezoelastic problem for a composite material to the one-dimensional problem for a piezoelastic beam. This is done using the asymptotic homogenization technique based on the separation of fast and slow variables in the solution. A special feature of the problem is the presence of two small parameters, one of which characterizes the microstructure of the composite material, and the other defines the cross-sectional size. Homogenized relations describing the piezoelastic beam and fast correctors were obtained. Their joint use makes it possible to correctly describe the total stress-strain state of the original three-dimensional body. The proposed method is suitable for solving the three-dimensional problem of deformation of an extended body with an arbitrary periodic structure as well as for solving new problems (e.g., the torsion problem) that have no analogues in the theory of piezoelastic plates. [ABSTRACT FROM AUTHOR]

We consider two-scale stress mixed finite element elasticity models using H(div)-conforming tensor approximations for the stress variable, whilst displacement and rotation fields are introduced to impose divergence and symmetry constraints. The variables are searched in composite FE spaces based on polyhedral subdomains, formed by the conglomeration of local shape-regular micro partitions. The two-scale characteristic is expressed in terms of refined discretizations inside the subdomains versus coarser normal components of tensors over their boundaries (traction), with respect to mesh size, polynomial degree, or both. General error estimates are derived and stability is proved for five particular cases, associated with stable single-scale local tetrahedral space settings. Enhanced accuracy rates for displacement and super-convergent divergence of the stress can be obtained. Stress, rotation, and stress symmetry errors keep the same accuracy order determined by the traction discretization. A static condensation procedure is designed for computational implementation. There is a global problem for primary variables at the coarser level, with a drastic reduction in the number of degrees of freedom, solving the traction variable and piecewise polyhedral rigid body motion components of the displacement. The fine details of the solution (secondary variables) are recovered by local Neumann problems in each polyhedron, the traction variable playing the role of boundary data. In this sense, the proposed formulation can be interpreted as an equivalent Multiscale Hybrid Mixed method, derived from a global-local characterization of the exact solution. A numerical example with known smooth solution is simulated to attest convergence properties of the method based on local B D F M divergence-compatible finite element pairs. Application to a problem with highly heterogeneous material is analyzed for robustness verification. • Multiscale method for 3D mixed weak symmetry elasticity approximations. • Theoretical analysis for the convergence of the stress and displacement. • Numerical results confirm theoretical convergence rates. • Method applied to highly heterogeneous 3D model. • Method results in elementwise equilibrated stress field. [ABSTRACT FROM AUTHOR]

This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is illustrated numerically and contrasted to the higher-dimensional case. For general unstructured high-contrast coefficients, we present the Localized Orthogonal Decomposition and show a priori error estimates in suitably weighted norms. Numerical experiments illustrate the convergence rates in various settings. [ABSTRACT FROM AUTHOR]

Lempel-Ziv complexity (LZC) is an algorithm used to quantify the complexity of a data sequence by calculating the number of independent substrings contained in the sequence. LZC succeeds in detecting abnormal patterns in signals and is widely employed for identifying anomalies and recognizing patterns in several fields, such as medical science, natural science, social science, and engineering. The objective of this study is to investigate the theory, improvement, and application of LZC in different fields. Firstly, a brief overview of the areas where LZC is utilized is provided. Next, the principle and process of signal complexity characterization are examined, along with a comparison of its advantages to entropy. Following this, we will present a detailed review of the improvement techniques and uses of LZC, focusing on three key areas: encoding methods, multiscale methods, and noise reduction methods. Lastly, this paper presents the unresolved matters and potential areas for further investigation LZC.

Multiscale high-contrast media can cause astonishing wave propagation phenomena through resonance effects. For instance, waves could be exponentially damped independent of the incident angle or waves could be re-focused as through a lense. In this review article, we discuss the numerical treatment of wave propagation through multiscale high-contrast media at the example of the Helmholtz equation. First, we briefly summarize the findings of analytical homogenization theory, which inspire the design of numerical methods and indicate interesting regimes for simulation. In the main part, we discuss two different classes of numerical multiscale methods and focus on how to treat especially high-contrast media. Some elements of a priori error analysis are discussed as well. Various numerical simulations showcase the applicability of the numerical methods to explore unusual wave phenomena, for instance exponential damping and lensing with flat interfaces. [ABSTRACT FROM AUTHOR]

This paper develops a material-structure integrated design and optimization method based on a multiscale approach for the lightweight design of CFRP car doors. Initially, parametric modeling of RVE is implemented, and their elastic performance parameters are predicted using the homogenization theory based on thermal stress, exploring the impact of RVE parameters on composite material performance. Subsequently, a finite element model of the CFRP car door is constructed based on the principle of equal stiffness, and a parameter transfer across microscale, mesoscale, and macroscale levels is achieved through Python programming. Finally, the particle generation and updating strategies in the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm are improved, enabling the algorithm to directly solve multi-constraint and multi-objective optimization problems that include various composite material layup process constraints. Case study results demonstrate that under layup process constraints and car door stiffness requirements, plain weave, twill weave, and satin weave composite car doors achieve weight reductions of 15.85%, 14.54%, and 15.35%, respectively, compared to traditional metal doors, fulfilling the requirements for a lightweight design. This also provides guidance for the lightweight design of other vehicle body components. [ABSTRACT FROM AUTHOR]

A generalized finite element method (FEM) is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter\varepsilon, based on locally approximating the solution on each subdomain by solution of a local reaction-diffusion equation and eigenfunctions of a local eigenproblem. These local problems are posed on some domains slightly larger than the subdomains with oversampling size ƍ\ast. The method is formulated at the continuous level as a direct discretization of the continuous problem and at the discrete level as a coarse-space approximation for its standard finite element (FE) discretizations. Exponential decay rates for local approximation errors with respect to ƍvarepsilon and ƍ(at the discrete level with h denoting the fine FE mesh size) and with the local degrees of freedom are established. In particular, it is shown that the method at the continuous level converges uniformly with respect to\varepsilon in the standard H 1 norm, and that if the oversampling size is relatively large with respect to\varepsilon and h (at the discrete level), the solutions of the local reaction-diffusion equations provide good local approximations for the solution and thus the local eigenfunctions are not needed. Numerical results are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a coarse-scale representation of the elliptic operator, enriched by fine-scale information on the diffusion. Optimal order strong convergence is derived. The LOD technique is combined with a (multilevel) Monte Carlo estimator and the weak error is analyzed. Numerical examples that confirm the theoretical findings are provided, and the computational efficiency of the method is highlighted. [ABSTRACT FROM AUTHOR]

Needled carbon/carbon composites contain complex microstructures such as irregular pores, anisotropic pyrolytic carbon, and interphases between fibers and pyrolytic carbon matrices. Additionally, these composites have hierarchical structures including weftless plies, short-cut fiber plies, and needled regions. To predict the effective elastic properties of needled carbon/carbon composites, this paper proposes a novel sequential multiscale method. At the microscale, representative volume element (RVE) models are established based on the microstructures of the weftless ply, short-cut fiber ply, and needled region, respectively. In the microscale RVE model, a modified Voronoi tessellation method is developed to characterize anisotropic pyrolytic carbon matrices. At the macroscale, an RVE model containing hierarchical structures is developed to predict the effective elastic properties of needled carbon/carbon composites. For the data interaction between scales, the homogenization results of microscale models are used as inputs for the macroscale model. By comparing these against the experimental results, the proposed multiscale model is validated. Furthermore, the effect of porosity on the effective elastic properties of needled carbon/carbon composites is investigated based on the multiscale model. The results show that the effective elastic properties of needled carbon/carbon composites decrease with the increase in porosity, but the extent of decrease is different in different directions.

This work, which can be considered as a small monograph, is devoted to the study of two-and three-dimensional boundary-value problems for eigenvalues of the Laplace operator with frequently alternating type of boundary conditions. The main goal is to construct asymptotic expansions of the eigenvalues and eigenfunctions of the considered problems. Asymptotic expansions are constructed on the basis of original combinations of asymptotic analysis methods: the method of compatibility of asymptotic expansions, the boundary layer method, and the multiscale method. We perform the analysis of the coefficients of the formally constructed asymptotic series. For strictly periodic and locally periodic alternation of the boundary conditions, the described approach allows one to construct complete asymptotic expansions of the eigenvalues and eigenfunctions. In the case of nonperiodic alternation and the averaged third boundary condition, sufficiently weak conditions on the alternation structure are obtained, under which it is possible to construct the first corrections in the asymptotics for the eigenvalues and eigenfunctions. These conditions include in consideration a wide class of different cases of nonperiodic alternation. With further, very essential weakening of the conditions on the structure of alternation, it is possible to obtain two-sided estimates for the rate of convergence of the eigenvalues of the perturbed problem. It is shown that these estimates are unimprovable in order. For the corresponding eigenfunctions, we also obtain unimprovable in order estimates for the rate of convergence. [ABSTRACT FROM AUTHOR]

The scientific community has witnessed, lately, a tremendous progress in the fabrication and synthesis of nanomaterials. As a result, it is essential to develop new and efficient numerical techniques that are capable of modeling the behavior of materials at nanoscale with sufficient accuracy. In this work, a novel approach is presented for the multiscale analysis of brittle failure in nanostructures using the phase-field modeling. The specimen at microscale is discretized using finite elements (FEs), whose integration points lie in the representative volume elements (RVEs) at nanoscale. The displacement computed in upper scale for a microstructure that contains an evolving crack is imposed on the boundaries of the RVE in lower scale. On the other hand, the stresses and material properties obtained for the RVE in lower scale are transferred to upper scale to compute stiffness matrices and load vectors. The evolution of the phase-field variable indicates the initiation and propagation of cracks at microscale. In order to avoid time-consuming molecular dynamics (MD) simulations at nanoscale in each step of the analysis, the Mooney–Rivlin material model is used to simulate the behavior of Aluminum (AL) nanostructure at this scale. The approach that is utilized to compute the material constants and the formulation for the multiscale technique combined with the phase-field modeling in upper scale are described in detail. It is discussed how the phase-field variable in microstructure is evolved based on the properties of the RVE in nanostructure. Many numerical examples are presented to demonstrate the application of the proposed multiscale technique in the solution of engineering problems. [ABSTRACT FROM AUTHOR]

Many biophysical effects of electromagnetic radiation are interpreted based on the induced voltage on cellular membranes. It is very instructive to study wideband frequency responses showing how an impinging electromagnetic wave carrying a certain time waveform translates into a time-dependent change in the cell-membrane potentials in any desired tissue. A direct numerical solution of this problem with realistic models for the body and cells results in meshcells of nanometer dimensions, which is unaffordable for almost any computing machine. In this paper, we exploit a multiscale method with serial frequency responses to arrive at the final frequency response for the induced transmembrane potential changes in cerebral cells induced by electromagnetic waves incident on the body. The results show a bandpass characteristic; a frequency window of approximately 10 kHz to 100 MHz as the most sensitive frequency band for neuronal membrane sensing of external electromagnetic fields. [ABSTRACT FROM AUTHOR]

Objective: In this paper, the dynamic characteristics of a miniature shock absorber by electrostatic excitation are studied. The 3 degrees of freedom (DOF) nonlinear forced vibration equations were established by Hamiltonian variational principle. The approximate analytical solution of the nonlinear differential equation is calculated. The nonlinear vibration behavior of the shock absorber under primary resonance was investigated. Methods: The amplitude-frequency response equation and the relational expression of the component system with two dampers (Tuned Mass Damper and Nonlinear Energy Sink passive vibration absorbers) were obtained using the multiscale method. Results: It is found that the amplitudes of main component and dampers may be in the same or opposite direction by adjusting the parameter values. Furthermore, the energy absorbed by the dampers results in decrease of the main component amplitude magically. Meanwhile, it is also concluded that the increase of the damping ratio and/or mass ratio of the two dampers on the system caused a decrease in the amplitude of the main components. Conclusions: TMD and/or NES play an important role in the shock absorption system which can kill the amplitude of the main component magically. The vibration amplitude of the main components can be largely decreased by increasing the mass ratio and damping ratio of TMD and NES. The association of external and internal resonances causes the energy of the external excitation moves to the TMD or NES, thus reducing the amplitude of main component. The amplitudes of main component and dampers may be in the same or opposite direction by adjusting the parameter values. [ABSTRACT FROM AUTHOR]

In this work, we consider a polymer flooding process in heterogeneous media. A system of equations for pressure, water saturation, and polymer concentration describes a mathematical model. For the construction of the fine grid approximation, we use a finite volume method with an explicit time approximation for the transports and implicit time approximation for the flow processes. We employ a loose coupling approach where we first perform an implicit pressure solve using a coarser time step. Subsequently, we execute the transport solution with a minor time step, taking into consideration the constraints imposed by the stability of the explicit approximation. We propose a coupled and splitted multiscale method with an online local correction step to construct a coarse grid approximation of the flow equation. We construct multiscale basis functions on the offline stage for a given heterogeneous field; then, we use it to define the projection/prolongation matrix and construct a coarse grid approximation. For an accurate approximation of the nonlinear pressure equation, we propose an online step with calculations of the local corrections based on the current residual. The splitted multiscale approach is presented to decoupled equations into two parts related to the first basis and all other basis functions. The presented technique provides an accurate solution for the nonlinear velocity field, leading to accurate, explicit calculations of the saturation and concentration equations. Numerical results are presented for two-dimensional model problems with different polymer injection regimes for two heterogeneity fields. [ABSTRACT FROM AUTHOR]

In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only. Hence, no restrictive assumptions on the coefficient, the domain, or the exact solution are required. In the spirit of localized orthogonal decomposition, the method constructs coarse problem-adapted ansatz spaces by solving auxiliary problems on local subdomains. More precisely, our approach is based on the strategy presented by Maier [SIAM J. Numer. Anal., 59 (2021), pp. 1067--1089]. The unique selling point of the proposed method is an improved localization strategy curing the effect of deteriorating errors with respect to the mesh size when the local subdomains are not large enough. We present a rigorous a priori error analysis and demonstrate the performance of the method in a series of numerical experiments. [ABSTRACT FROM AUTHOR]

This study develops a new clustering method for high-dimensional zero-inflated time series data. The proposed method is based on thick-pen transform (TPT), in which the basic idea is to draw along the data with a pen of a given thickness. Since TPT is a multi-scale visualization technique, it provides some information on the temporal tendency of neighborhood values. We introduce a modified TPT, termed 'ensemble TPT (e-TPT)', to enhance the temporal resolution of zero-inflated time series data that is crucial for clustering them efficiently. Furthermore, this study defines a modified similarity measure for zero-inflated time series data considering e-TPT and proposes an efficient iterative clustering algorithm suitable for the proposed measure. Finally, the effectiveness of the proposed method is demonstrated by simulation experiments and two real datasets: step count data and newly confirmed COVID-19 case data. [ABSTRACT FROM AUTHOR]

We studied two main bioactive molecules of oregano, carvacrol and thymol, in the present work. These bioactive conformers are linked to single wall carbon nanotubes (SWCNT) and so-called functionalized SWCNT (f-SWCNT) to find their application as anti-inflammatory drugs. We use the multiscale methods and the density functional theory (DFT) of formalism to achieve this aim. We have proposed two nanocarriers based on a finite size model of a metallic single wall carbon nanotube linked to carvacrol and thymol (with a size around 2.74 nm): the main bioactives present in oregano. The results show that the proposed molecules, Carva-SWCNT-Gluc and Thymol-SWCNT-Gluc, can be synthesized with the exposed condensation reaction; with an exergonic and spontaneous behavior, Gibbs free energies of the reaction are −1.75 eV and −1.81 eV, respectively. The studied molecules are subjected to an electronic characterization, considering the global descriptors based on the conceptual DFT formalism. Moreover, the results show that the studied molecules can present a possible biocompatibility due to the higher polarization of the molecule and the increase in apparent solubility. Finally, the interaction between the studied nanodevices (Carva-SWCNT-Gluc and Thymol-SWCNT-Gluc) with cancer and anti-inflammatory targets shows that the hydrogen bond and electrostatic interactions play a crucial role in the ligand–target interaction. The proposed f-SWCNT presents higher potentiality as a carrier vector nanodevice since it can deliver the oregano bioactives on the studied targets, promoting the putative apoptosis of neoplastic cells and simultaneously regulating the inflammatory process.

Vitrimer composites with bond- exchange reactions offer significant advantages in terms of repair and recyclability. The mechanical properties of such composites can be designed by modifying the epoxy/anhydride ratio, thus allowing their interface properties to be customised. In this study, the mode-I interfacial fracture properties of vitrimer carbon fibre composites with different epoxy/anhydride ratios are investigated experimentally and numerically. The results show that composites with an epoxy/anhydride group ratio of 1:0.5 exhibit the highest fracture toughness, with a maximum value of 1.6 mJ/mm2. Meanwhile, the analysis of the composites’ microscopic fracture morphology indicates their good bonding performance with carbon fibres. Subsequently, a multiscale numerical approach is developed to simulate the mode-I fracture response of composite laminates and establish a trilinear cohesive model to simulate the macroscopic interfacial fracture behaviour. In this approach, a matrix elastic–plastic constitutive model and the J-integral method are applied to obtain the stress distribution in the fibre-bridging phase via a double cantilever beam fracture test. The macroscopic fracture behaviour obtained via simulation is consistent with the experimental results. Therefore, the proposed multiscale numerical simulation method, which correlates the matrix properties with macroscopic fracture parameters, allows the interlaminar properties of composites with novel matrices to be evaluated effectively.

The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary and initial values instead of periodic boundary and time conditions. Further, we give a detailed a priori error analysis of the fully discretized, i.e., in space and time for both the macroscopic and the cell problem, method. Numerical experiments illustrate the theoretical convergence rates. [ABSTRACT FROM AUTHOR]

Mechanical responses and damage behaviors of asphalt pavement are closely associated with the mesostructure characteristics of the asphalt mixture. The aim of this research was to investigate the effect of the different mesostructure characteristics of asphalt mixtures on pavement damage behavior through a multiscale finite-element (FE) analysis method. A two-dimensional (2D) random aggregate generation algorithm was used to construct the mesostructures of asphalt mixtures with different characteristics, including aggregate distribution uniformity, shape, volume fraction, and size range. Bilinear cohesive elements were used to model damage initiation within asphalt pavement. Also, the nonuniformity coefficient (NUC) was applied to evaluate the uniformity of aggregate distribution within asphalt pavement. The results indicated that the NUC could well characterize the uniformity of coarse aggregate distribution in pavement, and the damage initiation zone became larger as the NUC increased. Compared with regular aggregates, irregular shape aggregates led to more damage initiation in asphalt pavement. For regular shape aggregates, the damage initiation zone became smaller as the aggregate shape approached the circle. In addition, the decrease of aggregate size and volume fraction could increase the possibility of "top-down" cracking of pavement. [ABSTRACT FROM AUTHOR]

In this paper, a generalized finite element (FE) method with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically studied. The local spaces are built from selected eigenvectors of carefully designed local eigenvalue problems defined on generalized harmonic spaces. At both continuous and discrete levels, (i) wavenumber explicit and nearly exponential decay rates for local and global approximation errors are obtained without any assumption on the size of subdomains and (ii) a quasi-optimal convergence of the method is established by assuming that the size of subdomains is O(1/k) (k is the wavenumber). A novel resonance effect between the wavenumber and the dimension of local spaces on the decay of error with respect to the oversampling size is implied by the analysis. Furthermore, for fixed dimensions of local spaces, the discrete local errors are proved to converge as h → 0 (h denoting the mesh size) toward the continuous local errors. The method at the continuous level extends the plane wave partition of unity method [I. Babuška and J. M. Melenk, Internat. J. Numer. Methods Engrg., 40 (1997), pp. 727-758] to the heterogeneous-coefficients case, and at the discrete level, it delivers an efficient noniterative domain decomposition method for solving discrete Helmholtz problems resulting from standard FE discretizations. Numerical results are provided to confirm the theoretical analysis and to validate the proposed method. [ABSTRACT FROM AUTHOR]

A multiscale procedure was proposed for modeling the kinetics of stress-strain state of large-sized structures during site welding. This procedure is based on finite-element solution of nonstationary thermoplasticity problems, characteristic for fusion welding technologies, at the mesoscale level with fine spatial breakdown of the region and with subsequent transfer of a certain amount of calculation data into a macroscopic model of a large-scale structure. Algorithms of the respective averaging of the properties and stress-strain state parameters are proposed for this purpose, which allows performing analysis of large-sized structures during welding without the need to involve significant computing power. A characteristic example of site welding of a cylindrical structure of a large diameter is used to show the applicability of the developed approach for prediction of spatial distribution of stresses and strains. Here, the most effective method is calculation of the stress fields, where a much greater sparseness of the spatial breakdown can be achieved, while calculation of the strained state is much more sensitive to finite element size. [ABSTRACT FROM AUTHOR]