Multiscale Analysis Research Articles

The implementation of M-integral in cross-scale correlation analysis of porous materials

The damage analysis caused by mesoscopic pores has attracted much attention in the development and application of porous materials. In this study, a novel application of M-integral is presented to establish a cross-scale correlation analysis of damaged porous materials. The multiscale damage analysis featured here can be proposed in two main steps. In detail, the first step is to construct a quantitative relationship between M-integral and porosity, where the values of M-integral for different porosity are calculated numerically. Subsequently, it applies the variation of M-integral with the material damage represented by a decrease in effective elastic modulus, and a cross-scale correlation between porosity and effective elastic modulus of porous material can be provided. In addition, an example is discussed to illustrate the specific application of this bridging parameter M-integral. The results confirm that M-integral can be an effective parameter bridging mesoscopic porosity and macroscopic damage, and is expected benefit to propose a convenient damage model of porous material. The findings should be of value in investigating the multiscale damage analysis of porous materials.

Exploring the Spatial-Temporal Patterns, Drivers, and Response Strategies of Desertification in the Mu Us Desert from Multiple Regional Perspectives

Desertification poses a serious threat to the global ecological environment and challenges the achievement of an ecological civilization. Understanding the spatial and temporal evolution of desertification in the Mu Us Desert, a key area in northern China, is crucial for predicting regional trends and analyzing causes. This study employs quantitative methods, including remote sensing data from Landsat satellites (2000–2020), combined with multi-scale analysis and statistical models, to systematically analyze desertification trends. The analysis reveals that desertification improved significantly after 2005 due to effective human intervention and governance efforts. In particular, the eastern regions (Shaanxi Province and Inner Mongolia) showed marked improvement, while the western regions exhibited limited change. The greatest progress was seen in the reduction in high-desertification areas to moderate levels. Quantitatively, human activities contributed to a 17.3% reduction in desertification (p < 0.05), while meteorological factors were responsible for a 45.8% reduction (p < 0.05). Conversely, desertification in Ningxia worsened by 41.8% due to unsustainable land use. Additionally, spatial correlation analysis highlighted that those areas of severe desertification became more uniformly distributed over time. The key drivers influencing desertification were agricultural development, urbanization, climate warming, and vegetation coverage, with human activities playing a substantial role. Initially, agricultural factors had the strongest correlation with desertification, but over time, population growth, rising temperatures, and vegetation cover (NDVI) became more prominent. These findings offer scientific support for desertification control in the Mu Us Desert and provide methodological insights for other severely desertified regions, contributing to sustainable ecological development.

Long-range Ising models: Contours, phase transitions and decaying fields

Inspired by Fröhlich–Spencer and subsequent authors who introduced the notion of contour for long-range systems, we provide a definition of contour and a direct proof for the phase transition for ferromagnetic long-range Ising models on \mathbb{Z}^{d} , d\geq 2 . The argument, which is based on a multiscale analysis, works for the sharp region \alpha>d and improves previous results obtained by Park for \alpha>3d+1 , and by Ginibre, Grossmann and Ruelle for \alpha> d+1 , where \alpha is the power of the coupling constant. The key idea is to avoid a large number of small contours. As an application, we prove the persistence of the phase transition when we add a polynomially decaying magnetic field with power \delta>0 as h^{*}|x|^{-\delta} , where h^{*} >0 . For d<\alpha<d+1 , the phase transition occurs when \delta>\alpha-d , and when h^{*} is small enough over the critical line \delta=\alpha-d . For \alpha \geq d+1 , \delta>1 is enough to prove the phase transition, and for \delta=1 we have to ask h^{*} small. The natural conjecture is that this region is also sharp for the phase transition problem when we have a decaying field.

Nonlinear vibro-acoustic analysis of an axially moving submerged circular cylindrical shell

In this study, the nonlinear vibro-acoustic dynamics and stability of doubly-clamped axially moving cylindrical shell are investigated. The exterior surface of the shell is in contact with fluid and subjected to oblique incident plane sound wave. Donnell’s nonlinear shallow shell theory is used to derive the nonlinear partial differential equation of the cylindrical shell for the radial motion. The Galerkin method is employed to discretize the equations of motion into the set of coupled nonlinear nonhomogeneous ordinary second order differential equations. Considering both driven and companion modes, Multiple Scales Method is used to obtain the response of the system. The effects of sound level, incident angle and axially velocity on the frequency response of the system are studied. The results show that, with increase in the shell velocity transmission loss of the circular shell increases. In addition, at low shell axial velocities simultaneous excitation of the driven and companion modes occurs.

Nonlinear resonance of fractional order viscoelastic PET films under temperature loading

The effects of oven temperature during printing on nonlinear vibration for fractional-order PET films are considered in this paper. The effect of temperature, fractional order modelling and some other parameters are analysed with respect to the response of the resonance. Fractional order kelvin-Voigt ontological relationship is used to describe the characteristics of viscoelastic materials. The differential equations for nonlinear vibrations are inferred according to the second law of Newton and the theory of von Karman. Discretization for nonlinear equations on locomotion using the Bubnov–Galerkin method. Forced co-oscillatory amplitude-frequency response equations for thin-films systems under temperature loading were calculated using the multiple scales method. Results of numeral results show that temperature, and fractional-order visco-elastic modelling influence the membrane's response to resonance. These results provide a basis for studying fractional-order visco-elastic films vibrations and identifying regions of stable operation in moving systems to prevent divergent instabilities for flexible electronic device manufacturing.

Multi-scale modeling and mechanical performance analysis of finger seals with plain woven C/C composite

The application of carbon fibers reinforced carbon matrix (C/C) composite can solve the local wear of metallic finger seals effectively. However, the performance of C/C composite finger seal is complex and variable, which further decreases the sealing performance and life. Therefore, a method of multi-scale modeling and mechanical performance analysis for plain woven C/C composite finger seals was conducted. The circumferential finger beams of C/C composite were modeled by multi-scale structural analysis and weaving simulation. The radial static and dynamic stiffness characteristics of finger beams were investigated. The results showed that the radial static stiffness of the finger beam with three layers was about 3 times that with single layer. The radial stiffness of circumferential finger beams presented a periodic distribution pattern with a period of 90°. The radial dynamic stiffness of C/C composite finger beams increased with the excitation displacement amplitude and rotor speed. But the magnitude and fluctuation degree of dynamic stiffness were greater than those of static stiffness. A large difference in radial stiffness will lead to local wear and hysteretic leakage. This study lays a foundation for the analysis and optimization of the hysteresis and wear characteristics of C/C composite finger seals.

Modelling of SARS-CoV-2 spike protein structures at varying pH values

ABSTRACT Recognising the fact that the SARS-CoV-2 spike glycoprotein is the most crucial protein for the virus's attachment to surfaces and subsequent infection, we carried out massive all-atom molecular dynamics studies of the conformational states of S-protein in solvents of various pH values, ranging from pH = 1 through pH = 11. Our studies found that: (1) The S-protein’s structural deviation measured in the backbone at pH = 1 is 185% higher than that of pH = 7, and most of this overall deviation occurs at the receptor-binding domain and N-terminal domain. (2) Structural changes are also observed at both pH = 3 and pH = 11, albeit to a lesser extent than at pH = 1. (3) Changes, as measured by various metrics at pH = 5, pH = 7 and pH = 9, are insignificant. Such a high degree of structural tolerance of the S-protein at these pH values corroborates indirectly with in vitro observations that the virus retains significant infectivity over a wide range of pH. The multiscale structural analyses pinpoint the critical regions that are responsible for the S-protein’s structural deviations.

Multidimensional multiscale complexity analysis of sediment dynamics in the Yanhe Watershed of the loess Plateau, China

The Yanhe Watershed, emblematic of the loess hilly-gully landscape and ecological fragility in China's Loess Plateau, has experienced significant soil erosion and extensive soil-water conservation measures. To elucidate sediment dynamics and identify influencing factors in this region from 1960 to 2020, a novel multidimensional multiscale complexity analysis (MMCA) method was developed, based on entropy and complexity perspectives. This method integrated the refined composite multiscale fuzzy entropy (RCMFE) with multidimensional complexity analysis, offering a nuanced evaluation of sediment complexity and its implications for water resource management and ecological restoration. The findings revealed two distinct stages of sediment complexity variations: 1971–1988 and 2000–present. During the first period, the operation of the Wangyao Reservoir predominantly influenced sediment dynamics, initially reducing sediment complexity through sediment interception but later increasing it during discharge phases, particularly at larger scales. After 2002, extensive vegetation restoration efforts significantly reduced sediment complexity but raised concerns about long-term ecosystem resilience. Over the past decade, urbanization and climate change have exacerbated sediment instability, especially over semi-annual scales. This study advocates for management strategies that prioritize ecosystem sustainability and address the challenges posed by climate change and urbanization, facilitating improved soil and water conservation efforts in the Yanhe Watershed and similar regions in the Loess Plateau.

Steady secondary flow in a turbulent boundary layer past a slender axisymmetric body

The turbulent boundary layer in a viscous incompressible fluid developing longitudinally past the surface of a thin cone or cylinder at a finite distance from the laminar–turbulent transition zone is studied. The characteristic Reynolds number, determined from the external flow velocity and the length of the body, is assumed to be large, and the thickness of the boundary layer is small and comparable to the radius of the body. The asymptotic method of multiple scales is used to find solutions to the Navier–Stokes equations. Instead of the traditional decomposition of the solution into time-averaged values and their fluctuations, the velocities and pressure are expressed as an asymptotic series consisting of steady and perturbed terms. As a result, the viscous steady flow (‘secondary’) that arises in the boundary layer as a mandatory component of fast turbulent fluctuations was described. Analytical and numerical solutions for the radial steady velocity are presented, describing the self-induced suction of fluid from the external flow into the boundary layer. Further analytical solutions are obtained for the longitudinal and circumferential velocities, which differ markedly from the laminar regime. The solutions found are somewhat similar to the degenerate (one-dimensional) case of self-sustaining longitudinal thin structures in turbulent shear flows. A qualitative comparison with direct numerical simulations is presented.

Multi-Scale Analysis of Water Purification Ecosystem Service Flow in Taihu Basin for Land Management and Ecological Compensation

This study investigates the spatial correlation and service flow of supply and demand for water purification ecosystem services at multiple scales (i.e., the Taihu Lake Basin, sub-basin, and county) by quantitatively assessing the supply–demand relationship of nitrogen and phosphorus and introducing the SPANS algorithm to characterize the service flow paths. Through quantitative analysis, the supply–demand relationship between nitrogen and phosphorus was evaluated, and the SPANS algorithm was introduced to characterize the service flow paths. The results show that the water purification ecosystem services in the southwestern region and around Taihu Lake exhibit a good supply–demand balance, while a significant supply–demand deficit is observed in the northern and southeastern regions. Service flow analysis indicates that surplus areas are primarily concentrated in hilly and urbanized central regions, whereas deficit areas are mainly located in non-urban centers. Based on these findings, ecological compensation suggestions are proposed, including dynamic adjustment, differentiated compensation, cross-city collaboration, and guidance of social capital participation, to promote continuous improvement in water quality and sustainable development within the basin.

Nonlinear deterministic dynamic analysis of a GPL micropipe conveying pulsating laminar flow

In several industries, the handling of fluid-filled micropipes is common. New-brand structures are increasingly being manufactured using advanced materials. This article tackles one of the crucial dynamic analyses that an advanced fluid-filled micropipe encounters. The dynamics of a graphene nanoplatelets-reinforced micropipe (GPL micropipe) under pulsating laminar flow for the first time is examined. The Euler-Bernoulli beam model follows the modified couple stress theory (MCST) and von-Karman’s nonlinear strain to formulate the problem. The impression of the flow profile exerted by a real flow as a consequence of fluid viscosity, is taken into account. The plug flow model results are compared to those regarding real flow consideration. Using the method of multiple scales (MMS), we determine the instability area and the steady state response of the GPL micropipe subjected to the principal parametric resonance of one of its modes due to pulsating laminar flow by applying this method to the discretized couple nonlinear gyroscopic governing equations. The Floquet theory treats the linear equations and fourth-order Runge–Kutta (RK4) method attacks nonlinear ones to validate MMS findings. It is confirmed that the 0.3 % addition of the GPL to matrix phase significantly enhances its advanced attributes, making it a highly effective material. The GPL reinforcement phase in the FGO pattern increases the critical flow velocity that exhibits the micropipe to static instability by 37.98 % , and critical flow stimulation amplitude fraction by 152.19 % , while declines instability area bandwidth by 36.95 % , and steady state response by 67.17 % relative to a non-reinforced micropipe. A denser flow degrades the corresponding values by 18.40 % , 42.59 % , 41.67 % , and 227.28 % in comparison to a lighter fluid. The declared findings provide crucial insights into the key design elements affecting significantly the functioning of fluid-filled GPL micropipes system, and regulate future research and expand openings for industry applications.

Advances in Multiscale Modeling and Mechanical Properties Characterization of 3D‐Braided Composites

The 3D‐braided composites have been widely used in aerospace and other fields due to the excellent mechanical properties, designability, and resistance to delamination. Accurately analyzing and evaluating mechanical properties of braided composite structures is the key, which successfully designs related structural components. However, 3D‐braided composites have complex internal meso–microscopic structures, and directly establishing a solid structure model to predict mechanical behavior poses certain challenges. The multiscale research methods are a type of approach that studies the cross‐scale structural characteristics at macro–meso–microscopic scales and couples relevant scales into a whole. Its emergence provides the possibility for evaluating the overall structural performance of 3D‐braided composites. In this article, first, the multiscale analysis models of 3D‐multidirectional‐braided composites are reviewed, and then the theoretical and numerical research progress on the static and dynamic multiscale mechanical performance of regular components of 3D‐braided composites is summarized. In addition, due to the distortion and variation of geometric shapes of 3D‐braided composites on the meso–microscopic structure; therefore, also in this article, the research progress on multiscale mechanical performance characteristics of special‐shaped components is summarized. Finally, the key problems in the multiscale research of 3D‐braided composites are presented.

Pull-in instability and nonlinear vibration of microbeam with piezoelectric patch driven by electrostatic force using modified couple stress theory

The static and dynamic pull-in characteristics of electrostatically and piezo-electrically actuated microbeam are investigated. The static pull-in voltage is evaluated using analytical methods based on MCST, CCMT and validated through the use of FE based COMSOL multiphysics tools. The dynamic pull-in voltage obtained from numerical technique and verified with existing literature, lower than the static pull-in voltage. The piezoelectric patch has a significant influence on the pull-in voltage and an effect on the aspect ratio. Moreover, the pull-in band and instability zone of the microbeam with weak and hard forcing function have been investigated using multiple scale method.

Knot data analysis using multiscale Gauss link integral

In the past decade, topological data analysis has emerged as a powerful algebraic topology approach in data science. Although knot theory and related subjects are a focus of study in mathematics, their success in practical applications is quite limited due to the lack of localization and quantization. We address these challenges by introducing knot data analysis (KDA), a paradigm that incorporates curve segmentation and multiscale analysis into the Gauss link integral. The resulting multiscale Gauss link integral (mGLI) recovers the global topological properties of knots and links at an appropriate scale and offers a multiscale geometric topology approach to capture the local structures and connectivities in data. By integration with machine learning or deep learning, the proposed mGLI significantly outperforms other state-of-the-art methods across various benchmark problems in 13 intricately complex biological datasets, including protein flexibility analysis, protein-ligand interactions, human Ether-à-go-go-Related Gene potassium channel blockade screening, and quantitative toxicity assessment. Our KDA opens a research area-knot deep learning-in data science.

Artificial neural network-enhanced mathematical simulation based on Carrera unified formulation for dynamic analysis and structural integrity assessment of advanced nanocomposites reinforced tunnel structures

This article presents the application of the Carrera Unified Formulation (CUF) for dynamic analysis and structural integrity assessment of advanced nanocomposite-reinforced tunnel structures. CUF offers a generalized framework that simplifies the modeling of complex structures, providing an efficient approach to address the dynamic behavior of nanocomposites. Advanced nanocomposites, which enhance mechanical performance and durability, are increasingly used in critical infrastructure such as tunnel systems. Traditional methods often fall short in capturing the intricate interactions within these materials, particularly under dynamic loads. CUF overcomes these challenges by incorporating higher-order theories and multi-scale analysis, allowing for accurate prediction of displacements, stresses, and potential failure modes. To further validate the results, an Artificial Neural Network (ANN) model is trained using simulated data, ensuring robust predictions for various loading conditions. The ANN assists in approximating the dynamic response and integrity of the structure, enabling real-time assessments with minimal computational expense. The combined CUF-ANN approach demonstrates high accuracy and efficiency, making it a reliable tool for the structural integrity assessment of nanocomposite-reinforced tunnels. This study highlights the significant potential of integrating CUF and ANN for the analysis and design of advanced engineering structures subjected to dynamic environmental conditions.

Quantitative characterization of rubber three-body abrasion wear: multi-scale testing and analysis methods based on defect detection

Abrasive wear is one of the main causes of rapid deterioration of rubber serviceability. Therefore, it is necessary to obtain information on the degree of rubber abrasion and the wear mechanism. Due to the complex nature of abrasive surfaces, obtaining accurate information on rubber abrasion is often difficult and provides limited quantitative parameters. This study presents a method to quantify rubber abrasion through defect detection and analysis. Accurate and fast identification of typical abrasion defects is achieved, and in addition, macro- and microscopic characterization data are provided based on the distribution of defects to understand the degree of abrasion and the wear mechanism. Experimental validation demonstrated the fast and accurate characterization capability of the method, especially the advanced advantages at the microscopic level. The method achieves accurate and efficient characterization of rubber abrasion, which helps to advance the study of rubber tribological behavior and is important for guiding engineering applications and improving design.

Multi-scale analysis of urban forests and socioeconomic patterns in a desert city, Phoenix, Arizona

Understanding the relationship between various socioeconomic factors and urban forest structure is essential for directing resources to ensure equitable distribution of green space. Through a case study of a desert city, i.e., Phoenix, AZ, this study provides a novel application of Multiscale Geographically Weighted Regression (MGWR) in which we explore the spatially variable relationships between a wide array of socioeconomic indicators and urban forest attributes. Through the computation of various scales of influence for different explanatory variables, MGWR enhances our analysis’s precision and stresses the association between socioeconomic status and urban forest structure at local and regional scales. Our results indicate that although there has been a pattern of green inequality where minority and low-income communities have less access to urban forests, education levels were mostly insignificant based on the MGWR results. In some instances, higher incomes are negatively correlated with tree canopy coverage. Additionally, the stem density model outperformed the canopy coverage model in terms of prediction accuracy. This research adds a new dimension to urban forestry literature and emphasizes the value of customized urban planning strategies and the environmental justice implications of urban forestry, particularly in arid environments.

Extending the Natural Neighbour Radial Point Interpolation Meshless Method to the Multiscale Analysis of Sandwich Beams with Polyurethane Foam Core

This work investigates the mechanical behaviour of sandwich beams with cellular cores using a multiscale approach combined with a meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The analysis is divided into two steps, aiming to analyse the efficiency of NNRPIM formulation when combined with homogenisation techniques for a multiscale computational framework of large-scale sandwich beam problems. In the first step, the cellular core material undergoes a controlled modification process in which circular holes are introduced into bulk polyurethane foam (PUF) to create materials with varying volume fractions. Subsequently, a homogenisation technique is combined with NNRPIM to determine the homogenised mechanical properties of these PUF materials with different porosities. In this step, NNRPIM solutions are compared with high-order FEM simulations. While the results demonstrate that RPIM can approximate high-order FEM solutions, it is observed that the computational cost increases significantly when aiming for comparable smoothness in the approximations. The second step applies the homogenised mechanical properties obtained in the first step to analyse large-scale sandwich beam problems with both homogeneous and functionally graded cores. The results reveal the capability of NNRPIM to closely replicate the solutions obtained from FEM analyses. Furthermore, an analysis of stress distributions along the beam thickness highlights a tendency for some NNRPIM formulations to yield slightly lower stress values near the domain boundaries. However, convergence towards agreement among different formulations is observed with mesh refinement. The findings of this study show that NNRPIM can be used as an alternative numerical method to FEM for analysing sandwich structures.

Effects of extreme temperature environments on nonlinear vibrations of the cable-stayed functionally graded beam

A cable-stayed functionally graded beam (CSFGB) model is proposed for the first time to study nonlinear behaviors of the system exposed to extreme temperatures. To this end, the in-plane one-to-one internal resonance between the global mode (FGB's mode) and the local mode (cable's mode) is explored under the condition of external primary resonance. First, governing differential equations of the system considering temperature effects are derived by using Hamilton's principle. To obtain the modal function of the FGB, the in-plane eigenvalue problem is solved through the separation-of-variables method. Subsequently, ordinary differential equations (ODEs) are yielded according to Galerkin discretization. The method of multiple time scales is then applied to deal with the ODEs and derive the modulation equations. Based on the above theoretical solutions, the frequency-/force-response curves at three different temperatures are delineated via Newton-Raphson method and the continuation of fixed points. Meanwhile, the time histories and phase portraits are also provided by directly integrating the ODEs. The results show that temperature changes have a significant influence on nonlinear characteristics of the system.

Approximate solution of a zero-sum linear-quadratic differential game by the auxiliary parameter method: analytical/numerical study

ABSTRACT A zero-sum finite horizon linear-quadratic differential game is considered. First, the terminal-value problem for the game-theoretic Riccati matrix differential equation, associated with the considered game by the solvability conditions, is analysed. This problem may not have the solution in the entire time-interval of the game's duration. Using the method of auxiliary parameter, a sufficient condition (in the terms of the game's data) for the existence of the solution to the aforementioned terminal-value problem in the entire time-interval of the game's duration is derived. An approximate analytical solution to this problem also is obtained as a partial sum of some infinite series of functions arising in the method of auxiliary parameter. Based on this approximate solution, suboptimal state-feedback controls of the players are formally designed and justified. It is shown that the pair of these controls constitutes an approximate-saddle point in the considered game. The theoretical results of the article are illustrated by their application to approximate solution of the problem of pursuit-evasion engagement between two flying vehicles.