Multiscale Analysis Research Articles

Determining reaction rate parameters for an energetic material through inverse multi-scale analysis of shock-to-detonation transition

Determining reaction rate parameters for an energetic material through inverse multi-scale analysis of shock-to-detonation transition

The Nonlinear Schrödinger Equation Derived from the Third Order Korteweg-de Vries Equation Using Multiple Scales Method

Nonlinear equations of evolution (NLEE) are mathematical models used in various branches of science. As a result, nonlinear equations of evolution have served as a language for formulating many engineering and scientific problems. For this reason, many different and effective techniques have been developed regarding nonlinear equations of evolution and solution methods. Although the origin of nonlinear equations of evolution dates back to ancient times, there have been significant developments regarding these equations from the past to the present. The main reason for this situation is that nonlinear equations of evolution involve the problem of nonlinear wave propagation. In recent years, equations of formation have become increasingly important in applied mathematics. This work focuses on the perturbation approach, often known as many scales, for nonlinear evolution equations. The article focuses on the analysis of the (1+1) dimensional third-order nonlinear Korteweg-de Vries (KdV) equation using the multiple scales method, which resulted in obtaining nonlinear Schrödinger (NLS) type equations.

Sufficient condition for polynomial solvability of random 3-CNF formulas

This paper is devoted to the localisation of random 3-CNF formulas that are polynomially solvable by the resolution algorithm. It is shown that random formulas with the number of clauses proportional to the square of the number of variables, are polynomially solvable with probability close to unity when the proportionality coefficient exceeds the found threshold.

Surrogate PHFGMC micromechanical models for multiscale analysis: AI-enhanced low-velocity impact analysis of hat-stiffened composite panels

The Parametric High-Fidelity Generalized Method of Cells (PHFGMC) has been established as an advanced micromechanical approach well-suited for analyzing the material nonlinearity and failure behavior of diverse periodic composite materials. In order to overcome the prohibitive computational cost of integrating micromechanical models into multiscale structural analyses as constitutive models, a proxy-surrogate modeling approach has been proposed by implementing a reduction modeling approach with deep Artificial Neural Networks (DNNs or ANNs). The PHFGMC-ANN approach has been employed to investigate the low velocity impact (LVI) analyses of hat-stiffened laminated composite panels under impact loading at various locations and energies with two different support conditions. Subsequent analysis of stiffened panels under compression loading has been conducted to understand the failure behavior of impacted panels. Further investigation was conducted into the separation between the skin and the stiffener, focusing on a single hat-stiffened coupon subjected to LVI. The analysis results have been compared against the experimental tests, and the comparison of interlaminar delamination has been used to demonstrate the efficacy of the new framework in integrating refined nonlinear micromechanical models within a multiscale analysis.

A novel epilepsy detection approach using intrinsic multiscale entropy analysis and DSEAM-enhanced 1D-ResNets

Abstract Epilepsy, a prevalent neurological disorder, typically requires a complex diagnostic process involving medical history inquiry, physical examination, head computed tomography, and electroencephalogram (EEG) visual examination. Among the existing epilepsy automated detection algorithms, machine learning methods require manual feature selection. Most of deep learning algorithms for automatic detection have high complexity and computational complexity. To address this issue, this study proposes a high-precision, robust, and low computational epilepsy automatic detection algorithm based on EEG signal processing. The study utilizes ensemble empirical mode decomposition to preprocess the original EEG signal, breaking it down into intrinsic mode functions (IMFs) across various frequency bands. These IMFs contain information about epilepsy occurrence within the signal at different frequency bands. To enhance computational efficiency and reduce data dimension, the refined composite multiscale dispersion entropy of each IMF is further computed at different scales, referred to as intrinsic multiscale entropy (IME) analysis. IME analysis consolidates epilepsy occurrence information from EEG signals across different frequency bands and scales, linking entropy values to generate feature vectors. Drawing inspiration from successful deep residual networks and Squeeze-and-Excitation networks, the study introduces a double Squeeze-and-Excitation attention module enhanced one-dimensional residual network to classify one-dimensional feature vectors. The proposed method was tested on epilepsy dataset from University of Bonn, and the results demonstrated superior classification performance. In the experiment, the distinction between normal and epileptic EEG signals achieved 100% accuracy rate, while distinguishing between normal, epileptic interval, and epileptic EEG signals achieved accuracy rate of 99.41%.

Multi-scale finite element analysis of laser-assisted forming of CF/PEEK composite corner structures

Laser-assisted forming can significantly increase the forming efficiency of thermoplastic composites. However, when forming CF/PEEK curved corner structures using laser-assisted forming, bending spring-back generated by the prepreg tape constrains the shape accuracy of the component. The bending deformation of unidirectional resin matrix composite materials is highly nonlinear. In this study, a multi-scale finite element method is used to obtain the bending properties of CF/PEEK composites for bending spring-back phenomenon of thermoplastic composite samples and predict the spring-back angle of CF/PEEK corner structures fabricated via laser-assisted forming. The average material properties were first calculated using RVE. Following this, a mesoscale model was developed to analyze kink deformation of the composite. Finally, the macroscopic prepreg bending spring-back was calculated. It was determined that the main mechanism of corner forming corresponds to the occurrence of a fiber kinking phenomenon on the interior of the corner. Furthermore, spring-back deformation is caused by residual stresses resulting from insufficient fiber kinking. The accuracy of the simulation results is verified via corner forming experiments. This study contributes to a deeper understanding of the spring-back mechanisms of laser-assisted forming of corner structures and provides a theoretical guidance for precision forming of multilayer thermoplastic composite bent structures.

Multi-scale stochastic dynamic analysis of a damaged pretwisted composite strip

Multi-scale stochastic dynamic analysis of a damaged pretwisted composite strip

Nanoconfined multiscale heat transfer analysis of hybrid nanofluid flow with magnetohydrodynamic effect and porous surface interaction

Nanoconfined multiscale heat transfer analysis of hybrid nanofluid flow with magnetohydrodynamic effect and porous surface interaction

An Efficient Analysis of Amplitude and Phase Dynamics in Networked MEMS-Colpitts Oscillators

Abstract This paper explores the interactions of both phase and amplitude in a network of N MEMS-Colpitts oscillators that are resistively coupled. The numerical simulations of the extensive networks of oscillators, required for emerging applications such as clock synchronization and neuromorphic computing, become computationally prohibitive as the number of oscillators increases. This complicates the design and evaluation of such systems, as understanding the effects of changes in coupling and design parameters can require many simulations. This study employs the method of multiple scales (MS) in combination with the harmonic balance method to convert the coupled differential equations governing the system of oscillators into a set of nonlinear evolution equations for the amplitude and phase of the oscillators. The amplitude and phase evolve on a timescale that is slow, commensurate with the damping in the system, compared with the fast timescale of the oscillation frequencies. The approach used in this study to describe the amplitude and phase dynamics offers significant computational efficiency (gains of 10× to 50× are shown) compared to direct numerical integration while maintaining an accurate representation of the response. The results of the presented simulations demonstrate the effect of coupling strength on the dynamics of the network, accounting for both phase and amplitude dynamics.

Multi-Scale Analysis of Carbon Emissions in Coastal Cities Based on Multi-Source Data: A Case Study of Qingdao, China

Coastal cities, as centers of economic and industrial activity, accommodate over 40% of the national population and generate more than 70% of the GDP. They are critical centers of carbon emissions, making the accurate and long-term analysis of spatiotemporal carbon emission patterns crucial for developing effective regional carbon reduction strategies. However, there is a scarcity of studies on continuous long-term carbon emissions in coastal cities. This study focuses on Qingdao and explores its carbon emission characteristics at the city, county, and grid scales. Data from multi-source are employed, integrating net primary production (NPP), energy consumption, and nighttime light data to construct a carbon emission estimation model. Additionally, the Tapio model is applied to examine the decoupling of GDP from carbon emissions. The results indicate that the R2 of the carbon emission inversion model is 0.948. The central urban areas of Qingdao’s coastal region are identified as hotspots for carbon emissions, exhibiting significantly higher emissions compared to inland areas. There is a notable dependence of economic development on carbon emissions, and the disparities in economic development between coastal and inland areas have resulted in significant geographical differentiation in the decoupling state. Furthermore, optimizing and transitioning the energy structure has primarily contributed to carbon reduction, while exceptional circumstances, such as the COVID-19 pandemic, have led to passive fluctuations in emissions. This study provides a scientific reference for coastal cities to formulate targeted carbon reduction policies.

Enhancing perceptual, attentional, and working memory demands through variable practice schedules: insights from high-density EEG multi-scale analyses.

Contextual interference (CI) enhances learning by practicing motor tasks in a random order rather than a blocked order. One hypothesis suggests that the benefits arise from enhanced early perceptual/attentional processes, while another posits that better learning is due to highly activated mnemonic processes. We used high-density electroencephalography in a multi-scale analysis approach, including topographic analyses, source estimations, and functional connectivity, to examine the intertwined dynamics of attentional and mnemonic processes within short time windows. We recorded scalp activity from 35 participants as they performed an aiming task at three different distances, under both random and blocked conditions using a crossover design. Our results showed that topographies associated with processes related to perception/attention (N1, P3a) and working memory (P3b) were more pronounced in the random condition. Source estimation analyses supported these findings, revealing greater involvement of the perceptual ventral pathway, anterior cingulate and parietal cortices, along with increased functional connectivity in ventral alpha and frontoparietal theta band networks during random practice. Our results suggest that CI is driven, in the random compared to the blocked condition, by enhanced specific processes such as perceptual, attentional, and working memory processes, as well as large-scale functional networks sustaining more general attentional and executive processes.

Regimes of stratified turbulence at low Prandtl number

Quantifying transport by strongly stratified turbulence in low Prandtl number ( $Pr$ ) fluids is critically important for the development of better models for the structure and evolution of stellar and planetary interiors. Motivated by recent numerical simulations showing strongly anisotropic flows suggestive of a scale-separated dynamics, we perform a multiscale asymptotic analysis of the governing equations. We find that, in all cases, the resulting slow–fast systems take a quasilinear form. Our analysis also reveals the existence of several distinct dynamical regimes depending on the emergent buoyancy Reynolds and Péclet numbers, $Re_b = \alpha ^2 Re$ and $Pe_b = Pr Re_b$ , respectively, where $\alpha$ is the aspect ratio of the large-scale turbulent flow structures, and $Re$ is the outer-scale Reynolds number. Scaling relationships relating the aspect ratio, the characteristic vertical velocity and the strength of the stratification (measured by the Froude number $Fr$ ) naturally emerge from the analysis. When $Pe_b \ll \alpha$ , the dynamics at all scales is dominated by buoyancy diffusion, and our results recover the scaling laws empirically obtained from direct numerical simulations by Cope et al. (J. Fluid Mech., vol. 903, 2020, A1). For $Pe_b \ge O(1)$ , diffusion is negligible (or at least subdominant) at all scales and our results are consistent with those of Chini et al. (J. Fluid Mech., vol. 933, 2022) for strongly stratified geophysical turbulence at $Pr =O(1)$ . Finally, we have identified a new regime for $\alpha \ll Pe_b \ll 1$ , in which slow, large scales are diffusive while fast, small scales are not. We conclude by presenting a map of parameter space that clearly indicates the transitions between isotropic turbulence, non-diffusive stratified turbulence, diffusive stratified turbulence and viscously dominated flows, and by proposing parameterisations of the buoyancy flux, mixing efficiency and turbulent diffusion coefficient for each regime.

Effect of Soret diffusion on the growth of spherical crystals in supercooled alloy melts under oscillatory flow.

The growth of spherical crystals in binary alloy melts with thermal diffusion effects under oscillatory flow is investigated analytically. Using the multiple scale method, we derive approximate analytical solutions for both the crystal interface growth rate and the solute concentration. Our results demonstrate that the Soret effect significantly influences both the solute concentration near the crystal interface and the crystal growth rate. Specifically, with a positive Soret coefficient, the growth rate of spherical crystals in a binary dilute alloy melt decreases as the coefficient increases, while the solute concentration near the interface increases. In contrast, with a negative Soret coefficient, the growth rate of the spherical crystals increases as the coefficient decreases, and the solute concentration near the interface decreases. Additionally, the presence of oscillatory flow markedly promotes the grain refinement induced by the Soret effect.

Multiscale Spectral Manifold Wavelet Regularizer for Unsupervised Deep Functional Maps

AbstractIn deep functional maps, the regularizer computing the functional map is especially crucial for ensuring the global consistency of the computed pointwise map. As the regularizers integrated into deep learning should be differentiable, it is not trivial to incorporate informative axiomatic structural constraints into the deep functional map, such as the orientation‐preserving term. Although commonly used regularizers include the Laplacian‐commutativity term and the resolvent Laplacian commutativity term, these are limited to single‐scale analysis for capturing geometric information. To this end, we propose a novel and theoretically well‐justified regularizer commuting the functional map with the multiscale spectral manifold wavelet operator. This regularizer enhances the isometric constraints of the functional map and is conducive to providing it with better structural properties with multiscale analysis. Furthermore, we design an unsupervised deep functional map with the regularizer in a fully differentiable way. The quantitative and qualitative comparisons with several existing techniques on the (near‐)isometric and non‐isometric datasets show our method's superior accuracy and generalization capabilities. Additionally, we illustrate that our regularizer can be easily inserted into other functional map methods and improve their accuracy.

3D morphometry of Martian craters from HRSC DEMs using a multi-scale semantic segmentation network and morphological analysis

The morphology of impact craters reveals the structure and composition of the Martian surface, especially the subsurface conditions and Martian geological history, which have increasing importance in Mars exploration missions. This work presents a 3D morphometric method for detecting and delineating Martian craters, and a 3D morphological analysis was conducted. Specifically, this work first focused on the segmentation of Martian craters. Based on the segmentation results, clustering of crater instances was then carried out. Finally, with the individual craters that were extracted, a morphological analysis involving the measurements of their diameter, depth, area, RMS height, rim height, circularity, and the statistics thereof was performed. Unlike previous studies, which have mainly used optical images and object detection approaches, this work regards crater extraction as a semantic segmentation task instead of an object detection task to better delineate the precise shape and boundary information. Digital elevation model (DEM) was utilized as primary data to directly obtain 3D information, which was converted into 3D point cloud format and fed to a multi-scale semantic segmentation network. The semantic segmentation results achieved an overall accuracy of 0.932 and mIOU of 0.871 on the test data. We automatically counted 63 craters in Noachis Terra and 40 craters in Terra Cimmeria. The 3D morphological measurements showed that 66% of the impact craters in the first region were larger than 10 km in diameter, while 50% of the impact craters in the second region were larger than 10 km. In both areas, craters could reach a maximum depth of 2000 m. With the proposed method, we can automatically conduct 3D morphological measurements of Martian craters with high efficiency that is improved by 15 times compared with that of manual crater analysis tools. The achieved 3D morphometric results can provide a reference and support for future research on Martian landforms.

Multiscale Analyses of Strain-Enhanced Charge Transport in Conjugated Polymers.

The advancement of flexible and wearable electronics relies on semiconducting polymers that can endure mechanical deformation while maintaining high electrical performance under strain. In this study, we demonstrate that fine-tuning backbone rigidity through the molecular design of donor moieties significantly enhances both the mechanical and charge transport properties of diketopyrrolopyrrole (DPP)-based polymers. Specifically, the flexible DPP-4T (quaterthiophene) exhibited a persistence length of 20.4 nm in solution, while DPP-DTT (dithienothiophene) showed a longer persistence length of 32.8 nm due to its stiff backbone, as confirmed by small-angle neutron scattering and Monte Carlo simulations. This flexibility enabled DPP-4T to achieve a crack-onset strain exceeding 100% via the film-on-elastomer method and a fracture strain of over 30% in quasi-free-standing films. Additionally, DPP-4T demonstrated a 180% increase in hole mobility at 80% strain, driven by strain-induced chain alignment and backbone planarization. Utilizing a range of characterization techniques, including ultraviolet-visible (UV-vis) spectroscopy, grazing incidence X-ray diffraction (XRD), and Raman spectroscopy, we characterized structural changes at multiple length scales under applied tensile strain. Notably, strain induced a transformation in chain conformation from a twisted to a flat structure, reducing the hopping energy barrier and enhancing charge transport. These structural rearrangements are crucial for sustaining efficient charge transport and ensuring the reliability of electronic performance under mechanical stress.

Stability and bifurcation analysis of a 2DOF dynamical system with piezoelectric device and feedback control

This study aims to demonstrate the behaviors of a two degree-of-freedom (DOF) dynamical system consisting of attached mass to a nonlinear damped harmonic spring pendulum with a piezoelectric device. Such a system is influenced by a parametric excitation force on the direction of the spring’s elongation and an operating moment at the supported point. A negative-velocity-feedback (NVF) controller is inserted into the main system to reduce the undesired vibrations that affect the system’s efficiency, especially at the resonance state. The equations of motion (EOM) are derived by using Lagrangian equations. Through the use of the multiple-scales-strategy (MSS), approximate solutions (AS) are investigated up to the third order. The accuracy of the AS is verified by comparing them to the obtained numerical solutions (NS) through the fourth-order Runge-Kutta Method (RK-4). The study delves into resonance cases and solvability conditions to provide the modulation equations (ME). Graphical representations showing the time histories of the obtained solutions and frequency responses are presented utilizing Wolfram Mathematica 13.2 in addition to MATLAB software. Additionally, discusses the bifurcation diagrams, Poincaré maps, and Lyapunov exponent spectrums to show the various behavior patterns of the system. To convert vibrating motion into electrical power, a piezoelectric sensor is connected to the dynamical model, which is just one of the energy harvesting (EH) technologies with extensive applications in the commercial, industrial, aerospace, automotive, and medical industries. Moreover, the time histories of the obtained solutions with and without control are analyzed graphically. Finally, resonance curves are used to discuss stability analysis and steady-state solutions.

Nonlinear simultaneous resonance behaviors of a shallow arch model under the moving load

By applying a moving load with the uniform velocity, this paper investigates nonlinear behaviors of a shallow arch model allowing for describing the effects of the initial configuration of the structure. Two different cases are taken into account, namely, simultaneous primary resonances of the first and third modes; simultaneous resonances of the first mode for two-term excitations. First, nonlinear ordinary differential equations (ODEs) of the shallow arch are derived by using Galerkin method. Through introducing different time scales, the ODEs are solved based on the widely utilized method of multiple time scales (MMTS). In this way, the modulation equations for the two cases are derived, on the basis of which the steady state frequency- and force-response curves are obtained. Meanwhile, phase portraits, power spectra and two-parameter bifurcation diagram are also given to assist in analysis on nonlinear behaviors. The results show that the large vibration of the shallow arch under the moving load may occur and primary resonance peaks of the different modes are located in distinct positions.

Effect of geometric variations on the wing rock of blended wing-body aircraft

Blended wing-body configurations are anticipated to dominate future transport and military aerospace designs. The departure of the conventional tube-wing configuration has opened several areas of investigation. These designs are susceptible to lateral instability during landing, takeoff, and maneuvering flight despite having improved aerodynamics because of their tailless nature. One of these instabilities, Wing-Rock, poses significant performance and operational difficulties and can potentially cause crashes. Though experimental and numerical studies of the aerodynamics and stability of blended wing-body configurations have been conducted, wing-rock characteristics still need to be identified in the literature. This research aims to investigate these characteristics at low subsonic speeds with varying outboard sweep and geometric twist angles. The study includes a numerical approach based on the rigid body free-vibration method in single roll degree of motion, which uses three-dimensional unsteady Reynolds’ Average Navier Stokes equations, and an analytical approach based on the multiple time scale method, which captures the crucial aspect of the wing rock system. The findings show that the geometrical parameters significantly impact the wing rock characteristics, which are unique to such novel tailless designs.

Vibration suppression of suspended cables with three-to-one internal resonances via time-delay feedback

Based on the time-delay feedback control, the vibration suppression of suspended cables with three-to-one internal resonances are investigated. Initially, the nonlinear differential equation of motion for a suspended cable under time-delay feedback control is considered, and a discrete model is derived using the Galerkin method. Subsequently, the method of multiple scales is employed to perturbatively solve the discrete time-delay differential equation, determining the modulation equations around the first primary resonance. Steady-state and periodic solutions of the modulation equations are detected numerically. Numerical results indicate that the internal resonance enhances the nonlinear dynamical complexity of the controlled suspended cable. It is observed that the time delay and control gain affect the controlled system: in particular, an increase in control gain leads to a reduction in response amplitude. By adjusting the time delay and control gain, the critical excitation can be altered, an aspect that could be very useful from a pratical point of view. This research sheds light on the intricate dynamics of suspended cable and provides a theoretical foundation for designing more effective control strategies in engineering applications.