Large Degree Of Freedom Research Articles

Stability of oscillation quenching in coupled oscillator populations with heterogeneous coupling.

Coupled oscillator models are of fundamental importance for understanding the collective dynamics that underlie many realistic applications ranging from physics andbiology to human society. Here, we investigate the dynamics of oscillation quenching in a system of globally coupled Stuart-Landau limit-cycle oscillators incorporating the random heterogeneous interactions. We aim to provide a generic approach to systematically comprehending stability properties, as well as to appreciating the underlying emergent mechanism, of the quenching dynamics under the impression of inhomogeneous couplings. Importantly, we uncover that the peculiar symmetry of the linearized system profoundly facilitates the analysis of the algebraic structures of the eigenspectrum, thereby reformulating the characteristic equationsdeciding the eigenvalues in the simple forms for both finite and infinite sizes of the coupled system. In particular, the critical conditions manifesting the onset of oscillation quenching can be analytically characterized in terms of the matrix theory with finite-rank perturbation. Our work, thus, is capable of providing insights for controlling and regulating the oscillatory dynamics in complex systems consisting of interacting agents with large degrees of freedom.

Dynamics of N-elastically longitudinal coupled rotating pendulums with smooth and discontinuous nonlinearities: Generation of chaotic bursting with many orbits as a solution

The dynamics of a mechanical network, consisting of a certain number (N) of cells, in which each unit cell consists of the irrational coupling of a simple pendulum and inclined mass-spring oscillator, is investigated. The single cell was recently introduced by Ning Han and Qingjie Cao, and it has strong irrational nonlinearity, exhibiting smooth and discontinuous characteristics due to the geometry configuration. The obtained network has a large degree of freedom and consequently has richer dynamics as compared to a single one. The set of discrete equations of this network is found, while the first equation is driven by an external sinusoidal force; the variables here are the angles between the vertical direction and the directions of mass in each unit cell. By using the non-driven version of this set of equations, the equilibrium points are found as well as their stability using the Jacobian matrix. Then, by using the multiple time scale method, the solutions of the set of the network equations are found for weak amplitude oscillations of the system, while the large amplitude solutions are found numerically, showing the ability of the network to transform the shape of some solutions at the input to other forms as the signals evolve in the network. One notices the generation of simple chaotic signals as well as the train of impulse signals. What is important here is the generation of the chaotic bursting with many orbits by the system, which are the simultaneous oscillations around several fixed points. For the case of numerous cells, the system can be used as a waveguide; this is why the set of the equation of the network is reduced to the extended complex Ginzburg Landau (ECGL) equation, with complex nonlinear dispersion and nonlocality terms, using the Tanuiti's reduction perturbation methods. The dissipative dark compacton and peakon as solutions for the ECGL equation are then found. The input-output matching of the network is next investigated via the transfer function of the system near the equilibrium points. The inverse Fourier transform of the transfer function multiplied by the Fourier transform of the input sinusoidal force gives the solution of the network equation for low amplitude oscillations. Finally, the supratransmission condition is studied, leading to the fact that the input sinusoidal signal with frequency nearly inside the forbidden gap zone gradually transforms into the train of chaotic bursting.

The external assurance of ESG reports in Poland on the example of companies from the WIG20 index

Purpose: The article identifies the basic practices that audit companies use when auditing ESG reports in Poland after 2017. Methodology/approach: The study covered 120 ESG reports published by companies included in the WIG20 index between 2017 and 2022. The first stage of the research involved selecting companies from the research sample whose reports were externally audited. The second stage involved analyzing the contents of the assurance reports. The article also used bibliometric analysis, a critical literature review, comparative analysis, and induction and synthesis methods. Findings: The empirical research shows that out of 120 sustainability reports, only 36 were externally audited. A detailed analysis allowed the identification of audit firms’ basic practices: (1) the most common reference is to a report from an independent assurance service with limited certainty, (2) half of the reports were prepared by the “Big Four”, (3) all reports followed the International Standard for Assurance Services 3000, (4) the most common subject of the audits was GRI indicators, which were listed exhaustively in the report.Research limitations/implications: The research was conducted on a relatively small sample – only companies from the WIG20 index; additionally, the time scope of the research only covered reports from 2017–2022.Originality/value: The article contributes to the Polish literature on the subject but also has practical significance. The results of the empirical study indicate that audit reports are created with a large degree of freedom, which may negatively affect their cognitive value and comparability.

Model order reduction of thermal-dynamic coupled flexible multibody system with multiple varying parameters

Spacecrafts usually suffer from the thermal shock during operation, leading to large control error or even failure. At the same time, spacecrafts are often rigid-flexible coupled multibody systems with large degrees of freedom and multiple varying parameters. The real-time control and condition monitoring require effective order reduction methods. In this investigation, the displacement and temperature fields are discretized by the Absolute Node Coordinate Formulation (ANCF) to achieve unified description. The coupled thermal-dynamic reduced-order model (ROM) is established based on the Proper Orthogonal Decomposition (POD) method. For the purpose of further increase efficiency, a linearization method is introduced so that the calculation times of the elastic force can be significantly reduced. In order to predict the response of the thermal-dynamic coupled system with multiple varying parameters, the interpolation on Grassmann manifold is introduced to maintain the orthogonality of the basis. As verification and validation, three numerical examples are presented to show the feasibility and efficacy of the proposed method.

Visuo-dynamic self-modelling of soft robotic systems.

Soft robots exhibit complex nonlinear dynamics with large degrees of freedom, making their modelling and control challenging. Typically, reduced-order models in time or space are used in addressing these challenges, but the resulting simplification limits soft robot control accuracy and restricts their range of motion. In this work, we introduce an end-to-end learning-based approach for fully dynamic modelling of any general robotic system that does not rely on predefined structures, learning dynamic models of the robot directly in the visual space. The generated models possess identical dimensionality to the observation space, resulting in models whose complexity is determined by the sensory system without explicitly decomposing the problem. To validate the effectiveness of our proposed method, we apply it to a fully soft robotic manipulator, and we demonstrate its applicability in controller development through an open-loop optimization-based controller. We achieve a wide range of dynamic control tasks including shape control, trajectory tracking and obstacle avoidance using a model derived from just 90 min of real-world data. Our work thus far provides the most comprehensive strategy for controlling a general soft robotic system, without constraints on the shape, properties, or dimensionality of the system.

Active Learning-Based Kriging Model with Noise Responses and Its Application to Reliability Analysis of Structures

This study introduces a reliability analysis methodology employing Kriging modeling enriched by a hybrid active learning process. Emphasizing noise integration into structural response predictions, this research presents a framework that combines Kriging modeling with regression to handle noisy data. The framework accommodates either constant variance of noise for all observed responses or varying, uncorrelated noise variances. Hyperparameters and the variance of the Kriging model with noisy data are determined through maximum likelihood estimation to address inherent uncertainties in structural predictions. An adaptive hybrid learning function guides design of experiment (DoE) point identification through an iterative enrichment process. This function strategically targets points near the limit-state approximation, farthest from existing training points, and explores candidate points to maximize the probability of misclassification. The framework’s application is demonstrated through metamodel-based reliability analysis for continuum and discrete structures with relatively large degrees of freedom, employing subset simulations. Numerical examples validate the framework’s effectiveness, highlighting its potential for accurate and efficient reliability assessments in complex structural systems.

An off-grid direction-of-arrival estimator based on sparse Bayesian learning with three-stage hierarchical Laplace priors

For direction-of-arrival (DOA) estimation problems, sparse Bayesian learning (SBL) has achieved excellent estimation performance, especially in sparse arrays. However, numerous SBL-based methods with hyperparameters assigned to Gaussian priors cannot enhance sparsity well, and mainly focus on the nested array (NA) or the co-prime array (CPA) that cause relatively large degree of freedom (DOF) losses. Based on this, we propose a novel method with a Bayesian framework containing three-stage hierarchical Laplace priors that significantly promote sparsity. Moreover, the proposed method is based on the minimum hole array (MHA) that retains a larger array aperture than NA or CPA after redundancy removal, which is required and achieved simultaneously by a denoising operation. In addition, to correct the intractable off-grid model errors caused by grid mismatch, a new refinement operation is developed. And, the refinement empirically outperforms others based on Taylor expansion. Extensive simulations are presented to confirm the superiority of the proposed method beyond state-of-the-art methods.

Dimensional reduction of dynamical systems by machine learning: automatic generation of the optimum extensive variables and their time-evolution map

A framework is proposed to generate a phenomenological model that extracts the essence of a dynamical system (DS) with large degrees of freedom using machine learning. For a given microscopic DS, the optimum transformation to a small number of macroscopic variables, which is expected to be extensive, and the rule of time evolution that the variables obey are simultaneously identified. The utility of this method is demonstrated through its application to the nonequilibrium relaxation of the three-state Potts model.

Calibration methods to fit parameters within complex biological models.

Mathematical and computational models of biological systems are increasingly complex, typically comprised of hybrid multi-scale methods such as ordinary differential equations, partial differential equations, agent-based and rule-based models, etc. These mechanistic models concurrently simulate detail at resolutions of whole host, multi-organ, organ, tissue, cellular, molecular, and genomic dynamics. Lacking analytical and numerical methods, solving complex biological models requires iterative parameter sampling-based approaches to establish appropriate ranges of model parameters that capture corresponding experimental datasets. However, these models typically comprise large numbers of parameters and therefore large degrees of freedom. Thus, fitting these models to multiple experimental datasets over time and space presents significant challenges. In this work we undertake the task of reviewing, testing, and advancing calibration practices across models and dataset types to compare methodologies for model calibration. Evaluating the process of calibrating models includes weighing strengths and applicability of each approach as well as standardizing calibration methods. Our work compares the performance of our model agnostic Calibration Protocol (CaliPro) with approximate Bayesian computing (ABC) to highlight strengths, weaknesses, synergies, and differences among these methods. We also present next-generation updates to CaliPro. We explore several model implementations and suggest a decision tree for selecting calibration approaches to match dataset types and modeling constraints.

Constrained Hybrid Monte Carlo Sampling Made Simple for Chemical Reaction Simulations.

Most electrochemical reactions should be studied under a grand canonical ensemble condition with a constant potential and/or a constant pH value. Free energy profiles provide key insights into understanding the reaction mechanisms. However, many molecular dynamics (MD)-based theoretical studies for electrochemical reactions did not employ an exact grand canonical ensemble sampling scheme for the free energy calculations, partially due to the issues of discontinuous trajectories induced by the particle-number variations during MD simulations. An alternative statistical sampling approach, the Monte Carlo (MC) method, is naturally appropriate for the open-system simulations if we focus on the thermodynamic properties. An advanced MC scheme, the hybrid Monte Carlo (HMC) method, which can efficiently sample the configurations of a system with large degrees of freedom, however, has limitations in the constrained-sampling applications. In this work, we propose an adjusted constrained HMC method to compute free energy profiles using the thermodynamic integration (TI) method. The key idea of the method for handling the constraint in TI is to integrate the reaction coordinate and sample the rest degrees of freedom by two types of MC schemes, the HMC scheme and the Metropolis algorithm with unbiased trials (M(RT)2-UB). We test the proposed method on three different systems involving two kinds of reaction coordinates, which are the distance between two particles and the difference of particles' distances, and compare the results to those generated by the constrained M(RT)2-UB method serving as benchmarks. We show that our proposed method has the advantages of high sampling efficiency and convenience of implementation, and the accuracy is justified as well. In addition, we show in the third test system that the proposed constrained HMC method can be combined with the path integral method to consider the nuclear quantum effects, indicating a broader application scenario of the sampling method reported in this work.

Embodied mechanisms of motor control in the octopus

Achieving complex behavior in soft-bodied animals is a hard task, because their body morphology is not constrained by a fixed number of jointed elements, as in skeletal animals, and thus the control system has to deal with practically an infinite number of control variables (degrees of freedom). Almost 30 years of research on Octopus vulgaris motor control has revealed that octopuses efficiently control their body with strategies that emerged during the adaptive coevolution of their nervous system and body morphology. In this minireview, we highlight principles of embodied organization that were revealed by studying octopus motor control, and that are used as inspiration for soft robotics. We describe the evolved solutions to the problem, implemented from the lowest level, the muscular system, to the network organization in higher motor control centers of the octopus brain. We show how the higher motor control centers, where the sensory-motor interface lies, can control and coordinate limbs with large degrees of freedom without using body-part maps to represent sensory and motor information, as they do in vertebrates. We demonstrate how this unique control mechanism, which allows efficient control of the body in a large variety of behaviors, is embodied within the animal's body morphology.

Orthotropic metamaterials with freely tailorable elastic constants

To control mechanical waves and structural vibrations, an important method is to design metamaterials with tailored elastic constants, but it is very difficult. In this paper, a simple and universal metamaterial design method is proposed. This orthotropic metamaterial is composed of elements arrayed periodically in space. The element includes two cuboid structures. The first structure is the basic structure of the element, and the second structure is the transformation of the first structure of the element. The first structure of the element is a cuboid structure composed of 24 bars connected by 8 nodes, and the second structure of the element is a cuboid structure composed of 36 bars connected by 14 nodes. This metamaterial has six independent elastic constants, so there is a large degree of freedom in the material design. Therefore, it has great application value in the fields of mechanical metamaterials, elastic wave metamaterials, acoustic metamaterials, and seismic metamaterials, and has also laid the foundation for realizing the dream of controlling mechanical waves and structural vibrations.

Direction of Arrival Estimation of Coherent Wideband Sources Using Nested Array.

Due to their ability to achieve higher DOA estimation accuracy and larger degrees of freedom (DOF) using a fixed number of antennas, sparse arrays, etc., nested and coprime arrays have attracted a lot of attention in relation to research into direction of arrival (DOA) estimation. However, the usage of the sparse array is based on the assumption that the signals are independent of each other, which is hard to guarantee in practice due to the complex propagation environment. To address the challenge of sparse arrays struggling to handle coherent wideband signals, we propose the following method. Firstly, we exploit the coherent signal subspace method (CSSM) to focus the wideband signals on the reference frequency and assist in the decorrelation process, which can be implemented without any pre-estimations. Then, we virtualize the covariance matrix of sparse array due to the decorrelation operation. Next, an enhanced spatial smoothing algorithm is applied to make full use of the information available in the data covariance matrix, as well as to improve the decorrelation effect, after which stage the multiple signal classification (MUSIC) algorithm is used to obtain DOA estimations. In the simulation, with reference to the root mean square error (RMSE) that varies in tandem with the signal-to-noise ratio (SNR), the algorithm achieves satisfactory results compared to other state-of-the-art algorithms, including sparse arrays using the traditional incoherent signal subspace method (ISSM), the coherent signal subspace method (CSSM), spatial smoothing algorithms, etc. Furthermore, the proposed method is also validated via real data tests, and the error value is only 0.2 degrees in real data tests, which is lower than those of the other methods in real data tests.

Hole-Free Nested Array with Three Sub-ULAs for Direction of Arrival Estimation.

Sparse arrays are of deep concern due to their ability to identify more sources than the number of sensors, among which the hole-free difference co-array (DCA) with large degrees of freedom (DOFs) is a topic worth discussing. In this paper, we propose a novel hole-free nested array with three sub-uniform line arrays (NA-TS). The one-dimensional (1D) and two-dimensional (2D) representations demonstrate the detailed configuration of NA-TS, which indicates that both nested array (NA) and improved nested array (INA) are special cases of NA-TS. We subsequently derive the closed-form expressions for the optimal configuration and the available number of DOFs, concluding that the DOFs of NA-TS is a function of the number of sensors and the number of the third sub-ULA. The NA-TS possesses more DOFs than several previously proposed hole-free nested arrays. Finally, the superior direction of arrival (DOA) estimation performance based on the NA-TS is supported by numerical examples.

Implicit inverse force identification method for vibroacoustic finite element model

The two-field vibroacoustic finite-element (FE) model requires a relatively large number of degrees of freedom compared to the monophysics model, and the conventional force identification method for structural vibration can be adjusted for multiphysics problems. In this study, an effective inverse force identification method for an FE vibroacoustic interaction model of an interior fluid–structure system was proposed. The method consists of: (1) implicit inverse force identification based on the Newmark-β time integration algorithm for stability and efficiency, (2) second-order ordinary differential formulation by avoiding the state-space form causing large degrees of freedom, (3) projection-based multiphysics reduced-order modeling for further reduction of degrees of freedom, and (4) Tikhonov regularization to alleviate the measurement noise. The proposed method can accurately identify the unmeasured applied forces on the in situ application and concurrently reconstruct the response fields. The accuracy, stability, and computational efficiency of the proposed method were evaluated using numerical models and an experimental testbed. A comparative study with the augmented Kalman filter method was performed to evaluate its relative performance.

Spherical Hybrid Nanoparticles for Homann Stagnation-Point Flow in Porous Media via Homotopy Analysis Method

Non-axisymmetric stagnant-point flows for flat plates in porous media containing spherical Cu-Al2O3-H2O nanoparticles are studied using the homotopy analysis method (HAM). The governing equations are transformed into three coupled non-linear ordinary differential equations through similarity transformations. A large degree of freedom is provided by HAM when selecting auxiliary linear operators. By transforming nonlinear coupled ordinary differential equations with variable coefficients into linear ordinary differential equations with constant coefficients, nonlinear coupled ordinary differential equations can be solved. Over the entire domain, these equations can be solved approximately analytically. The analysis involves a discussion of the impact of many physical parameters generated in the proposed model. The results have shown that skin friction coefficients of Cfx and Cfy increase with volume fraction of hybrid nanofluid and the coefficient of permeability increasing. For the axisymmetric case of γ = 0, when volume fraction, φ, φ1, φ2 = 0, 5%, 10%, 20%, Cfx = Cfy = 1.33634, 1.51918, 1.73905, 2.33449, it can be found that the wall shear stress values increase by 13.68%, 30.14%, and 74.69%, respectively. In response to an increase in hybrid nanofluid volume fractions, local Nusselt numbers Nux increase. Nux decrease and change clearly with the coefficient of permeability increasing in the range of γ < 0; the values of Nux are less affected in the range of γ > 0.

Electromagnetic monitoring with local mesh for time-lapse monitoring of hydraulic fracturing

The controlled-source electromagnetic method (CSEM) is a useful tool for monitoring underground fluid movement due to hydraulic fracturing. To understand the characteristics of time-lapse monitoring, an efficient three dimensional(3D) forward modeling is a premise. However, 3D finite element method (FEM) employs the normal mesh that applies fine grids to model the whole sensitive area, resulting in a large degree of freedom (DOF) of the equation that is associated with expensive computation cost. Moreover, time-lapse monitoring requires continual expensive calculations, which lead even an unacceptable computational burden. Inspired by the fact that during the hydraulic fracturing, the resistivity changes occur in a limited domain, we propose a method called as the FEM with local mesh, which is based on secondary field equation to model the EM field perturbation due to hydraulic fracture, and uses fine grids on the fracturing area with resistivity change and as large grids as possible to represent other areas without resistivity change. Therefore, the DOF can be reduced significantly. The numerical tests demonstrate that our method is accurate and has only 10% of the DOF of conventional method.

Laser-printed emissive metasurface as an optical security platform

Optical security is a promising application of metasurfaces because light has large degrees of freedom in metasurfaces. Although many different structures/materials have been proposed for this purpose, the fabrication of dynamic metasurfaces in a straightforward and scalable manner while maintaining a high security level remains a significant challenge. Herein, a metasurface consisting of a phase-changing Ge2Sb2Te5 (GST) layer and a thin metal back reflector is presented to space-selectively and dynamically control the infrared emission of the surface by a spatially modulated pulsed laser beam. Unlike conventional laser processes using a focused beam, the employed laser printing is an expanded beam-based parallel process that enables the fabrication of wafer-sized emission patterns. Owing to the multispectral responses of GST, mutually independent visible and infrared images can be printed in one region. Grayscale emission patterns can also be obtained by gradually modulating the spatial profile of the laser beam, which makes the replication of laser-printed emission patterns extremely difficult. We also demonstrate that colors images can be obtained by depositing IR lossless layer on the GST surface. All these features indicate that the presented emissive metasurface has the potential for use as an effective platform for anti-counterfeiting.

Multi-objective optimization of actuation waveform for high-precision drop-on-demand inkjet printing

High-precision drop-on-demand (DOD) inkjet printing has been considered as one of the promising technologies for the fabrication of advanced functional materials. For a DOD printer, high-precision dispensing techniques for achieving satellite-free smaller droplets have long been desired for patterning thin-film structures. Optimization of an actuation waveform driving a DOD inkjet printer is one of the most versatile and effective strategies to obtain high-precision droplets. Considering the complexity of physics behind the droplet dispensing mechanisms and the large degrees of freedom in the applied waveforms, conventional trial-and-error approaches are not effective for searching the optimal waveform. The present study considers the inlet velocity of a liquid chamber located upstream of a dispensing nozzle as a control variable and aims to develop an automated waveform tuning framework to optimize its waveform using a sample-efficient Bayesian optimization (BO) algorithm. First, the droplet dispensing dynamics are numerically reproduced by using an open-source OpenFOAM solver, interFoam, and the results are passed on to another code based on PyFoam. Then, the parameters characterizing the actuation waveform driving a DOD printer are determined by the BO algorithm so as to maximize a prescribed multi-objective function expressed as the sum of two factors, i.e., the size of a primary droplet and the presence of satellite droplets. The results show that the present BO algorithm can successfully find high-precision dispensing waveforms within 150 simulations. Specifically, satellite droplets can be effectively eliminated and the droplet diameter can be significantly reduced to 24.9% of the nozzle diameter by applying the optimal waveform. Moreover, the prediction using the Gaussian process regression suggests that the size of the primal droplet is highly correlated with the period of a waveform. Finally, the criterion for achieving single-droplet dispensing is proposed based on the energy budget analysis.

Progress and challenges in the development of ultra-wide bandgap semiconductor α-Ga2O3 toward realizing power device applications

Ultra-wide-bandgap (UWBG) semiconductors, such as Ga2O3 and diamond, have been attracting increasing attention owing to their potential to realize high-performance power devices with high breakdown voltage and low on-resistance beyond those of SiC and GaN. Among numerous UWBG semiconductors, this work focuses on the corundum-structured α-Ga2O3, which is a metastable polymorph of Ga2O3. The large bandgap energy of 5.3 eV, a large degree of freedom in band engineering, and availability of isomorphic p-type oxides to form a hetero p–n junction make α-Ga2O3 an attractive candidate for power device applications. Promising preliminary prototype device structures have been demonstrated without advanced edge termination despite the high dislocation density in the epilayers owing to the absence of native substrates and lattice-matched foreign substrates. In this Perspective, we present an overview of the research and development of α-Ga2O3 for power device applications and discuss future research directions.