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Journal articles on the topic 'Multi-Scale nonlinear dynamics'
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1
Sivapalan, Murugesu, Praveen Kumar, and Daniel Harris. "Nonlinear propagation of multi-scale dynamics through hydrologic subsystems." Advances in Water Resources 24, no. 9-10 (November 2001): 935–40. http://dx.doi.org/10.1016/s0309-1708(01)00028-8.
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LAMARQUE, C. H., A. TURE SAVADKOOHI, E. ETCHEVERRIA, and Z. DIMITRIJEVIC. "MULTI-SCALE DYNAMICS OF TWO COUPLED NONSMOOTH SYSTEMS." International Journal of Bifurcation and Chaos 22, no. 12 (December 2012): 1250295. http://dx.doi.org/10.1142/s0218127412502951.
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Dynamical behavior of a nonsmooth master system which is coupled to a nonsmooth Nonlinear Energy Sink (NES) during free and forced oscillations is studied analytically and numerically. Invariant manifolds of the system and their stable zones at different time scales are revealed and finally application of coupled nonsmooth NES to the passive control process of the main nonsmooth system is highlighted.
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Bartelt, Matthias, and Michael Groß. "Galerkin-based multi-scale time integration for nonlinear structural dynamics." PAMM 14, no. 1 (December 2014): 215–16. http://dx.doi.org/10.1002/pamm.201410095.
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Wu, Zhe, Guang Yang, Qiang Zhang, Shengyue Tan, and Shuyong Hou. "Information Dynamic Correlation of Vibration in Nonlinear Systems." Entropy 22, no. 1 (December 31, 2019): 56. http://dx.doi.org/10.3390/e22010056.
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In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we propose a new method to describe the nonlinear features and coupling relationship of mechanical systems. This manuscript verifies the above hypothesis by using a typical chaotic system and a real macroscopic physical nonlinear system through theory and practical methods. The nonlinear vibration correlation in multi-body mechanical systems is very complex. We propose a full-vector multi-scale Rényi entropy for exploring the chaos and correlation between the dynamic behaviors of mechanical nonlinear systems. The research results prove the effectiveness of the proposed method in modal identification, system dynamics evolution and fault diagnosis of nonlinear systems. It is of great significance to extend these studies to the field of mechanical nonlinear system dynamics.
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KOVALEV, VLADIMIR F. "LIE GROUP ANALYSIS FOR MULTI-SCALE PLASMA DYNAMICS." Journal of Nonlinear Mathematical Physics 18, sup1 (January 2011): 163–75. http://dx.doi.org/10.1142/s1402925111001349.
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KUSKE, R. "MULTI-SCALE DYNAMICS IN STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH MULTIPLICATIVE NOISE." Stochastics and Dynamics 05, no. 02 (June 2005): 233–46. http://dx.doi.org/10.1142/s0219493705001390.
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We apply multi-scale analysis to stochastic delay-differential equations with multiplicative or parametric noise, deriving approximate stochastic equations for the amplitudes of oscillatory solutions near critical delays. Reduced equations for the envelope of the oscillations provides an efficient analysis of the dynamics by separating the influence of the noise from the intrinsic oscillations over long time scales. We show how this analysis can be used to compute Lyapunov exponents and extended to nonlinear models where the noise has additional resonances.
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Quaranta, Giuseppe, Giovanni Formica, J. Tenreiro Machado, Walter Lacarbonara, and Sami F. Masri. "Understanding COVID-19 nonlinear multi-scale dynamic spreading in Italy." Nonlinear Dynamics 101, no. 3 (August 2020): 1583–619. http://dx.doi.org/10.1007/s11071-020-05902-1.
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Abstract The outbreak of COVID-19 in Italy took place in Lombardia, a densely populated and highly industrialized northern region, and spread across the northern and central part of Italy according to quite different temporal and spatial patterns. In this work, a multi-scale territorial analysis of the pandemic is carried out using various models and data-driven approaches. Specifically, a logistic regression is employed to capture the evolution of the total positive cases in each region and throughout Italy, and an enhanced version of a SIR-type model is tuned to fit the different territorial epidemic dynamics via a differential evolution algorithm. Hierarchical clustering and multidimensional analysis are further exploited to reveal the similarities/dissimilarities of the remarkably different geographical epidemic developments. The combination of parametric identifications and multi-scale data-driven analyses paves the way toward a closer understanding of the nonlinear, spatially nonuniform epidemic spreading in Italy.
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Knar, Zakaria, Jean-Jacques Sinou, Sébastien Besset, and Vivien Clauzon. "An Adapted Two-Steps Approach to Simulate Nonlinear Vibrations of Solid Undergoing Large Deformation in Contact with Rigid Plane—Application to a Grooved Cylinder." Applied Sciences 12, no. 3 (January 28, 2022): 1447. http://dx.doi.org/10.3390/app12031447.
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Simulating the full dynamic response of a rolling sculpted tire requires not only taking into account various non-linearities but also considering the multi-scale nature of the dynamic response itself. On one hand, there is the macroscopic rolling dynamic behavior that operates around the rotating frequency with relatively high amplitudes. On the other hand, the vibratory response operates in a larger frequency window with relatively low amplitudes. In contrast to a straightforward strategy that consists of using an energy-conserving stable time integrator to predict the multi-scale dynamic response, the proposed strategy is based on a two-steps approach to separate the dynamics operating at different scales. This methodology is applied to simulate the nonlinear vibrations of a hyperelastic solid undergoing large deformations in contact with a rigid plane. In order to illustrate the potential of the proposed numerical method, the nonlinear vibrations response of a grooved cylinder rolling on a rigid plane is investigated.
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Rundle, J. B., D. L. Turcotte, P. B. Rundle, G. Yakovlev, R. Shcherbakov, A. Donnellan, and W. Klein. "Pattern dynamics, pattern hierarchies, and forecasting in complex multi-scale earth systems." Hydrology and Earth System Sciences Discussions 3, no. 3 (June 20, 2006): 1045–69. http://dx.doi.org/10.5194/hessd-3-1045-2006.
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Abstract. Catastrophic disasters afflicting human society are often triggered by tsunamis, earthquakes, widespread flooding, and weather and climate events. As human populations increasingly move into geographic areas affected by these earth system hazards, forecasting the onset of these large and damaging events has become increasingly urgent. In this paper we consider the fundamental problem of forecasting in complex multi-scale earth systems when the basic dynamical variables are either unobservable or incompletely observed. In such cases, the forecaster must rely on incompletely determined, but "tunable" models to interpret observable space-time patterns of events. The sequence of observable patterns constitute an apparent pattern dynamics, which is related to the underlying but hidden Newtonian dynamics by a complex dimensional reduction process. As an example, we examine the problem of earthquakes, which must utilize current and past observations of observables such as seismicity and surface strain to produce forecasts of future activity. We show that numerical simulations of earthquake fault systems are needed in order to relate the fundamentally unobservable nonlinear dynamics to the readily observable pattern dynamics. We also show that the space-time patterns produced by the simulations lead to a scale-invariant hierarchy of patterns, similar to other nonlinear systems. We point out that a similar program of simulations has been very successful in weather forecasting, in which current and past observations of weather patterns are routinely extrapolated forward in time via numerical simulations in order to forecast future weather patterns.
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Rundle, J. B., D. L. Turcotte, P. B. Rundle, R. Shcherbakov, G. Yakovlev, A. Donnellan, and W. Klein. "Pattern dynamics, pattern hierarchies, and forecasting in complex multi-scale earth systems." Hydrology and Earth System Sciences 10, no. 6 (October 30, 2006): 789–96. http://dx.doi.org/10.5194/hess-10-789-2006.
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Abstract. Catastrophic disasters afflicting human society are often triggered by tsunamis, earthquakes, widespread flooding, and weather and climate events. As human populations increasingly move into geographic areas affected by these earth system hazards, forecasting the onset of these large and damaging events has become increasingly urgent. In this paper we consider the fundamental problem of forecasting in complex multi-scale earth systems when the basic dynamical variables are either unobservable or incompletely observed. In such cases, the forecaster must rely on incompletely determined, but "tunable" models to interpret observable space-time patterns of events. The sequence of observable patterns constitute an apparent pattern dynamics, which is related to the underlying but hidden dynamics by a complex dimensional reduction process. As an example, we examine the problem of earthquakes, which must utilize current and past observations of observables such as seismicity and surface strain to produce forecasts of future activity. We show that numerical simulations of earthquake fault systems are needed in order to relate the fundamentally unobservable nonlinear dynamics to the readily observable pattern dynamics. We also show that the space-time patterns produced by the simulations lead to a scale-invariant hierarchy of patterns, similar to other nonlinear systems. We point out that a similar program of simulations has been very successful in weather forecasting, in which current and past observations of weather patterns are routinely extrapolated forward in time via numerical simulations in order to forecast future weather patterns.
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MAJDA, ANDREW J., YULONG XING, and MAJID MOHAMMADIAN. "Moist multi-scale models for the hurricane embryo." Journal of Fluid Mechanics 657 (June 30, 2010): 478–501. http://dx.doi.org/10.1017/s0022112010001515.
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Determining the finite-amplitude preconditioned states in the hurricane embryo, which lead to tropical cyclogenesis, is a central issue in contemporary meteorology. In the embryo there is competition between different preconditioning mechanisms involving hydrodynamics and moist thermodynamics, which can lead to cyclogenesis. Here systematic asymptotic methods from applied mathematics are utilized to develop new simplified moist multi-scale models starting from the moist anelastic equations. Three interesting multi-scale models emerge in the analysis. The balanced mesoscale vortex (BMV) dynamics and the microscale balanced hot tower (BHT) dynamics involve simplified balanced equations without gravity waves for vertical vorticity amplification due to moist heat sources and incorporate nonlinear advective fluxes across scales. The BMV model is the central one for tropical cyclogenesis in the embryo. The moist mesoscale wave (MMW) dynamics involves simplified equations for mesoscale moisture fluctuations, as well as linear hydrostatic waves driven by heat sources from moisture and eddy flux divergences. A simplified cloud physics model for deep convection is introduced here and used to study moist axisymmetric plumes in the BHT model. A simple application in periodic geometry involving the effects of mesoscale vertical shear and moist microscale hot towers on vortex amplification is developed here to illustrate features of the coupled multi-scale models. These results illustrate the use of these models in isolating key mechanisms in the embryo in a simplified content.
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Hajjaj, Amal Z., Jonathan Ortiz, and Abdessattar Abdelkefi. "Nonlinear size-dependent modeling and dynamics of nanocrystalline arc resonators." International Journal of Mechanics and Materials in Design 18, no. 1 (October 28, 2021): 105–23. http://dx.doi.org/10.1007/s10999-021-09574-6.
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AbstractThe adequate modeling of the micro/nano arc resonators' dynamics is vital for their successful implementation. Here, a size-dependent model, wherein material structure, porosity, and micro-rotation effects of the grains are considered, is derived by combining the couple stress theory, multi-phase model, and the classical Euler–Bernoulli beam model, aiming to characterize the frequency tunability of micro/nano arc resonators as monitoring either the axial load or the electrostatic force for the first time. The arc dimensions are optimized to show various phenomena in the same arc, namely snap-through, crossing, and veering. The first three natural frequencies are monitored, showing the size dependency on the frequency tuning, snap-through/back, and pull-in instability as shrinking the scale from micro- to nano-scale. Significant changes in the static snap-through and pull-in voltages and the resonance frequencies were shown as scale shrinks. A dynamic analysis of the resonator's vibration shows a dramatic effect of the size-dependency as shrinking dimensions around the veering zone.
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Su, C. H., and D. Ryu. "Multi-scale analysis of bias correction of soil moisture." Hydrology and Earth System Sciences Discussions 11, no. 7 (July 29, 2014): 8995–9026. http://dx.doi.org/10.5194/hessd-11-8995-2014.
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Abstract. Remote sensing, in situ networks and models are now providing unprecedented information for environmental monitoring. To conjunctively use multi-source data nominally representing an identical variable, one must resolve biases existing between these disparate sources, and the characteristics of the biases can be non-trivial due to spatiotemporal variability of the target variable, inter-sensor differences with variable measurement supports. One such example is of soil moisture (SM) monitoring. Triple collocation (TC) based bias correction is a powerful statistical method that increasingly being used to address this issue but is only applicable to the linear regime, whereas nonlinear method of statistical moment matching is susceptible to unintended biases originating from measurement error. Since different physical processes that influence SM dynamics may be distinguishable by their characteristic spatiotemporal scales, we propose a multi-time-scale linear bias model in the framework of a wavelet-based multi-resolution analysis (MRA). The joint MRA-TC analysis was applied to demonstrate scale-dependent biases between in situ, remotely-sensed and modelled SM, the influence of various prospective bias correction schemes on these biases, and lastly to enable multi-scale bias correction and data adaptive, nonlinear de-noising via wavelet thresholding.
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Lyu, Weipeng, Shaolong Li, Zhenyang Chen, and Qinsheng Bi. "Bursting Dynamics in a Singular Vector Field with Codimension Three Triple Zero Bifurcation." Mathematics 11, no. 11 (May 28, 2023): 2486. http://dx.doi.org/10.3390/math11112486.
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As a kind of dynamical system with a particular nonlinear structure, a multi-time scale nonlinear system is one of the essential directions of the current development of nonlinear dynamics theory. Multi-time scale nonlinear systems in practical applications are often complex forms of coupling of high-dimensional and high codimension characteristics, leading to various complex bursting oscillation behaviors and bifurcation characteristics in the system. For exploring the complex bursting dynamics caused by high codimension bifurcation, this paper considers the normal form of the vector field with triple zero bifurcation. Two kinds of codimension-2 bifurcation that may lead to complex bursting oscillations are discussed in the two-parameter plane. Based on the fast–slow analysis method, by introducing the slow variable W=Asin(ωt), the evolution process of the motion trajectory of the system changing with W was investigated, and the dynamical mechanism of several types of bursting oscillations was revealed. Finally, by varying the frequency of the slow variable, a class of chaotic bursting phenomena caused by the period-doubling cascade is deduced. Developing related work has played a positive role in deeply understanding the nature of various complex bursting phenomena and strengthening the application of basic disciplines such as mechanics and mathematics in engineering practice.
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Armand, J., L. Pesaresi, L. Salles, C. Wong, and C. W. Schwingshackl. "A modelling approach for the nonlinear dynamics of assembled structures undergoing fretting wear." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2223 (March 2019): 20180731. http://dx.doi.org/10.1098/rspa.2018.0731.
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Assembled structures tend to exhibit nonlinear dynamic behaviour at high excitation levels due to the presence of contact interfaces. The possibility of building predictive models relies on the ability of the modelling strategy to capture the complex nonlinear phenomena occurring at the interface. One of these phenomena, normally neglected, is the fretting wear occurring at the frictional interface. In this paper, a computationally efficient modelling approach which enables considerations of the effect of fretting wear on the nonlinear dynamics is presented. A multi-scale strategy is proposed, in which two different time scales and space scales are used for the contact analysis and dynamic analysis. Thanks to the de-coupling of the contact and dynamic analysis, a more realistic representation of the contact interface, which includes surface roughness, is possible. The proposed approach is applied to a single bolted joint resonator with a simulated rough contact interface. A tendency towards an increase of real contact area and contact stiffness at the interface is clearly observed. The dynamic response of the system is shown to evolve over time, with a slight decrease of damping and an increase of resonance frequency, highlighting the impact of fretting wear on the system dynamics.
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Li, Hong-Wei, Ting Wang, Chang Chang, Bin Sun, Wen-peng Hong, and Yun-long Zhou. "Multi-scale nonlinear analysis of drying dynamics in the mixed pulsed drying fluidized beds." Powder Technology 339 (November 2018): 958–69. http://dx.doi.org/10.1016/j.powtec.2018.08.078.
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Montegiglio, Pasquale, Claudio Maruccio, Giuseppe Acciani, Gianluca Rizzello, and Stefan Seelecke. "Nonlinear multi-scale dynamics modeling of piezoceramic energy harvesters with ferroelectric and ferroelastic hysteresis." Nonlinear Dynamics 100, no. 3 (May 2020): 1985–2003. http://dx.doi.org/10.1007/s11071-020-05660-0.
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Mendez, M. A., M. Balabane, and J. M. Buchlin. "Multi-scale proper orthogonal decomposition of complex fluid flows." Journal of Fluid Mechanics 870 (May 15, 2019): 988–1036. http://dx.doi.org/10.1017/jfm.2019.212.
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Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.
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Hou, Shuangshan, Jinde Zheng, Haiyang Pan, Ke Feng, Qingyun Liu, and Qing Ni. "Multivariate multi-scale cross-fuzzy entropy and SSA-SVM-based fault diagnosis method of gearbox." Measurement Science and Technology 35, no. 5 (February 5, 2024): 056102. http://dx.doi.org/10.1088/1361-6501/ad2053.
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Abstract Fuzzy entropy (FuzzyEn) is widely recognized as a powerful tool for analyzing nonlinear dynamics and measuring the complexity of time series data. It has been utilized as an effective indicator to capture nonlinear fault features in gearbox vibration signals. However, FuzzyEn only measures complexity at a single scale, ignoring the valuable information contained in large-scale features of the time series. Furthermore, FuzzyEn does not account for coupling characteristics between related or synchronized time series. To address these limitations, a novel entropy-based approach called multivariate multi-scale cross-fuzzy entropy (MvMCFE) is proposed in this paper for measuring the complexity and mutual predictability of two multivariate time series. Relying on the advantages of MvMCFE in nonlinear feature extraction, a new fault diagnosis method for gearboxes is proposed based on MvMCFE and an optimized support vector machine (SVM) using the salp swarm algorithm (SSA-SVM). Ultimately, the proposed gearbox diagnostic method is employed to analyze the gearbox experimental data and a comparison with existing fault diagnosis approaches is conducted. The comparison results indicate that the proposed method can effectively extract nonlinear fault features of gearboxes and achieve the highest recognition rate compared to the other methods.
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Doelman, Arjen, Peter van Heijster, and Jianhe Shen. "Pulse dynamics in reaction–diffusion equations with strong spatially localized impurities." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2117 (March 5, 2018): 20170183. http://dx.doi.org/10.1098/rsta.2017.0183.
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In this article, a general geometric singular perturbation framework is developed to study the impact of strong, spatially localized, nonlinear impurities on the existence, stability and bifurcations of localized structures in systems of linear reaction–diffusion equations. By taking advantage of the multiple-scale nature of the problem, we derive algebraic conditions determining the existence and stability of pinned single- and multi-pulse solutions. Our methods enable us to explicitly control the spectrum associated with a (multi-)pulse solution. In the scalar case, we show how eigenvalues may move in and out of the essential spectrum and that Hopf bifurcations cannot occur. By contrast, even a pinned 1-pulse solution can undergo a Hopf bifurcation in a two-component system of linear reaction–diffusion equations with (only) one impurity. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.
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Wertheim, Kenneth Y., Bhanwar Lal Puniya, Alyssa La Fleur, Ab Rauf Shah, Matteo Barberis, and Tomáš Helikar. "A multi-approach and multi-scale platform to model CD4+ T cells responding to infections." PLOS Computational Biology 17, no. 8 (August 3, 2021): e1009209. http://dx.doi.org/10.1371/journal.pcbi.1009209.
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Immune responses rely on a complex adaptive system in which the body and infections interact at multiple scales and in different compartments. We developed a modular model of CD4+ T cells, which uses four modeling approaches to integrate processes at three spatial scales in different tissues. In each cell, signal transduction and gene regulation are described by a logical model, metabolism by constraint-based models. Cell population dynamics are described by an agent-based model and systemic cytokine concentrations by ordinary differential equations. A Monte Carlo simulation algorithm allows information to flow efficiently between the four modules by separating the time scales. Such modularity improves computational performance and versatility and facilitates data integration. We validated our technology by reproducing known experimental results, including differentiation patterns of CD4+ T cells triggered by different combinations of cytokines, metabolic regulation by IL2 in these cells, and their response to influenza infection. In doing so, we added multi-scale insights to single-scale studies and demonstrated its predictive power by discovering switch-like and oscillatory behaviors of CD4+ T cells that arise from nonlinear dynamics interwoven across three scales. We identified the inflamed lymph node’s ability to retain naive CD4+ T cells as a key mechanism in generating these emergent behaviors. We envision our model and the generic framework encompassing it to serve as a tool for understanding cellular and molecular immunological problems through the lens of systems immunology.
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Zhang, Shu, Joseph Bentsman, Xinsheng Lou, Carl Neuschaefer, Yongseok Lee, and Hamza El-Kebir. "Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed." Energies 13, no. 7 (April 7, 2020): 1759. http://dx.doi.org/10.3390/en13071759.
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Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.
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Liu, Yan, Kai Ma, Hao He, and Kuan Gao. "Obtaining Information about Operation of Centrifugal Compressor from Pressure by Combining EEMD and IMFE." Entropy 22, no. 4 (April 9, 2020): 424. http://dx.doi.org/10.3390/e22040424.
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Based on entropy characteristics, some complex nonlinear dynamics of the dynamic pressure at the outlet of a centrifugal compressor are analyzed, as the centrifugal compressor operates in a stable and unstable state. First, the 800-kW centrifugal compressor is tested to gather the time sequence of dynamic pressure at the outlet by controlling the opening of the anti-surge valve at the outlet, and both the stable and unstable states are tested. Then, multi-scale fuzzy entropy and an improved method are introduced to analyze the gathered time sequence of dynamic pressure. Furthermore, the decomposed signals of dynamic pressure are obtained using ensemble empirical mode decomposition (EEMD), and are decomposed into six intrinsic mode functions and one residual signal, and the intrinsic mode functions with large correlation coefficients in the frequency domain are used to calculate the improved multi-scale fuzzy entropy (IMFE). Finally, the statistical reliability of the method is studied by modifying the original data. After analysis of the relationships between the dynamic pressure and entropy characteristics, some important intrinsic dynamics are captured. The entropy becomes the largest in the stable state, but decreases rapidly with the deepening of the unstable state, and it becomes the smallest in the surge. Compared with multi-scale fuzzy entropy, the curve of the improved method is smoother and could show the change of entropy exactly under different scale factors. For the decomposed signals, the unstable state is captured clearly for higher order intrinsic mode functions and residual signals, while the unstable state is not apparent for lower order intrinsic mode functions. In conclusion, it can be observed that the proposed method can be used to accurately identify the unstable states of a centrifugal compressor in real-time fault diagnosis.
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Crouseilles, Nicolas, Shi Jin, and Mohammed Lemou. "Nonlinear geometric optics method-based multi-scale numerical schemes for a class of highly oscillatory transport equations." Mathematical Models and Methods in Applied Sciences 27, no. 11 (August 30, 2017): 2031–70. http://dx.doi.org/10.1142/s0218202517500385.
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We introduce a new numerical strategy to solve a class of oscillatory transport partial differential equation (PDE) models which is able to capture accurately the solutions without numerically resolving the high frequency oscillations in both space and time. Such PDE models arise in semiclassical modeling of quantum dynamics with band-crossings, and other highly oscillatory waves. Our first main idea is to use the geometric optics ansatz, which builds the oscillatory phase into an independent variable. We then choose suitable initial data, based on the Chapman–Enskog expansion, for the new model. For a scalar model, we prove that so constructed models will have certain smoothness, and consequently, for a first-order approximation scheme we prove uniform error estimates independent of the (possibly small) wavelength. The method is extended to systems arising from a semiclassical model for surface hopping, a non-adiabatic quantum dynamic phenomenon. Numerous numerical examples demonstrate that the method has the desired properties.
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Luchinsky, Dmitry G., Vasyl Hafiychuck, Kevin R. Wheeler, Sudipta Biswas, Christopher E. Roberts, Ian M. Hanson, Tracie J. Prater, and Peter V. E. McClintock. "Multi-Scale Modelling of the Bound Metal Deposition Manufacturing of Ti6Al4V." Thermo 2, no. 3 (June 23, 2022): 116–48. http://dx.doi.org/10.3390/thermo2030011.
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Nonlinear shrinkage of the metal part during manufacturing by bound metal deposition, both on the ground and under microgravity, is considered. A multi-scale physics-based approach is developed to address the problem. It spans timescales from atomistic dynamics on the order of nanoseconds to full-part shrinkage on the order of hours. This approach enables estimation of the key parameters of the problem, including the widths of grain boundaries, the coefficient of surface diffusion, the initial redistribution of particles during the debinding stage, the evolution of the microstructure from round particles to densely-packed grains, the corresponding changes in the total and chemical free energies, and the sintering stress. The method has been used to predict shrinkage at the levels of two particles, of the filament cross-section, of the sub-model, and of the whole green, brown, and metal parts.
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Chen, Yong Xiang, Jin Biao Liu, and Nan Zhang. "Research on Supply Chain Network System Based on Industrial Cluster." Applied Mechanics and Materials 587-589 (July 2014): 1907–11. http://dx.doi.org/10.4028/www.scientific.net/amm.587-589.1907.
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The reliability of supply chain network system design and optimization based on the industrial cluster was discussed, that is, the operational platform of multi-objective supply chain network was moved to industrial cluster, so the platform has the effects of both regional radiation and scale of economy. Instead of some static research methods such as former traditional mathematic planning, systematic and dynamic analysis, this paper put forward a coordinative mechenism construction, this mechenism used dynamic simulation method which combined the supply chain system with industrial cluster multi-objective weighing in the region, the mechenism should be cost efficient and satisfy the application in the industrial cluster radiation region, the mechenism should integrate all possible resources in the industrial cluster and consider heterogeneity, layout, nonlinear, limitation and dynamics of the supply chain network system.
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Ge, Hao, and Hong Qian. "Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond." Journal of The Royal Society Interface 8, no. 54 (May 13, 2010): 107–16. http://dx.doi.org/10.1098/rsif.2010.0202.
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A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation–dephosphorylation system with feedback that exhibits bistability, we show that the non-equilibrium steady-state (NESS) phase transition has all the characteristics of classic equilibrium phase transition: Maxwell construction, a discontinuous first-derivative of the ‘free energy function’, Lee–Yang's zero for a generating function and a critical point that matches the cusp in nonlinear bifurcation theory. To the biochemical system, the mathematical analysis suggests three distinct timescales and needed levels of description. They are (i) molecular signalling, (ii) biochemical network nonlinear dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. Both (ii) and (iii) are emergent properties of a dynamic biochemical network.
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Ling, Liwen, Dabin Zhang, Amin W. Mugera, Shanying Chen, and Qiang Xia. "A Forecast Combination Framework with Multi-Time Scale for Livestock Products’ Price Forecasting." Mathematical Problems in Engineering 2019 (October 20, 2019): 1–11. http://dx.doi.org/10.1155/2019/8096206.
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China’s livestock market has experienced exceptionally severe price fluctuations over the past few years. In this paper, based on the well-established idea of “forecast combination,” a forecast combination framework with different time scales is proposed to improve the forecast accuracy for livestock products. Specifically, we combine the forecasts from multi-time scale, i.e., the short-term forecast and the long-term forecast. Forecasts derived from multi-time scale introduce complementary information about the dynamics of price movements, thus increasing the diversities within the modeling process. Moreover, we investigate a total of ten combination methods with different weighting schemes, including linear and nonlinear combination. The empirical results show that (i) forecast performance can be remarkably improved with this novel combination idea, and short-term forecast model is more suitable for the products with a relatively high volatility, e.g., mutton and beef; (ii) geometric mean, which provides a nonlinear combination, is the most effective one among all the combination methods; and (iii) variance-based weighting scheme can yield a superior result compared to the best individual forecast, especially for the products such as egg and beef.
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Rizzo, Fabio, Chiara Bedon, Sulyman Mansour, Aleksander Pistol, Maria Francesca Sabbà, Łukasz Flaga, Renata Klaput, and Dora Foti. "Dynamics of a Flexible Roof Test Model under Ambient Vibrations Measurements." Applied Sciences 13, no. 7 (March 24, 2023): 4135. http://dx.doi.org/10.3390/app13074135.
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Flexible roofs are sensitive to wind actions because they are light, and their deformability can induce local or global instability. In most cases, their design requires experimental wind tunnel testing to investigate the aeroelastic phenomena and the structural response under the wind. However, the reduced scale necessary in wind tunnels makes the dynamic identification of the test model difficult. Several approaches of multi-modal dynamic identification can be used, even if a specific approach is not defined for geometric nonlinear flexible roofs. Many times, the choice of the position of the sensors is affected by the unknown roof dynamics. This paper investigates the ambient vibration time-dependent accelerations for a flexible roof scaled model through Singular Value Decomposition (SVD) and their spatial correlations with the purpose of analyzing the signal structure and its acquisition to perform the dynamic identification of the test model.
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Xu, Chao, Chen-Chen Huang, and Wei-Dong Zhu. "Bolt loosening detection in a jointed beam using empirical mode decomposition–based nonlinear system identification method." International Journal of Distributed Sensor Networks 15, no. 9 (September 2019): 155014771987565. http://dx.doi.org/10.1177/1550147719875656.
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In this work, a state-of-art nonlinear system identification method based on empirical mode decomposition is utilized and extended to detect bolt loosening in a jointed beam. This nonlinear system identification method is based on identifying the multi-scale dynamics of the underlying system. Only structural dynamic response signals are needed to construct a reduced-order model to represent the system concerned. It makes the method easy to use in practice. A new bolt loosening identification procedure based on the constructed system nonlinear reduced-order model is proposed. A new damage feature to indicate bolt loosening is presented. Experimental works are carried out to validate the proposed method. The results show that the proposed damage detection method can detect bolt loosening effectively, and the proposed damage feature values increase with the increase of bolt torques. The damage feature calculated from the response solution of the reduced-order model can give robust and sensitive indication of bolt loosening.
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Yang, Yi, Hang Li, and Yiping Dai. "Nonlinear vibration characteristics of spur gear system subjected to multiple harmonic excitations." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 17 (June 24, 2019): 6026–50. http://dx.doi.org/10.1177/0954406219858171.
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Due to the complicated working conditions, the gear systems are often subjected to multifrequency excitations in practical situations. This paper is concerned with the nonlinear vibration behaviors of a spur gear pair to excitations that involve multiple frequencies. The spur gear system is described by a typical single degree of freedom model, in which the nonlinear backlash, static transmission error, and multiple harmonic excitations are taken into consideration. With the help of the multi-scale method, the nonlinear frequency–response characteristics of the spur gear system are derived and analyzed. Further, the numerical simulation and the published experimental data are utilized to validate the developed dynamic model of gear pair and to prove the practicality of the analytical method. Results show that the multifrequency excitation-based gear model could be more reliable than the simplified gear model subjected to single-frequency excitation. Thus, the established model in this work would be capable of predicting the nonlinear vibration behaviors of spur gear systems under complicated excitations. The purpose of this study is to provide references that may be of interest to engineers and researchers attempting to handle the nonlinear dynamics of gear systems.
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Vakakis, Alexander F. "Passive nonlinear targeted energy transfer." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2127 (July 23, 2018): 20170132. http://dx.doi.org/10.1098/rsta.2017.0132.
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Nonlinearity in dynamics and acoustics may be viewed as scattering of energy across frequencies/wavenumbers. This is in contrast with linear systems when no such scattering exists. Motivated by irreversible large-to-small-scale energy transfers in turbulent flows, passive targeted energy transfers (TET) in mechanical and structural systems incorporating intentional strong nonlinearities are considered. Transient or permanent resonance captures are basic mechanisms for inducing TET in such systems, as well as nonlinear energy scattering across scales caused by strongly nonlinear resonance interactions. Certain theoretical concepts are reviewed, and some TET applications are discussed. Specifically, it is shown that the addition of strongly nonlinear local attachments in an otherwise linear dynamical system may induce energy scattering across scales and ‘redistribution' of input energy from large to small scales in the linear modal space, in similarity to energy cascades that occur in turbulent flows. Such effects may be intentionally induced in the design stage and may lead to improved performance, e.g. it terms of vibration and shock isolation or energy harvesting. In addition, a simple mechanical analogue in the form of a nonlinear planar chain of particles composed of linear stiffness elements but exhibiting strong nonlinearity due to kinematic and geometric effects is discussed, exhibiting similar energy scattering across scales in its acoustics. These results demonstrate the efficacy of intentional utilization of strong nonlinearity in design to induce predictable and controlled intense multi-scale energy transfers in the dynamics and acoustics of a broad class of systems and structures, thus achieving performance objectives that would be not possible in classical linear settings. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.
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Castiglioni, Paolo, Stefano Omboni, Gianfranco Parati, and Andrea Faini. "Day and Night Changes of Cardiovascular Complexity: A Multi-Fractal Multi-Scale Analysis." Entropy 22, no. 4 (April 18, 2020): 462. http://dx.doi.org/10.3390/e22040462.
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Recently, a multifractal-multiscale approach to detrended fluctuation analysis (DFA) was proposed to evaluate the cardiovascular fractal dynamics providing a surface of self-similarity coefficients α(q,τ), function of the scale τ, and moment order q. We hypothesize that this versatile DFA approach may reflect the cardiocirculatory adaptations in complexity and nonlinearity occurring during the day/night cycle. Our aim is, therefore, to quantify how α(q, τ) surfaces of cardiovascular series differ between daytime and night-time. We estimated α(q,τ) with −5 ≤ q ≤ 5 and 8 ≤ τ ≤ 2048 s for heart rate and blood pressure beat-to-beat series over periods of few hours during daytime wake and night-time sleep in 14 healthy participants. From the α(q,τ) surfaces, we estimated short-term (<16 s) and long-term (from 16 to 512 s) multifractal coefficients. Generating phase-shuffled surrogate series, we evaluated short-term and long-term indices of nonlinearity for each q. We found a long-term night/day modulation of α(q,τ) between 128 and 256 s affecting heart rate and blood pressure similarly, and multifractal short-term modulations at q < 0 for the heart rate and at q > 0 for the blood pressure. Consistent nonlinearity appeared at the shorter scales at night excluding q = 2. Long-term circadian modulations of the heart rate DFA were previously associated with the cardiac vulnerability period and our results may improve the risk stratification indicating the more relevant α(q,τ) area reflecting this rhythm. Furthermore, nonlinear components in the nocturnal α(q,τ) at q ≠ 2 suggest that DFA may effectively integrate the linear spectral information with complexity-domain information, possibly improving the monitoring of cardiac interventions and protocols of rehabilitation medicine.
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Kuske, R., and D. Yurchenko. "Editorial." European Journal of Applied Mathematics 30, no. 5 (September 9, 2019): 829. http://dx.doi.org/10.1017/s0956792518000694.
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The origin of this special issue took place at the 9th European Nonlinear Dynamics Conference (ENOC 2017) in Budapest, Hungary. Specifically, the mini-symposium on Random Dynamical Systems – Recent Advances and New Directions brought together novel perspectives on analyzing stochastic dynamics with applications including biology, structural dynamics, control, energy and mechanics. The expanded use of stochasticity in more realistic models exposes questions related to bifurcations, meta-stability, tipping and early warning signals, multiscale dynamics, and connections between chaos and stochastic dynamics. The observed phenomena in applications drive new methodologies and analyses, needed to understand the interplay between different sources of stochastic effects and nonlinearities, network structure, multi-mode and multi-scale behavior, non-smooth dynamics, energy transfer, and spatio-temporal phenomena. Of course, a single issue cannot hope to cover all of the new topics in stochastic analysis for applications. Nevertheless, we hope that the collection of applications and stochastic models presented in this issue illustrates some of the exciting advances and perspectives relevant for broad classes of stochastic models and demonstrates the need in advancing the theory of stochastic processes.
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Ukhorskiy, A. Y., M. I. Sitnov, A. S. Sharma, and K. Papadopoulos. "Combining global and multi-scale features in a description of the solar wind-magnetosphere coupling." Annales Geophysicae 21, no. 9 (September 30, 2003): 1913–29. http://dx.doi.org/10.5194/angeo-21-1913-2003.
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Abstract. The solar wind-magnetosphere coupling during substorms exhibits dynamical features in a wide range of spatial and temporal scales. The goal of our work is to combine the global and multi-scale description of magnetospheric dynamics in a unified data-derived model. For this purpose we use deterministic methods of nonlinear dynamics, together with a probabilistic approach of statistical physics. In this paper we discuss the mathematical aspects of such a combined analysis. In particular we introduce a new method of embedding analysis based on the notion of a mean-field dimension. For a given level of averaging in the system the mean-filed dimension determines the minimum dimension of the embedding space in which the averaged dynamical system approximates the actual dynamics with the given accuracy. This new technique is first tested on a number of well-known autonomous and open dynamical systems with and without noise contamination. Then, the dimension analysis is carried out for the correlated solar wind-magnetosphere database using vBS time series as the input and AL index as the output of the system. It is found that the minimum embedding dimension of vBS - AL time series is a function of the level of ensemble averaging and the specified accuracy of the method. To extract the global component from the observed time series the ensemble averaging is carried out over the range of scales populated by a high dimensional multi-scale constituent. The wider the range of scales which are smoothed away, the smaller the mean-field dimension of the system. The method also yields a probability density function in the reconstructed phase space which provides the basis for the probabilistic modeling of the multi-scale dynamical features, and is also used to visualize the global portion of the solar wind-magnetosphere coupling. The structure of its input-output phase portrait reveals the existence of two energy levels in the system with non-equilibrium dynamical features such as hysteresis which are typical for non-equilibrium phase transitions. Further improvements in space weather forecasting tools may be achieved by a combination of the dynamical description for the global component and a statistical approach for the multi-scale component.Key words. Magnetospheric physics (solar wind– magnetosphere interactions; storms and substorms) – Space plasma physics (nonlinear phenomena)
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Chakravarty, Sarbarish, and Michael Zowada. "Dynamics of KPI lumps." Journal of Physics A: Mathematical and Theoretical 55, no. 19 (April 12, 2022): 195701. http://dx.doi.org/10.1088/1751-8121/ac37e7.
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Abstract A family of nonsingular rational solutions of the Kadomtsev–Petviashvili (KP) I equation are investigated. These solutions have multiple peaks whose heights are time-dependent and the peak trajectories in the xy-plane are altered after collision. Thus they differ from the standard multi-peaked KPI simple n-lump solutions whose peak heights as well as peak trajectories remain unchanged after interaction. The anomalous scattering occurs due to a non-trivial internal dynamics among the peaks in a slow time scale. This phenomena is explained by relating the peak locations to the roots of complex heat polynomials. It follows from the long time asymptotics of the solutions that the peak trajectories separate as O ( | t | ) as |t| → ∞, and all the peak heights approach the same constant value corresponding to that of the simple one-lump solution. Consequently, a multi-peaked n-lump solution evolves to a superposition of n one-lump solutions asymptotically as |t| → ∞.
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Ramírez, Adrián, Rifat Sipahi, Sabine Mondié, and Rubén Garrido. "Fast consensus in a large-scale multi-agent system with directed graphs using time-delayed measurements." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2153 (July 22, 2019): 20180130. http://dx.doi.org/10.1098/rsta.2018.0130.
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This article is on fast-consensus reaching in a class of multi-agent systems (MAS). We present an analytical approach to tune controllers for the agents based on the premise that delayed measurements in the controller can be preferable to standard controllers relying only on current measurements. Controller tuning in this setting is however challenging due to the presence of delays. To tackle this problem, we propose an analytic geometry approach. The key contribution is that the tuning can be implemented for complex eigenvalues of the arising graph Laplacian of the network, complementing the current state of the art, which is limited to real eigenvalues. Results, therefore, extend our knowledge beyond symmetric graphs and enable the study of the MAS under directed graphs. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.
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de La Parra, Rafael Bravo, Eva Sánchez, and Pierre Auger. "Time Scales in Density Dependent Discrete Models." Journal of Biological Systems 05, no. 01 (March 1997): 111–29. http://dx.doi.org/10.1142/s0218339097000096.
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The aim of this work is to extend approximate aggregation methods for multi-time scale systems of nonlinear ordinary differential equations to time discrete models. Approximate aggregation consist on describing the dynamics of a general system involving many coupled variables by means of the dynamics of a reduced system with a few global variables. We present discrete time models with two different time scales, the fast one considered linear and the slow one generally nonlinear. We transform the system to make the global variables appear, and use a version of center manifold theory to build up the aggregated system. Simple forms of the aggregated system are enough for the local study of the asymptotic behaviour of the general system provided that it has certain stability under perturbations. The general method is applied to aggregate a multiregional density dependent Leslie model into a density dependent Leslie model in which the demographic rates are expressed in terms of the equilibrium proportions of individuals in the different patches.
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Sivakumar, B., W. W. Wallender, C. E. Puente, and M. N. Islam. "Streamflow disaggregation: a nonlinear deterministic approach." Nonlinear Processes in Geophysics 11, no. 3 (September 8, 2004): 383–92. http://dx.doi.org/10.5194/npg-11-383-2004.
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Abstract. This study introduces a nonlinear deterministic approach for streamflow disaggregation. According to this approach, the streamflow transformation process from one scale to another is treated as a nonlinear deterministic process, rather than a stochastic process as generally assumed. The approach follows two important steps: (1) reconstruction of the scalar (streamflow) series in a multi-dimensional phase-space for representing the transformation dynamics; and (2) use of a local approximation (nearest neighbor) method for disaggregation. The approach is employed for streamflow disaggregation in the Mississippi River basin, USA. Data of successively doubled resolutions between daily and 16 days (i.e. daily, 2-day, 4-day, 8-day, and 16-day) are studied, and disaggregations are attempted only between successive resolutions (i.e. 2-day to daily, 4-day to 2-day, 8-day to 4-day, and 16-day to 8-day). Comparisons between the disaggregated values and the actual values reveal excellent agreements for all the cases studied, indicating the suitability of the approach for streamflow disaggregation. A further insight into the results reveals that the best results are, in general, achieved for low embedding dimensions (2 or 3) and small number of neighbors (less than 50), suggesting possible presence of nonlinear determinism in the underlying transformation process. A decrease in accuracy with increasing disaggregation scale is also observed, a possible implication of the existence of a scaling regime in streamflow.
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Yu, Jiawei, Ziqian Yang, Jurgen Kurths, and Meng Zhan. "Small-Signal Stability of Multi-Converter Infeed Power Grids with Symmetry." Symmetry 13, no. 2 (January 20, 2021): 157. http://dx.doi.org/10.3390/sym13020157.
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Traditional power systems have been gradually shifting to power-electronic-based ones, with more power electronic devices (including converters) incorporated recently. Faced with much more complicated dynamics, it is a great challenge to uncover its physical mechanisms for system stability and/or instability (oscillation). In this paper, we first establish a nonlinear model of a multi-converter power system within the DC-link voltage timescale, from the first principle. Then, we obtain a linearized model with the associated characteristic matrix, whose eigenvalues determine the system stability, and finally get independent subsystems by using symmetry approximation conditions under the assumptions that all converters’ parameters and their susceptance to the infinite bus (Bg) are identical. Based on these mathematical analyses, we find that the whole system can be decomposed into several equivalent single-converter systems and its small-signal stability is solely determined by a simple converter system connected to an infinite bus under the same susceptance Bg. These results of large-scale multi-converter analysis help to understand the power-electronic-based power system dynamics, such as renewable energy integration. As well, they are expected to stimulate broad interests among researchers in the fields of network dynamics theory and applications.
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Jeyarani, R., N. Nagaveni, and R. Vasanth Ram. "Self Adaptive Particle Swarm Optimization for Efficient Virtual Machine Provisioning in Cloud." International Journal of Intelligent Information Technologies 7, no. 2 (April 2011): 25–44. http://dx.doi.org/10.4018/jiit.2011040102.
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Cloud Computing provides dynamic leasing of server capabilities as a scalable, virtualized service to end users. The discussed work focuses on Infrastructure as a Service (IaaS) model where custom Virtual Machines (VM) are launched in appropriate servers available in a data-center. The context of the environment is a large scale, heterogeneous and dynamic resource pool. Nonlinear variation in the availability of processing elements, memory size, storage capacity, and bandwidth causes resource dynamics apart from the sporadic nature of workload. The major challenge is to map a set of VM instances onto a set of servers from a dynamic resource pool so the total incremental power drawn upon the mapping is minimal and does not compromise the performance objectives. This paper proposes a novel Self Adaptive Particle Swarm Optimization (SAPSO) algorithm to solve the intractable nature of the above challenge. The proposed approach promptly detects and efficiently tracks the changing optimum that represents target servers for VM placement. The experimental results of SAPSO was compared with Multi-Strategy Ensemble Particle Swarm Optimization (MEPSO) and the results show that SAPSO outperforms the latter for power aware adaptive VM provisioning in a large scale, heterogeneous and dynamic cloud environment.
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Papageorgiou, Demetrios T., and Saleh Tanveer. "Mathematical study of a system of multi-dimensional non-local evolution equations describing surfactant-laden two-fluid shear flows." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2252 (August 2021): 20210307. http://dx.doi.org/10.1098/rspa.2021.0307.
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This article studies a coupled system of model multi-dimensional partial differential equations (PDEs) that arise in the nonlinear dynamics of two-fluid Couette flow when insoluble surfactants are present on the interface. The equations have been derived previously, but a rigorous study of local and global existence of their solutions, or indeed solutions of analogous systems, has not been considered previously. The evolution PDEs are two-dimensional in space and contain novel pseudo-differential terms that emerge from asymptotic analysis and matching in the multi-scale problem at hand. The one-dimensional surfactant-free case was studied previously, where travelling wave solutions were constructed numerically and their stability investigated; in addition, the travelling wave solutions were justified mathematically. The present study is concerned with some rigorous results of the multi-dimensional surfactant system, including local well posedness and smoothing results when there is full coupling between surfactant dynamics and interfacial motion, and global existence results when such coupling is absent. As far as we know such results are new for non-local thin film equations in either one or two dimensions.
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Fatehi, Mohammad H., Mohammad Eghtesad, Dan S. Necsulescu, and Ali A. Fatehi. "Tracking control design for a multi-degree underactuated flexible-cable overhead crane system with large swing angle based on singular perturbation method and an energy-shaping technique." Journal of Vibration and Control 25, no. 11 (March 6, 2019): 1752–67. http://dx.doi.org/10.1177/1077546319833881.
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A flexible-cable overhead crane system having large swing is studied as a multi-degree underactuated system. To resolve the system dynamics complexities, a second order singular perturbation (SP) formulation is developed to divide the crane dynamics into two one-degree underactuated fast and slow subsystems. Then, a control system is designed based on the two-time scale control (TTSC) method to: (a) transfer the payload to a desired location and decrease the payload swing, by a nonlinear controller for slow dynamics; and (b) suppress transverse vibrations of the cable, by a linear controller for fast dynamics. The nonlinear controller is designed based on an energy shaping technique according to the controlled Lagrangian method. To demonstrate the control system effectiveness, an example of the flexible cable crane systems with a lightweight payload is considered to perform simulations. In addition to the proposed control system, two other controllers; namely, a linear controller based on the linear–quadratic regulator method and a TTSC based on the approximate SP model and partial feedback linearization, are applied to the system for comparison. Also, by applying a disturbance force to the trolley and considering 10% uncertainty in crane parameters, the control performance against disturbances and parameter uncertainties is investigated.
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Bagherinia, Mehrdad, and Stefano Mariani. "Stochastic Effects on the Dynamics of the Resonant Structure of a Lorentz Force MEMS Magnetometer." Actuators 8, no. 2 (April 30, 2019): 36. http://dx.doi.org/10.3390/act8020036.
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Resonance features of slender mechanical parts of Lorentz force MEMS magnetometers are affected by the (weakly) coupled thermo-electro-magneto-mechanical multi-physics governing their dynamics. We recently showed that reduced-order models for such parts can be written in the form of the Duffing equation, whose nonlinear term stems from the mechanical constraint on the vibrations and is affected by the driving voltage. As some device performance indices vary proportionally to the amplitude of oscillations at resonance, an optimization of the operational conditions may lead to extremely slender, imperfection-sensitive movable structures. In this work, we investigate the effects of imperfections on the mechanical response of a single-axis magnetometer. At the microscopic length-scale, imperfections are given in terms of uncertainties in the values of the over-etch depth and of the Young’s modulus of the vibrating polycrystalline silicon film. Their effects on the nonlinear structural dynamics are investigated through a Monte Carlo analysis, to show how the output of real devices can be scattered around the reference response trend.
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Huang, Zerong, Daxing Zhang, Xiangdong Wang, Xiaolong Huang, Chunsheng Wang, Liqing Liao, Yaolin Dong, Xiaoshuang Hou, Yuan Cao, and Xinyao Zhou. "Machine Learning Prediction of Fuel Cell Remaining Life Enhanced by Variational Mode Decomposition and Improved Whale Optimization Algorithm." Mathematics 12, no. 19 (September 24, 2024): 2959. http://dx.doi.org/10.3390/math12192959.
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In predicting the remaining lifespan of Proton Exchange Membrane Fuel Cells (PEMFC), it is crucial to accurately capture the multi-scale variations in cell performance. This study employs Variational Mode Decomposition (VMD) to decompose performance data into intrinsic modes, elucidating critical multi-scale dynamics vital for understanding the complex degradation processes in fuel cells. In addition to VMD, this research utilizes an Improved Whale Optimization Algorithm (IWOA) to optimize a Back Propagation (BP) Neural Network. The IWOA focuses on precise adjustments of weights and biases, enabling the BP network to effectively interpret complex nonlinear relationships within the dataset. This optimization enhances the predictive model’s reliability and stability. Extensive experimental evaluations demonstrate that the integration of VMD, and the learning capabilities of the IWOA-optimized BP network significantly improves the model’s accuracy and stability across multiple predictions, thereby increasing the reliability of lifespan predictions for PEMFCs. This methodology offers a robust framework for extending the operational life and efficiency of fuel cells.
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Wang, Bo, and Youqi Tang. "Research on Time Delay Feedback Control of Lateral Vibration Axially Moving Viscoelastic Beam." Journal of Physics: Conference Series 2215, no. 1 (February 1, 2022): 012012. http://dx.doi.org/10.1088/1742-6596/2215/1/012012.
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Abstract The nonlinear dynamic behavior of a viscoelastic beam in axially variable motion under time delay is studied. Considering that the axial velocity pulsation and radial tension change periodically with time under the action of time delay, the viscous damping and finite support stiffness are taken into account, and the viscoelastic constitutive relationship adopts Kelvin model. A mathematical model of lateral vibration of an axially moving viscoelastic beam with changes in axial velocity and tension under time delay is established, and a partial differential-integral control equation describing the lateral nonlinear vibration of an axially moving beam is given. Based on the Galerkin truncation method, the control equations established based on the mechanical model are discretized, so that the direct multi-scale method obtains the numerical solution of the lateral nonlinear vibration of the axially moving beam under the action of time delay, and determines the nonlinear dynamic behavior of the system under the action of time delay. By analyzing the numerical solution of the vibration displacement and velocity at the midpoint of the beam, the whole process of the average velocity of the axially moving structure along the axis, the amplitude of the disturbance tension and the change of the viscoelastic coefficient is simulated. It provides a numerical theoretical basis for the study of the nonlinear dynamic behavior of axially moving beams under time delay. Through the research in this article, the introduction of time delay is studied, and the time delay is used to analyze the axial force that changes along the radial direction of the beam caused by the speed pulsation, and the theoretical framework for nonlinear vibration analysis of the axially moving viscoelastic beam is constructed to expand the time delay. The application scope of the nonlinear vibration theory and nonlinear dynamics theory, the development and improvement of the approximate analysis and numerical solution of the nonlinear continuum (especially the gyro body) under the action of time delay, to provide a theoretical basis for the analysis and design of the corresponding engineering system and technical reserves.
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Castillo, A., F. Castelli, and D. Entekhabi. "Gravitational and capillary soil moisture dynamics for distributed hydrologic models." Hydrology and Earth System Sciences 19, no. 4 (April 21, 2015): 1857–69. http://dx.doi.org/10.5194/hess-19-1857-2015.
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Abstract. Distributed and continuous catchment models are used to simulate water and energy balance and fluxes across varied topography and landscape. The landscape is discretized into computational plan elements at resolutions of 101–103 m, and soil moisture is the hydrologic state variable. At the local scale, the vertical soil moisture dynamics link hydrologic fluxes and provide continuity in time. In catchment models these local-scale processes are modeled using 1-D soil columns that are discretized into layers that are usually 10−3–10−1 m in thickness. This creates a mismatch between the horizontal and vertical scales. For applications across large domains and in ensemble mode, this treatment can be a limiting factor due to its high computational demand. This study compares continuous multi-year simulations of soil moisture at the local scale using (i) a 1-pixel version of a distributed catchment hydrologic model and (ii) a benchmark detailed soil water physics solver. The distributed model uses a single soil layer with a novel dual-pore structure and employs linear parameterization of infiltration and some other fluxes. The detailed solver uses multiple soil layers and employs nonlinear soil physics relations to model flow in unsaturated soils. Using two sites with different climates (semiarid and sub-humid), it is shown that the efficient parameterization in the distributed model captures the essential dynamics of the detailed solver.
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Castillo, A., F. Castelli, and D. Entekhabi. "Gravitational and capillary soil moisture dynamics for hillslope-resolving models." Hydrology and Earth System Sciences Discussions 11, no. 6 (June 30, 2014): 7133–68. http://dx.doi.org/10.5194/hessd-11-7133-2014.
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Abstract. Distributed and continuous catchment models are used to simulate water and energy balance and fluxes across varied topography and landscape. The landscape is discretized into plan computational elements at resolutions of 101–103 m, and soil moisture is the hydrologic state variable. At the local scale, the vertical soil moisture dynamics link hydrologic fluxes and provide continuity in time. In catchment models these local scale processes are modeled using one-dimensional soil columns that are discretized into layers that are usually 10−3–10−1 m in thickness. This creates a mismatch between the horizontal and vertical scales. For applications across large domains and in ensemble mode, this treatment can be a limiting factor due to its high computational demand. This study compares continuous multi-year simulations of soil moisture at the local scale using (i) a 1-D version of a distributed catchment hydrologic model; and (ii) a benchmark detailed soil water physics solver. The distributed model uses a single soil layer with a novel dual-pore structure, and employs linear parameterization of infiltration and some other fluxes. The detailed solver uses multiple soil layers and employs nonlinear soil physics relations to model flow in unsaturated soils. Using two sites with different climates (semiarid and sub-humid), it is shown that the efficient parameterization in the distributed model captures the essential dynamics of the detailed solver.
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REZNIK, G. M., V. ZEITLIN, and M. BEN JELLOUL. "Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model." Journal of Fluid Mechanics 445 (October 16, 2001): 93–120. http://dx.doi.org/10.1017/s002211200100550x.
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We develop a theory of nonlinear geostrophic adjustment of arbitrary localized (i.e. finite-energy) disturbances in the framework of the non-dissipative rotating shallow-water dynamics. The only assumptions made are the well-defined scale of disturbance and the smallness of the Rossby number Ro. By systematically using the multi-time-scale perturbation expansions in Rossby number it is shown that the resulting field is split in a unique way into slow and fast components evolving with characteristic time scales f−10 and (f0Ro)−1 respectively, where f0 is the Coriolis parameter. The slow component is not influenced by the fast one and remains close to the geostrophic balance. The algorithm of its initialization readily follows by construction.The scenario of adjustment depends on the characteristic scale and/or initial relative elevation of the free surface ΔH/H0, where ΔH and H0 are typical values of the initial elevation and the mean depth, respectively. For small relative elevations (ΔH/H0 = O(Ro)) the evolution of the slow motion is governed by the well-known quasi-geostrophic potential vorticity equation for times t [les ] (f0Ro)−1. We find modifications to this equation for longer times t [les ] (f0Ro2)−1. The fast component consists mainly of linear inertia–gravity waves rapidly propagating outward from the initial disturbance.For large relative elevations (ΔH/H0 [Gt ] Ro) the slow field is governed by the frontal geostrophic dynamics equation. The fast component in this case is a spatially localized packet of inertial oscillations coupled to the slow component of the flow. Its envelope experiences slow modulation and obeys a Schrödinger-type modulation equation describing advection and dispersion of the packet. A case of intermediate elevation is also considered.
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Smith, F. T., and P. A. Stewart. "The resonant-triad nonlinear interaction in boundary-layer transition." Journal of Fluid Mechanics 179 (June 1987): 227–52. http://dx.doi.org/10.1017/s0022112087001502.
Full textAbstract:
Recent controlled experiments by Kachanov & Levchenko (1984) and others indicate that, during some slower kinds of transition to turbulence in boundary layers, three-dimensionality can come into play initially as a resonant-triad phenomenon, depending on the disturbance sizes present. The triad interaction, suggested theoretically in the boundary-layer context by Craik (1971) and others, is studied in the present work by means of multi-structured analysis for high characteristic Reynolds numbers. A finite-amplitude/relatively high-frequency approach leads rationally to the nonlinear triad equations, solutions for which are then obtained analytically and computationally in certain central cases of interest (temporal and spatial). The solutions have a rather chaotic spiky appearance as continual energy exchange develops between the two- and three-dimensional nonlinear modes, whose large-scale response seems governed by inviscid dynamics but subject to important, continual ‘rejuvenation’ from small- (fast-) scale viscous action in-between. The three-dimensional growth rate is thereby increased, but not the two-dimensional. Subsequently the disturbed flow enters a higher-amplitude regime similar to that studied in some related papers by the authors and co-workers. Comparisons with the experiments are very supportive of the theory (in the small and in the large), yielding both qualitative and quantitative agreement.