Experimental Nonlinear Physics

The review gives and account of the historical development, the current state and possible future developments of experimental nonlinear physics, with emphasis on acoustics, hydrodynamics and optics. The concepts of nonlinear time-series analysis which are the basis of the analysis of experimental outcomes from nonlinear systems are explained and recent developments pertaining to such different fields as modeling, prediction, nonlinear noise reduction, detecting determinism, synchronization, and spatio-temporal time series are surveyed. An overview is given of experiments on acoustic cavitation, a field rich of nonlinear phenomena such as nonlinear oscillations, chaotic dynamics and structure formation, and one of the first physical systems to exhibit period-doubling and chaos in experiment.

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Time-Series Models in Marketing: Some Recent Developments

Marketing ZFP ◽

10.15358/0344-1369-2010-jrm-1-24 ◽

2010 ◽

Vol 32 (JRM 1) ◽

pp. 24-29

Author(s):

Marnik G. Dekimpe ◽

Dominique M. Hanssens

Keyword(s):

Time Series ◽

Time Series Models ◽

Recent Developments

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A spatio-temporal specification language and its completeness & decidability

Journal of Cloud Computing Advances Systems and Applications ◽

10.1186/s13677-020-00209-3 ◽

2020 ◽

Vol 9 (1) ◽

Author(s):

Tengfei Li ◽

Jing Liu ◽

Haiying Sun ◽

Xiang Chen ◽

Lipeng Zhang ◽

...

Keyword(s):

Intelligent Transportation System ◽

Cyber Physical Systems ◽

Specification Language ◽

Finite Model ◽

Critical Systems ◽

Physical Systems ◽

Spatial Objects ◽

Temporal Properties ◽

Spatio Temporal ◽

Temporal Specification

AbstractIn the past few years, significant progress has been made on spatio-temporal cyber-physical systems in achieving spatio-temporal properties on several long-standing tasks. With the broader specification of spatio-temporal properties on various applications, the concerns over their spatio-temporal logics have been raised in public, especially after the widely reported safety-critical systems involving self-driving cars, intelligent transportation system, image processing. In this paper, we present a spatio-temporal specification language, STSL PC, by combining Signal Temporal Logic (STL) with a spatial logic S4 u, to characterize spatio-temporal dynamic behaviors of cyber-physical systems. This language is highly expressive: it allows the description of quantitative signals, by expressing spatio-temporal traces over real valued signals in dense time, and Boolean signals, by constraining values of spatial objects across threshold predicates. STSL PC combines the power of temporal modalities and spatial operators, and enjoys important properties such as finite model property. We provide a Hilbert-style axiomatization for the proposed STSL PC and prove the soundness and completeness by the spatio-temporal extension of maximal consistent set and canonical model. Further, we demonstrate the decidability of STSL PC and analyze the complexity of STSL PC. Besides, we generalize STSL to the evolution of spatial objects over time, called STSL OC, and provide the proof of its axiomatization system and decidability.

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Efficient Long-Term Degradation Profiling in Time Series for Complex Physical Systems

Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '15 ◽

10.1145/2783258.2788572 ◽

2015 ◽

Cited By ~ 6

Author(s):

Liudmila Ulanova ◽

Tan Yan ◽

Haifeng Chen ◽

Guofei Jiang ◽

Eamonn Keogh ◽

...

Keyword(s):

Time Series ◽

Physical Systems

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Nondegenerate Bright Solitons in Coupled Nonlinear Schrödinger Systems: Recent Developments on Optical Vector Solitons

Photonics ◽

10.3390/photonics8070258 ◽

2021 ◽

Vol 8 (7) ◽

pp. 258

Author(s):

S. Stalin ◽

R. Ramakrishnan ◽

M. Lakshmanan

Keyword(s):

Propagation Constant ◽

Short Wave ◽

Nonlinear Phenomena ◽

Bilinear Method ◽

Nonlinear Schrödinger ◽

Bright Solitons ◽

Nonlinear Schrödinger Systems ◽

Recent Developments ◽

Potential Applications ◽

Photorefractive Materials

Nonlinear dynamics of an optical pulse or a beam continue to be one of the active areas of research in the field of optical solitons. Especially, in multi-mode fibers or fiber arrays and photorefractive materials, the vector solitons display rich nonlinear phenomena. Due to their fascinating and intriguing novel properties, the theory of optical vector solitons has been developed considerably both from theoretical and experimental points of view leading to soliton-based promising potential applications. Mathematically, the dynamics of vector solitons can be understood from the framework of the coupled nonlinear Schrödinger (CNLS) family of equations. In the recent past, many types of vector solitons have been identified both in the integrable and non-integrable CNLS framework. In this article, we review some of the recent progress in understanding the dynamics of the so called nondegenerate vector bright solitons in nonlinear optics, where the fundamental soliton can have more than one propagation constant. We address this theme by considering the integrable two coupled nonlinear Schrödinger family of equations, namely the Manakov system, mixed 2-CNLS system (or focusing-defocusing CNLS system), coherently coupled nonlinear Schrödinger (CCNLS) system, generalized coupled nonlinear Schrödinger (GCNLS) system and two-component long-wave short-wave resonance interaction (LSRI) system. In these models, we discuss the existence of nondegenerate vector solitons and their associated novel multi-hump geometrical profile nature by deriving their analytical forms through the Hirota bilinear method. Then we reveal the novel collision properties of the nondegenerate solitons in the Manakov system as an example. The asymptotic analysis shows that the nondegenerate solitons, in general, undergo three types of elastic collisions without any energy redistribution among the modes. Furthermore, we show that the energy sharing collision exhibiting vector solitons arises as a special case of the newly reported nondegenerate vector solitons. Finally, we point out the possible further developments in this subject and potential applications.

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Evolving Fuzzy Time Series for Spatio-temporal Forecasting in Renewable Energy Systems

Renewable Energy ◽

10.1016/j.renene.2021.02.117 ◽

2021 ◽

Author(s):

Carlos A. Severiano ◽

Petrônio de Cândido de Lima e Silva ◽

Miri Weiss Cohen ◽

Frederico Gadelha Guimarães

Keyword(s):

Time Series ◽

Renewable Energy ◽

Energy Systems ◽

Fuzzy Time Series ◽

Renewable Energy Systems ◽

Spatio Temporal

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Adjoint-based direct data assimilation of GNSS time series for optimizing frictional parameters and predicting postseismic deformation following the 2003 Tokachi-oki earthquake

Earth Planets and Space ◽

10.1186/s40623-020-01293-0 ◽

2020 ◽

Vol 72 (1) ◽

Author(s):

Masayuki Kano ◽

Shin’ichi Miyazaki ◽

Yoichi Ishikawa ◽

Kazuro Hirahara

Keyword(s):

Time Series ◽

Data Assimilation ◽

Evaluation Method ◽

Temporal Evolution ◽

Recovery Process ◽

Postseismic Deformation ◽

Coseismic Slip ◽

Megathrust Earthquakes ◽

Spatio Temporal ◽

Gnss Time Series

Abstract Postseismic Global Navigation Satellite System (GNSS) time series followed by megathrust earthquakes can be interpreted as a result of afterslip on the plate interface, especially in its early phase. Afterslip is a stress release process accumulated by adjacent coseismic slip and can be considered a recovery process for future events during earthquake cycles. Spatio-temporal evolution of afterslip often triggers subsequent earthquakes through stress perturbation. Therefore, it is important to quantitatively capture the spatio-temporal evolution of afterslip and related postseismic crustal deformation and to predict their future evolution with a physics-based simulation. We developed an adjoint data assimilation method, which directly assimilates GNSS time series into a physics-based model to optimize the frictional parameters that control the slip behavior on the fault. The developed method was validated with synthetic data. Through the optimization of frictional parameters, the spatial distributions of afterslip could roughly (but not in detail) be reproduced if the observation noise was included. The optimization of frictional parameters reproduced not only the postseismic displacements used for the assimilation, but also improved the prediction skill of the following time series. Then, we applied the developed method to the observed GNSS time series for the first 15 days following the 2003 Tokachi-oki earthquake. The frictional parameters in the afterslip regions were optimized to A–B ~ O(10 kPa), A ~ O(100 kPa), and L ~ O(10 mm). A large afterslip is inferred on the shallower side of the coseismic slip area. The optimized frictional parameters quantitatively predicted the postseismic GNSS time series for the following 15 days. These characteristics can also be detected if the simulation variables can be simultaneously optimized. The developed data assimilation method, which can be directly applied to GNSS time series following megathrust earthquakes, is an effective quantitative evaluation method for assessing risks of subsequent earthquakes and for monitoring the recovery process of megathrust earthquakes.

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