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  3. Chaos Theory

Fractional Dispersive Models and Applications: Recent Developments and Future Perspectives

Posted By: AvaxGenius
Date: 19 Apr 2024 02:00:16
Fractional Dispersive Models and Applications: Recent Developments and Future Perspectives

Fractional Dispersive Models and Applications: Recent Developments and Future Perspectives by Panayotis G. Kevrekidis, Jesús Cuevas-Maraver
English | PDF EPUB (True) | 2024 | 337 Pages | ISBN : 3031549775 | 58.5 MB

This book explores the role of fractional calculus and associated partial differential equations in modeling multiscale phenomena and overlapping macroscopic & microscopic scales, offering an innovative and powerful tool for modeling complex systems. While integer order PDEs have a long-standing history, the novel setting of fractional PDEs opens up new possibilities for the simulation of multi-physics phenomena. The book examines a range of releavant examples that showcase the seamless transition from wave propagation to diffusion or from local to non-local dynamics in both continuum and discrete systems. These systems have been argued as being particularly relevant in contexts such as nonlinear optics, lattice nonlinear dynamical systems, and dispersive nonlinear wave phenomena, where the exploration of the potential fractionality has emerged as a highly active topic for current studies.
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The Art of Randomness: Randomized Algorithms in the Real World

Posted By: First1
Date: 24 Feb 2024 16:04:30
The Art of Randomness: Randomized Algorithms in the Real World

The Art of Randomness: Randomized Algorithms in the Real World by Ronald T. Kneusel
English | March 5th, 2024 | ISBN: 1718503245 | 400 pages | True EPUB (Retail Copy) | 27.37 MB

Harness the power of randomness (and Python code) to solve real-world problems in fun, hands-on experiments—from simulating evolution to encrypting messages to making machine-learning algorithms!
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Schrödinger Equations in Nonlinear Systems (Repost)

Posted By: AvaxGenius
Date: 31 Jan 2024 03:32:48
Schrödinger Equations in Nonlinear Systems (Repost)

Schrödinger Equations in Nonlinear Systems by Wu-Ming Liu , Emmanuel Kengne
English | EPUB (True) | 2019 | 576 Pages | ISBN : 9811365806 | 159 MB

This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions.
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Deterministic Nonlinear Systems: A Short Course (Repost)

Posted By: AvaxGenius
Date: 31 Jan 2024 03:11:54
Deterministic Nonlinear Systems: A Short Course (Repost)

Deterministic Nonlinear Systems: A Short Course by Vadim S. Anishchenko , Tatyana E. Vadivasova , Galina I. Strelkova
English | EPUB (True) | 2014 | 300 Pages | ISBN : 3319068709 | 4.5 MB

This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems.
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Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics (Repost)

Posted By: AvaxGenius
Date: 31 Jan 2024 03:08:41
Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics (Repost)

Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics by Ramon G. Rubio, Yuri S. Ryazantsev, Victor M Starov, Guo-Xiang Huang, Alexander P Chetverikov, Paolo Arena, Alex A. Nepomnyashchy, Alberto Ferrus, Eugene G. Morozov
English | EPUB (True) | 2013 | 781 Pages | ISBN : 3642340695 | 16 MB

Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.
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Strongly Nonlinear Oscillators: Analytical Solutions (Repost)

Posted By: AvaxGenius
Date: 31 Jan 2024 03:05:30
Strongly Nonlinear Oscillators: Analytical Solutions (Repost)

Strongly Nonlinear Oscillators: Analytical Solutions by Livija Cveticanin
English | EPUB (True) | 2014 | 241 Pages | ISBN : 3319052713 | 4.6 MB

This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.
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Schrödinger Equations in Nonlinear Systems (Repost)

Posted By: AvaxGenius
Date: 30 Jan 2024 05:18:48
Schrödinger Equations in Nonlinear Systems (Repost)

Schrödinger Equations in Nonlinear Systems by Wu-Ming Liu , Emmanuel Kengne
English | PDF (True) | 2019 | 576 Pages | ISBN : 9811365806 | 25.6 MB

This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions.
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Avalanches in Functional Materials and Geophysics (Repost)

Posted By: AvaxGenius
Date: 30 Jan 2024 05:06:13
Avalanches in Functional Materials and Geophysics (Repost)

Avalanches in Functional Materials and Geophysics by Ekhard K.H. Salje, Avadh Saxena, Antoni Planes
English | PDF (True) | 2017 | 310 Pages | ISBN : 3319456105 | 19.4 MB

This book provides the state-of-the art of the present understanding of avalanche phenomena in both functional materials and geophysics. The main emphasis of the book is analyzing these apparently different problems within the common perspective of out-of-equilibrium phenomena displaying spatial and temporal complexity that occur in a broad range of scales. Many systems, when subjected to an external force, respond intermittently in the form of avalanches that often span over a wide range of sizes, energies and durations. This is often related to a class of critical behavior characterized by the absence of characteristic scales. Typical examples are magnetization processes, plastic deformation and failure occuring in functional materials. These phenomena share many similarities with seismicity arising from the earth crust failure due to stresses that originate from plate tectonics.
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Nonlinear Photonics in Mid-infrared Quantum Cascade Lasers

Posted By: AvaxGenius
Date: 30 Jan 2024 05:03:02
Nonlinear Photonics in Mid-infrared Quantum Cascade Lasers

Nonlinear Photonics in Mid-infrared Quantum Cascade Lasers by Louise Jumpertz
English | PDF (True) | 2017 | 152 Pages | ISBN : 3319658786 | 17.4 MB

This thesis presents the first comprehensive analysis of quantum cascade laser nonlinear dynamics and includes the first observation of a temporal chaotic behavior in quantum cascade lasers. It also provides the first analysis of optical instabilities in the mid-infrared range.
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Fractional Dynamics, Anomalous Transport and Plasma Science (Repost)

Posted By: AvaxGenius
Date: 30 Jan 2024 04:48:34
Fractional Dynamics, Anomalous Transport and Plasma Science (Repost)

Fractional Dynamics, Anomalous Transport and Plasma Science: Lectures from CHAOS2017 by Christos H. Skiadas
English | EPUB (True) | 2018 | 201 Pages | ISBN : 3030044823 | 31 MB

This book collects interrelated lectures on fractal dynamics, anomalous transport and various historical and modern aspects of plasma sciences and technology.
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Ultrafast Strong Field Dynamics in Dielectrics

Posted By: AvaxGenius
Date: 30 Jan 2024 04:30:15
Ultrafast Strong Field Dynamics in Dielectrics

Ultrafast Strong Field Dynamics in Dielectrics by Annkatrin Madlen Sommer
English | PDF (True) | 2016 | 134 Pages | ISBN : 331941206X | 6 MB

This thesis presents a systematic discussion of experimental approaches to investigating the nonlinear interaction of ultrashort visible strong fields with dielectrics directly in the time domain. The key finding is the distinctly different peak-intensity dependence of the light-matter energy transfer dynamics on the one hand, and the observed transient optical and electronic modifications on the other. As the induced electron dynamics evolve on sub-femtosecond timescales, real-time spectroscopy requires attosecond temporal resolution. This allows a range of parameters to be identified where the optical properties of the samples exposed to ultrashort light fields suffer dramatic changes allowing signal metrology while real absorption leading to dissipation is essentially absent. These findings indicate the feasibility of efficient optical switching at frequencies several orders of magnitude faster than current state-of-the-art electronics and thus have far-reaching technological consequences.
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The Foundations of Chaos Revisited: From Poincaré to Recent Advancements

Posted By: AvaxGenius
Date: 30 Jan 2024 04:23:27
The Foundations of Chaos Revisited: From Poincaré to Recent Advancements

The Foundations of Chaos Revisited: From Poincaré to Recent Advancements by Christos Skiadas
English | PDF (True) | 2016 | 268 ages | ISBN : 331929699X | 9.5 MB

With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré.
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Synergetics of Molecular Systems (Repost)

Posted By: AvaxGenius
Date: 30 Jan 2024 03:16:07
Synergetics of Molecular Systems (Repost)

Synergetics of Molecular Systems by Lev N. Lupichev , Alexander V. Savin , Vasiliy N. Kadantsev
English | PDF (True) | 2015 | 337 Pages | ISBN : 3319081942 | 10.6 MB

Synergetics is the quantitative study of multicomponent systems that exhibit nonlinear dynamics and cooperativity. This book specifically considers basic models of the nonlinear dynamics of molecular systems and discusses relevant applications in biological physics and the polymer sciences.
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Time-Symmetry Breaking in Turbulent Multi-Particle Dispersion (Repost)

Posted By: AvaxGenius
Date: 30 Jan 2024 03:13:36
Time-Symmetry Breaking in Turbulent Multi-Particle Dispersion (Repost)

Time-Symmetry Breaking in Turbulent Multi-Particle Dispersion by Jennifer Jucha
English | PDF (True) | 2015 | 121 Pages | ISBN : 3319191918 | 9.8 MB

This thesis presents experimental and theoretical investigations of the connection between the time asymmetry in the short-time evolution of particle clusters and the intrinsic irreversibility of turbulent flows due to the energy cascade.
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Structural Nonlinear Dynamics and Diagnosis

Posted By: AvaxGenius
Date: 30 Jan 2024 03:10:46
Structural Nonlinear Dynamics and Diagnosis

Structural Nonlinear Dynamics and Diagnosis: Selected papers from CSNDD 2012 and CSNDD 2014 by Mohamed Belhaq
English | PDF (True) | 2015 | 511 Pages | ISBN : 3319198505 | 28.2 MB

This book, which presents the peer-reviewed post-proceedings of CSNDD 2012 and CSNDD 2014, addresses the important role that relevant concepts and tools from nonlinear and complex dynamics could play in present and future engineering applications. It includes 22 chapters contributed by outstanding researchers and covering various aspects of applications, including: structural health monitoring, diagnosis and damage detection, experimental methodologies, active vibration control and smart structures, passive control of structures using nonlinear energy sinks, vibro-impact dynamic MEMS/NEMS/AFM, energy-harvesting materials and structures, and time-delayed feedback control, as well as aspects of deterministic versus stochastic dynamics and control of nonlinear phenomena in physics.
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