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This book details the development of techniques and ideas from the radial basis function. It begins with a mathematical description of the basic concept of radial function method with chapters progressively delving into the derivation and construction of radial basis functions for large-scale wave propagation problems including singularity problems, high-frequency wave problems and large-scale computation problems. This reference, written by experts in numerical analysis, demonstrates how the functions arise naturally in mathematical analyses of structures responding to external loads. Readers are also equipped with mathematical knowledge about the radial basis function for understanding key algorithms required for practical solutions.

Radial basis functions.

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The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.

Lyapunov functions. --- Radial basis functions. --- Electronic books. -- local. --- Lyapunov functions --- Radial basis functions --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Mathematical Theory --- Basis functions, Radial --- Functions, Radial basis --- Radial basis function method --- Functions, Liapunov --- Liapunov functions --- Mathematics. --- Approximation theory. --- Dynamics. --- Ergodic theory. --- Differential equations. --- Dynamical Systems and Ergodic Theory. --- Approximations and Expansions. --- Ordinary Differential Equations. --- 517.91 Differential equations --- Differential equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Math --- Science --- Approximation theory --- Differentiable dynamical systems. --- Differential Equations. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics

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As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications.

radial basis functions --- finite difference methods --- traveling waves --- non-uniform grids --- chaotic oscillator --- one-step method --- multi-step method --- computer arithmetic --- FPGA --- high strain rate impact --- modeling and simulation --- smoothed particle hydrodynamics --- finite element analysis --- hybrid nanofluid --- heat transfer --- non-isothermal --- shrinking surface --- MHD --- radiation --- multilayer perceptrons --- quaternion neural networks --- metaheuristic optimization --- genetic algorithms --- micropolar fluid --- constricted channel --- MHD pulsatile flow --- strouhal number --- flow pulsation parameter --- multiple integral finite volume method --- finite difference method --- Rosenau-KdV --- conservation --- solvability --- convergence --- transmission electron microscopy (TEM) --- convolutional neural networks (CNN) --- anomaly detection --- principal component analysis (PCA) --- machine learning --- deep learning --- neural networks --- Gallium-Arsenide (GaAs) --- radiation-based flowmeter --- two-phase flow --- feature extraction --- artificial intelligence --- time domain --- Boltzmann equation --- collision integral --- convolutional neural network --- annular regime --- scale layer-independent --- petroleum pipeline --- volume fraction --- dual energy technique --- prescribed heat flux --- similarity solutions --- dual solutions --- stability analysis --- RBF-FD --- node sampling --- lebesgue constant --- complex regions --- finite-difference methods --- data assimilation --- model order reduction --- finite elements analysis --- high dimensional data --- welding

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With rapid developments being made in the exploration of marine resources, coastal geohazard and offshore geotechnics have attracted a great deal of attention from coastal geotechnical engineers, with significant progress being made in recent years. Due to the complicated nature of marine environmnets, there are numerous natural marine geohazard preset throughout the world’s marine areas, e.g., the South China Sea. In addition, damage to offshore infrastructure (e.g., monopiles, bridge piers, etc.) and their supporting installations (pipelines, power transmission cables, etc.) has occurred in the last decades. A better understanding of the fundamental mechanisms and soil behavior of the seabed in marine environments will help engineers in the design and planning processes of coastal geotechnical engineering projects. The purpose of this book is to present the recent advances made in the field of coastal geohazards and offshore geotechnics. The book will provide researchers with information reagrding the recent developments in the field, and possible future developments. The book is composed of eighteen papers, covering three main themes: (1) the mechanisms of fluid–seabed interactions and the instability associated with seabeds when they are under dynamic loading (papers 1–5); (2) evaluation of the stability of marine infrastructure, including pipelines (papers 6–8), piled foundation and bridge piers (papers 9–12), submarine tunnels (paper 13), and other supported foundations (paper 14); and (3) coastal geohazards, including submarine landslides and slope stability (papers 15–16) and other geohazard issues (papers 17–18). The editors hope that this book will functoin as a guide for researchers, scientists, and scholars, as well as practitioners of coastal and offshore engineering.

wave motion --- offshore deposits --- seabed response --- FEM --- pore pressure --- wave-current-seabed interaction --- RANS equations --- k-ε model --- current velocity --- seabed liquefaction --- liquefaction --- lateral displacement --- response surface method (RSM) --- artificial neural network (ANN) --- wave action --- silty sand --- seepage flow --- soil erosion --- pore-pressure accumulation --- three-phase soil model --- immersed tunnel --- trench --- numerical study --- porous seabed --- pumping well test --- groundwater fluctuation --- stratum deformation --- micro-confined aquifer --- wave–current–seabed interaction --- Reynolds-Averaged Navier-Stokesequations --- buried pipeline --- k-ε turbulence model --- oscillatory liquefaction --- wave-soil-pipeline interactions --- meshfree model --- local radial basis functions collocation method --- hydrate-bearing sediments --- damage statistical constitutive model --- multi-field coupling --- wellbore stability --- bridge scour --- identification --- ambient vibration --- field application --- natural frequency --- mode shape --- superstructure --- cable-stayed bridge --- Principal stress rotation --- dynamic loading --- wave (current)-induced soil response --- open-ended pile --- soil plug --- offshore wind turbines --- lateral cyclic loading --- model test --- discrete element simulation --- rock-socketed piles --- monopiles --- impedances --- dynamic responses --- buoyancy --- bottom-supported foundation --- field test --- numerical analysis --- giant submarine landslides --- shelf break --- South China Sea --- Himalayan orogeny --- repeated submarine landslides --- coastal-embankment slope --- stability --- unsaturated soil --- multilayered --- matric suction --- random searching algorithm --- rainfall infiltration --- scour --- soft clay --- monopile --- stress history --- hypoplastic model --- submarine pipeline --- dense seabed foundation --- seismic dynamics --- resonance of submarine pipeline --- FSSI-CAS 2D --- n/a