Advances in Nonlinear Geosciences
Advances in Nonlinear Geosciences

Author: Anastasios A. Tsonis

Publisher: Springer

Published: 2017-10-13

Total Pages: 708

ISBN-13: 3319588958

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Advances in Nonlinear Geosciences is a set of contributions from the participants of “30 Years of Nonlinear Dynamics” held July 3-8, 2016 in Rhodes, Greece as part of the Aegean Conferences, as well as from several other experts in the field who could not attend the meeting. The volume brings together up-to-date research from the atmospheric sciences, hydrology, geology, and other areas of geosciences and presents the new advances made in the last 10 years. Topics include chaos synchronization, topological data analysis, new insights on fractals, multifractals and stochasticity, climate dynamics, extreme events, complexity, and causality, among other topics.

Nonlinear Analysis
Nonlinear Analysis

Author: Leszek Gasinski

Publisher: CRC Press

Published: 2005-07-27

Total Pages: 992

ISBN-13: 9781584884842

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Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.

Advances in Earth Science
Advances in Earth Science

Author: Peter R. Sammonds

Publisher: World Scientific

Published: 2007

Total Pages: 343

ISBN-13: 186094762X

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" ... articles originating from invited papers published in the Philosophical Transactions of the Royal Society, [series A]."-- P. [4] of cover.

Nonlinear Analysis - Theory and Methods
Nonlinear Analysis - Theory and Methods

Author: Nikolaos S. Papageorgiou

Publisher: Springer

Published: 2019-02-26

Total Pages: 586

ISBN-13: 3030034305

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This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.

Mathematical Geosciences
Mathematical Geosciences

Author: Joseph L. Awange

Publisher: Springer

Published: 2018-01-29

Total Pages: 615

ISBN-13: 3319673718

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This book showcases powerful new hybrid methods that combine numerical and symbolic algorithms. Hybrid algorithm research is currently one of the most promising directions in the context of geosciences mathematics and computer mathematics in general. One important topic addressed here with a broad range of applications is the solution of multivariate polynomial systems by means of resultants and Groebner bases. But that’s barely the beginning, as the authors proceed to discuss genetic algorithms, integer programming, symbolic regression, parallel computing, and many other topics. The book is strictly goal-oriented, focusing on the solution of fundamental problems in the geosciences, such as positioning and point cloud problems. As such, at no point does it discuss purely theoretical mathematics. "The book delivers hybrid symbolic-numeric solutions, which are a large and growing area at the boundary of mathematics and computer science." Dr. Daniel Li chtbau

Data Assimilation for the Geosciences
Data Assimilation for the Geosciences

Author: Steven J. Fletcher

Publisher: Elsevier

Published: 2017-03-10

Total Pages: 978

ISBN-13: 0128044845

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Data Assimilation for the Geosciences: From Theory to Application brings together all of the mathematical,statistical, and probability background knowledge needed to formulate data assimilation systems in one place. It includes practical exercises for understanding theoretical formulation and presents some aspects of coding the theory with a toy problem. The book also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to the atmosphere, oceans, as well as the land surface and other geophysical situations. It offers a comprehensive presentation of the subject, from basic principles to advanced methods, such as Particle Filters and Markov-Chain Monte-Carlo methods. Additionally, Data Assimilation for the Geosciences: From Theory to Application covers the applications of data assimilation techniques in various disciplines of the geosciences, making the book useful to students, teachers, and research scientists. Includes practical exercises, enabling readers to apply concepts in a theoretical formulation Offers explanations for how to code certain parts of the theory Presents a step-by-step guide on how, and why, data assimilation works and can be used

Hamilton-Jacobi-Bellman Equations
Hamilton-Jacobi-Bellman Equations

Author: Dante Kalise

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-08-06

Total Pages: 245

ISBN-13: 3110542714

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Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme

Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data
Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data

Author: Stephen J. Guastello

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 616

ISBN-13: 1439820023

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Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflect

Machine Learning in Geomechanics 1
Machine Learning in Geomechanics 1

Author: Ioannis Stefanou

Publisher: John Wiley & Sons

Published: 2024-11-13

Total Pages: 276

ISBN-13: 1789451922

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Machine learning has led to incredible achievements in many different fields of science and technology. These varied methods of machine learning all offer powerful new tools to scientists and engineers and open new paths in geomechanics. The two volumes of Machine Learning in Geomechanics aim to demystify machine learning. They present the main methods and provide examples of its applications in mechanics and geomechanics. Most of the chapters provide a pedagogical introduction to the most important methods of machine learning and uncover the fundamental notions underlying them. Building from the simplest to the most sophisticated methods of machine learning, the books give several hands-on examples of coding to assist readers in understanding both the methods and their potential and identifying possible pitfalls.