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1 Kulasiri, Don Stochastic Differential Equations for Chemical Transformations in White Noise Probability Space I13295 2024 eBook  
2 Qin, Yuming Prandtl Equations and Related Boundary Layer Equations I13249 2024 eBook  
3 Yang, Bo Rogue Waves in Integrable Systems I13194 2024 eBook  
4 Selinger, Jonathan V Introduction to Topological Defects and Solitons I13189 2024 eBook  
5 Moshagen, Hermann The General Kelvin-Helmholtz Stability Model I13113 2024 eBook  
6 Madenci, Erdogan Peridynamics and Its Applications Using Ansys I13106 2024 eBook  
7 Dhurandhar, Sanjeev Understanding Mathematical Concepts in Physics I13100 2024 eBook  
8 Altenbach, Holm Selected Problems of Solid Mechanics and Solving Methods I13058 2024 eBook  
9 Kevrekidis, Panayotis G Fractional Dispersive Models and Applications I13005 2024 eBook  
10 Veliev, Oktay Multidimensional Periodic Schr??dinger Operator I12979 2024 eBook  
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TitleStochastic Differential Equations for Chemical Transformations in White Noise Probability Space : Wick Products and Computations
Author(s)Kulasiri, Don
PublicationSingapore, 1. Imprint: Springer 2. Springer Nature Singapore, 2024.
DescriptionXVI, 155 p. 43 illus., 41 illus. in color : online resource
Abstract NoteThis book highlights the applications of stochastic differential equations in white noise probability space to chemical reactions that occur in biology. These reactions operate in fluctuating environments and are often coupled with each other. The theory of stochastic differential equations based on white noise analysis provides a physically meaningful modelling framework. The Wick product-based calculus for stochastic variables is similar to regular calculus; therefore, there is no need for Ito calculus. Numerical examples are provided with novel ways to solve the equations. While the theory of white noise analysis is well developed by mathematicians over the past decades, applications in biophysics do not exist. This book provides a bridge between this kind of mathematics and biophysics
ISBN,Price9789819793921
Keyword(s)1. BIOINFORMATICS 2. BIOMATHEMATICS 3. Computational and Systems Biology 4. Computational Physics and Simulations 5. COMPUTER SIMULATION 6. DIFFERENTIAL EQUATIONS 7. EBOOK 8. EBOOK - SPRINGER 9. Mathematical and Computational Biology 10. MATHEMATICAL PHYSICS
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TitlePrandtl Equations and Related Boundary Layer Equations
Author(s)Qin, Yuming;Dong, Xiaolei;Wang, Xiuqing
PublicationSingapore, 1. Imprint: Springer 2. Springer Nature Singapore, 2024.
DescriptionX, 373 p : online resource
Abstract NoteThis book aims to present some recent results on Prandtl equations and MHD boundary layer equations. This book is essentially divided into two parts. Chapter 1 as the first part systematically surveys the results till 2020 on Prandtl equations and MHD boundary layer equations. Chapter 2 to 6 are the main part of the book, which presents the local and the global well-posedness of solutions to the Prandtl equations and MHD boundary layer equations. In detail, Chapter 2 is concerned with global well-posedness of solutions to the 2D Prandtl-Hartmann equations in an analytic framework. Chapter 3 investigates the local existence of solutions to the 2D Prandtl equations in a weighted Sobolev space. Chapter 4 studies the local well-posedness of solutions to the 2D mixed Prandtl equations in a Sobolev space without monotonicity and lower bound. Chapter 5 is concerned with global existence of solutions to the 2D magnetic Prandtl equations in the Prandtl-Hartmann regime. Chapter 6 proves the local existence of solutions to the 3D Prandtl equations with a special structure. Mathematicians and physicists who are interested in fluid dynamics will find this book helpful
ISBN,Price9789819745654
Keyword(s)1. DIFFERENTIAL EQUATIONS 2. EBOOK 3. EBOOK - SPRINGER 4. FLUIDS 5. INTEGRAL EQUATIONS 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. Soft condensed matter
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TitleRogue Waves in Integrable Systems
Author(s)Yang, Bo;Yang, Jianke
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2024.
DescriptionXI, 416 p. 102 illus., 99 illus. in color : online resource
Abstract NoteThis book offers a holistic picture of rogue waves in integrable systems. Rogue waves are a rare but extreme phenomenon that occur most famously in water, but also in other diverse contexts such as plasmas, optical fibers and Bose-Einstein condensates where, despite the seemingly disparate settings, a common theoretical basis exists. This book presents the physical derivations of the underlying integrable nonlinear partial differential equations, derives the explicit and compact rogue wave solutions in these integrable systems, and analyzes rogue wave patterns that arise in these solutions, for many integrable systems and in multiple physical contexts. Striking a balance between theory and experiment, the book also surveys recent experimental insights into rogue waves in water, optical fibers, plasma, and Bose-Einstein condensates. In taking integrable nonlinear wave systems as a starting point, this book will be of interest to a broad cross section of researchers and graduate students in physics and applied mathematics who encounter nonlinear waves
ISBN,Price9783031667930
Keyword(s)1. CONTINUUM MECHANICS 2. DIFFERENTIAL EQUATIONS 3. EBOOK 4. EBOOK - SPRINGER 5. FIBER OPTICS 6. MATHEMATICAL PHYSICS 7. PLASMA WAVES 8. Quantum Gases and Condensates 9. QUANTUM STATISTICS 10. Waves, instabilities and nonlinear plasma dynamics
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TitleIntroduction to Topological Defects and Solitons : In Liquid Crystals, Magnets, and Related Materials
Author(s)Selinger, Jonathan V
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2024.
DescriptionXIII, 213 p. 80 illus., 77 illus. in color : online resource
Abstract NoteThis textbook introduces topological defects and solitons at a level suitable for advanced undergraduates and beginning graduate students in physics and materials science. It avoids the formal mathematics of topology, and instead concentrates on the physical properties of these topological structures. The first half of the book concentrates on fundamental principles of defects and solitons, and illustrates these principles with a single example???the xy model for 2D magnetic order. It begins by defining the concept of a winding number, and uses this concept to describe the topology of defects (vortices or disclinations) and solitons (domain walls), carefully identifying the similarities and differences between these two types of topological structures. It then goes on to discuss physical properties of defects and solitons, including free energy, dynamics, statistical mechanics, and coupling with curvature. It shows how these concepts emerge from a theory with variable magnitude of order, and hence how topology can be viewed as an approximation to physics. The second half goes on to explore a wider range of topological defects and solitons. First, it considers more complex types of order???2D nematic liquid crystals, 3D magnetic or liquid-crystal order, 2D or 3D crystalline solids???and shows how each type of order leads to specific topological structures. Next, it discusses defects and solitons that are characterized by 2D or 3D measuring surfaces, not just 1D loops, including hedgehogs, skyrmions, and hopfions. These structures are more complex, but they can still be understood using the same fundamental principles. A final chapter describes the formation of phases with regular arrays of defects or solitons
ISBN,Price9783031702006
Keyword(s)1. CONDENSED MATTER 2. CONDENSED MATTER PHYSICS 3. DIFFERENTIAL EQUATIONS 4. EBOOK 5. EBOOK - SPRINGER 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. Soft condensed matter 9. Soft Materials
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TitleThe General Kelvin-Helmholtz Stability Model : With Applications to Sand Wave and Water Wave Generation
Author(s)Moshagen, Hermann
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2024.
DescriptionXII, 102 p. 37 illus., 22 illus. in color : online resource
Abstract NoteThis book presents a generalized version of the classical Kelvin-Helmholtz instability, a useful tool which allows for new approaches when studying stability problems in fluid mechanics, as well as its important applications. It begins by providing an introduction to hydrodynamic stability and the Kelvin-Helmholtz (KH) instability. The author then develops the general KH stability model for a multi-layer flow system, which includes the conventional KH instability as a special case. This book also includes the detailed discussion of two important applications of this model: the generation of sand waves in alluvial channels and the generation of wind waves on water. Additionally, the effects of nonlinearities and the use of computational methods to study KH instability are included. This book serves as a concise and modern treatment of the KH stability model with specific attention paid to hydrodynamic stability analysis. It is ideal for graduate students interested in fluid dynamics as well as scientists and engineers in the fields of oceanography, geophysics, offshore engineering, and more
ISBN,Price9783031619847
Keyword(s)1. CONTINUUM MECHANICS 2. DIFFERENTIAL EQUATIONS 3. EBOOK 4. EBOOK - SPRINGER 5. Engineering Fluid Dynamics 6. FLUID MECHANICS 7. FLUIDS 8. MATHEMATICAL PHYSICS 9. Soft and Granular Matter 10. Soft condensed matter
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TitlePeridynamics and Its Applications Using Ansys
Author(s)Madenci, Erdogan;Anicode, Sundaram Vinod Kumar;Zhang, Yanan
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2024.
DescriptionXIV, 495 p. 450 illus., 442 illus. in color : online resource
Abstract NoteThis book introduces a unified implementation of bond- and state-based peridynamic theory (PD) within a commercial finite element framework, Ansys, utilizing its native elements. It details the implementation of the PD theory and its integration with traditional finite elements. The primary objective is to equip students, researchers, and practicing engineers with both theoretical and practical knowledge of the PD theory, along with the skills necessary for analyzing engineering problems using Ansys. The book demonstrates that, unlike the conventional finite element method (FEM), the PD theory is highly suitable for progressive failure analysis, the multi-scale analysis of materials involving fracture and failure, and multi-physics analysis, including electromigration, corrosion, and electrodeposition. Additionally, it provides a step-by-step illustration of the specific procedures in the pre-processing, solution, and post-processing phases of the analysis through the Graphical User Interface (GUI) for various applications. The book is designed to be introductory and self-contained, minimizing the need for additional reference material. Describes an implementation of PD theory and its coupling to finite element method in Ansys, using its native elements; Utilization of Ansys through both the Graphics User Interface (GUI) and the Ansys Parametric Design Language (APDL); Explains the process for solving problems in various applications with the Ansys GUI, includes Ansys input files
ISBN,Price9783031598968
Keyword(s)1. Computational Physics and Simulations 2. Computer Modelling 3. COMPUTER SIMULATION 4. CONTINUUM MECHANICS 5. DIFFERENTIAL EQUATIONS 6. EBOOK 7. EBOOK - SPRINGER 8. MATHEMATICAL PHYSICS
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TitleUnderstanding Mathematical Concepts in Physics : Insights from Geometrical and Numerical Approaches
Author(s)Dhurandhar, Sanjeev
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2024.
DescriptionXVI, 351 p. 57 illus., 42 illus. in color : online resource
Abstract NoteModern mathematics has become an essential part of today???s physicist???s arsenal and this book covers several relevant such topics. The primary aim of this book is to present key mathematical concepts in an intuitive way with the help of geometrical and numerical methods - understanding is the key. Not all differential equations can be solved with standard techniques. Examples illustrate how geometrical insights and numerical methods are useful in understanding differential equations in general but are indispensable when extracting relevant information from equations that do not yield to standard methods. Adopting a numerical approach to complex analysis it is shown that Cauchy???s theorem, the Cauchy integral formula, the residue theorem, etc. can be verified by performing hands-on computations with Python codes. Figures elucidate the concept of poles and essential singularities. Further the book covers topology, Hilbert spaces, Fourier transforms (discussing how fast Fourier transform works), modern differential geometry, Lie groups and Lie algebras, probability and useful probability distributions, and statistical detection of signals. Novel features include: (i) Topology is introduced via the notion of continuity on the real line which then naturally leads to topological spaces. (ii) Data analysis in a differential geometric framework and a general description of ??2 discriminators in terms of vector bundles. This book is targeted at physics graduate students and at theoretical (and possibly experimental) physicists. Apart from research students, this book is also useful to active physicists in their research and teaching
ISBN,Price9783031603945
Keyword(s)1. ANALYSIS 2. DIFFERENTIAL EQUATIONS 3. EBOOK 4. EBOOK - SPRINGER 5. FOURIER ANALYSIS 6. LIE GROUPS 7. MATHEMATICAL ANALYSIS 8. MATHEMATICAL PHYSICS 9. Theoretical, Mathematical and Computational Physics 10. TOPOLOGICAL GROUPS 11. Topological Groups and Lie Groups
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8.     
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TitleSelected Problems of Solid Mechanics and Solving Methods
Author(s)Altenbach, Holm;Bogdanov, Viacheslav;Grigorenko, Alexander Ya;Kushnir, Roman M;Nazarenko, Vladimir M;Eremeyev, Victor A
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2024.
DescriptionXII, 532 p. 203 illus., 79 illus. in color : online resource
Abstract NoteThis book examines new approaches for the estimation of errors in approximate theories. Numerical and analytical methods in mechanics often require the establishment of a set of basic equations, and various approaches exist to create approximate theories from them. The problem is that nobody knows the boundaries of the estimation of errors in approximate theories. This book presents new approaches to overcome this problem and to provide the reader with suitable methods for the relevant field, including a representation of different scientific schools and different countries. These new methods are helping to solve many problems not only in analytical Mechanics but also in Physics, Mathematics, and Civil Engineering
ISBN,Price9783031540639
Keyword(s)1. CIVIL ENGINEERING 2. CONTINUUM MECHANICS 3. DIFFERENTIAL EQUATIONS 4. EBOOK 5. EBOOK - SPRINGER 6. Mechanics, Applied 7. Solid Mechanics 8. SOLIDS
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TitleFractional Dispersive Models and Applications : Recent Developments and Future Perspectives
Author(s)Kevrekidis, Panayotis G;Cuevas-Maraver, Jes??s
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2024.
DescriptionXV, 328 p. 94 illus., 78 illus. in color : online resource
Abstract NoteThis 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 relevant 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. The volume consists of contributions from a diverse group of active scholars and experts across different fields, providing a detailed examination of the field's past, present, and future state-of-the-art in the interplay of fractional PDEs and nonlinear wave phenomena. It is intended to be of wide interest to both seasoned researchers and beginners in the Field of Nonlinear Science. This book sets the stage for the next decade of research and beyond and is a timely and relevant reference of choice for this crucial junction of current research
ISBN,Price9783031549786
Keyword(s)1. BIOINFORMATICS 2. COMPLEX SYSTEMS 3. Computational and Systems Biology 4. DIFFERENTIAL EQUATIONS 5. EBOOK 6. EBOOK - SPRINGER 7. NONLINEAR OPTICS 8. PLASMA WAVES 9. SYSTEM THEORY 10. Waves, instabilities and nonlinear plasma dynamics
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10.    
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TitleMultidimensional Periodic Schr??dinger Operator : Perturbation Theories for High Energy Regions and Their Applications
Author(s)Veliev, Oktay
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2024.
DescriptionXIII, 411 p. 1 illus : online resource
Abstract NoteThis book describes the direct and inverse problems of the multidimensional Schr??dinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the Bethe???Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential. This updated and significantly expanded third edition features an extension of this framework to all dimensions, offering a now complete theory of self-adjoint Schr??dinger operators within periodic potentials. Drawing from recent advancements in mathematical analysis, this edition delves even deeper into the intricacies of the subject. It explores the connections between the multidimensional Schr??dinger operator, periodic potentials, and other fundamental areas of mathematical physics. The book's comprehensive approach equips both students and researchers with the tools to tackle complex problems and contribute to the ongoing exploration of quantum phenomena
ISBN,Price9783031490354
Keyword(s)1. CONDENSED MATTER 2. CONDENSED MATTER PHYSICS 3. DIFFERENTIAL EQUATIONS 4. EBOOK 5. EBOOK - SPRINGER 6. MATHEMATICAL PHYSICS 7. OPERATOR THEORY 8. QUANTUM PHYSICS
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