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This open access book deals with a rich variety of taxis-type cross-diffusive equations. Particularly, it intends to show the key role played by quasi-energy inequality in the derivation of some necessary a priori estimates. This book addresses applied mathematics and all researchers interested in mathematical development of reaction-diffusion theory and its application and can be a basis for a graduate course in applied mathematics.

Boundary value problems. --- Chemotaxis --- Navier-Stokes equations. --- Mathematical models. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Chemiotaxis --- Chemotropism --- Biochemistry --- Growth --- Taxes (Biology) --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Problemes de contorn --- Quimiotaxi --- Models matemàtics --- Equacions de Navier-Stokes --- Navier-Stokes (Equacions) --- Dinàmica de fluids --- Equacions en derivades parcials --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Anàlisi de sistemes --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Simulació per ordinador --- Teoria de màquines --- Models biològics --- Bioquímica --- Creixement --- Problemes de valor límit --- Equacions diferencials --- Física matemàtica --- Funcions de variables complexes --- Dispersió (Matemàtica) --- Equacions de Von Kármán --- Problema de Dirichlet --- Problema de Neumann --- Problemes de Riemann-Hilbert --- Problemes de valor inicial --- Reaction-Diffusion --- Haptotaxis --- Navier-Stokes --- Cancer invasion --- Coral fertilization --- Sensity-suppressed motility --- Oncolytic virotherapy --- Foraging scrounging interplay

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The authors begin this book with a systematic overview of superconductivity, superconducting materials, magnetic levitation, and superconducting magnetic levitation - the prerequisites to understand the latter part of the book - that forms a solid foundation for further study in High Temperature Superconducting Magnetic Levitation (HTS Maglev). This book presents our research progress on HTS Maglev at Applied Superconductivity Laboratory (ASCLab) of Southwest Jiaotong University (SWJTU), China, with an emphasis on the findings that led to the world's first manned HTS Maglev test vehicle "Century". The book provides a detailed description on our previous work at ASCLab including the designing of the HTS Maglev test and measurement method as well as the apparatus, building "Century", developing the HTS Maglev numerical simulation system, and making new progress on HTS Maglev. The final parts of this book discuss research and prototyping efforts at ASCLab in several adjacent fi elds including HTS Maglev bearing, Flywheel Energy Storage System (FESS) and HTS maglev launch technology. We hope this book becomes a valuable source for researchers and engineers working in the fascinating field of HTS Maglev science and engineering. ContentsFundamentals of superconductivitySuperconducting materialsMagnetic levitationSuperconducting magnetic levitationHTS Maglev experimental methods and set-upFirst manned HTS Maglev vehicle in the worldNumerical simulations of HTS MaglevNew progress of HTS Maglev vehicleHTS Maglev bearing and flywheel energy storage systemHTS Maglev launch technology

Superconducting magnets. --- Magnets, Superconducting --- Superconducting high-field magnets --- Electromagnets --- Superconductors