Note: Intro -- Series preface -- Preface -- Acknowledgement -- Editor biography -- Jian Liu -- List of contributors -- Chapter 1 Research and application of reflective microscopy -- 1.1 Introduction -- 1.2 Current situation of research on reflective microscopy -- 1.3 The current situation of application of reflective microscopy -- 1.4 Summary -- References -- Chapter 2 Apodization factor and linearly polarized light focusing properties of elliptical mirror -- 2.1 Introduction -- 2.2 Elliptical mirror model -- 2.3 Apodization factor -- 2.4 Apodization factor under different parametric variables -- 2.4.1 Apodization factor in terms of z -- 2.4.2 Apodization factor in terms of θ -- 2.5 Focusing properties based on the vector theory -- 2.5.1 Vector theories -- 2.5.2 Three-dimensional expression of the focused electric field -- 2.5.3 Numerical simulation of the focusing field -- 2.6 Comparison of focusing properties among elliptical mirror, parabolic mirror and lens -- 2.7 Summary -- References -- Chapter 3 Focusing characteristic of polarized light -- 3.1 Basic model of an elliptical mirror -- 3.2 Vector focus model of elliptical mirror with extra high aperture angle -- 3.2.1 Analysis of focusing characteristic of elliptical mirror under circularly polarized illumination -- 3.2.2 Analysis of focusing characteristics of the elliptical mirror under radially polarized illumination -- 3.3 Conclusion -- References -- Chapter 4 Imaging analysis of dipole vector in an elliptical mirror -- 4.1 Introduction -- 4.2 Imaging model of dipole vector in elliptical mirror -- 4.3 Imaging characteristics of the electric dipole in the elliptical mirror -- 4.4 Imaging characteristics of the electric dipole in a dual-lens system -- 4.5 Comparison on imaging characteristics of dipole in elliptical mirror, parabolic mirror and lens -- 4.6 Summary -- References. , Chapter 5 Scalar approximation for the focusing property of an elliptical mirror -- 5.1 Introduction -- 5.2 Influence factors of focusing property -- 5.2.1 Apodization factor -- 5.2.2 Polarization state -- 5.2.3 Wave aberration -- 5.3 Apodization factor of elliptical mirror -- 5.3.1 Apodization factor of thin lens -- 5.3.2 Apodization factor of the elliptical mirror with rotational symmetry -- 5.4 Analysis on focusing property of elliptical mirror -- 5.4.1 Focusing property of elliptical mirror with circular aperture -- 5.4.2 Focusing property of elliptical mirror with ring-shaped aperture -- 5.5 Comparative analysis on vector diffraction model -- 5.6 Summary -- References -- Chapter 6 Aberration analysis of an elliptical mirror with a high numerical aperture -- 6.1 Introduction -- 6.2 Analysis of geometrical aberration of elliptical mirror -- 6.2.1 Reflected ray formula of elliptical mirror -- 6.2.2 Analysis of the aberration coefficient of a single rotating elliptical mirror -- 6.3 Diffraction integral in the presence of aberration -- 6.3.1 Debye diffraction integral in the presence of aberration -- 6.3.2 Strehl intensity -- 6.4 Zernike circle polynomial expansion of aberration function -- 6.4.1 Transference theorem -- 6.4.2 Zernike circle polynomial -- 6.5 Primary aberration and its influence on the focusing characteristic of the elliptical mirror -- 6.5.1 Primary spherical aberration -- 6.5.2 Primary coma -- 6.5.3 Primary astigmatism -- 6.5.4 Field curvature and distortion -- 6.5.5 Aberration tolerance of elliptical mirror -- 6.6 Conclusion -- References -- Chapter 7 Three-dimensional transfer function -- 7.1 Introduction -- 7.2 Point spread function -- 7.2.1 Coherent transfer function -- 7.2.2 Optical transfer function of elliptical mirror -- 7.3 Three-dimensional transfer function of an elliptical reflective confocal microscopic system. , 7.3.1 Coherent transfer function of elliptical reflective confocal microscopic system -- 7.3.2 Two-dimensional transfer function of the elliptical reflective confocal microscopic imaging system -- 7.4 Summary -- References -- Chapter 8 Design and application of an aspherical mirror -- 8.1 Introduction -- 8.2 Basic knowledge -- 8.2.1 Mathematical representation of aspherical surface -- 8.2.2 Taylor series -- 8.3 Design of reflective objective -- 8.3.1 Head design model -- 8.3.2 Aperture diaphragm and field diaphragm -- 8.4 Decoupled model based on the Taylor series expansion -- 8.4.1 Taylor series expansion of the Head polar coordinate model -- 8.4.2 Taylor series expansion of a quadric surface -- 8.4.3 Determination of reflective objective parameters -- 8.4.4 Derivation and truncation error of a high-order aspherical surface parameter -- 8.4.5 Effect of numerical aperture on a decoupled model -- 8.5 Design method based on an obscuration constraint -- 8.5.1 Analysis of the obscuration effect on a reflective objective -- 8.5.2 Obscuration constraint model -- 8.5.3 Design method based on obscuration constraint -- 8.6 Industrial application -- 8.6.1 Structural parameter calculation -- 8.6.2 Obscuration verification -- 8.6.3 Analysis of initial configuration imaging characteristics -- 8.6.4 Whole equipment and specific application -- 8.7 Summary -- References -- Chapter 9 Elliptical mirror applied in TIRF microscopy -- 9.1 Introduction -- 9.2 Background -- 9.3 Basic theory -- 9.4 Experiments -- 9.5 Summary -- References.

Note: Cover -- Title page -- Chapter 1. Introduction -- 1.1. Presentation of the problem -- 1.2. Some known results -- 1.3. Main results -- 1.4. Main ideas -- Chapter 2. Tools of paradifferential operators -- 2.1. Paradifferential operators -- 2.2. Functional spaces -- 2.3. Symbolic calculus -- 2.4. Tame estimates in Sobolev space -- 2.5. Tame estimates in Chemin-Lerner spaces -- 2.6. Commutator estimates -- Chapter 3. Parabolic evolution equation -- Chapter 4. Elliptic estimates in a strip -- 4.1. Elliptic boundary problem -- 4.2. Flattening the boundary and paralinearization -- 4.3. Elliptic estimates in Sobolev space -- 4.4. Tame elliptic estimates -- 4.5. Elliptic estimates in Besov space -- 4.6. Interior ^{1, } estimate -- Chapter 5. Dirichlet-Neumann operator -- 5.1. Definition and paralinearization -- 5.2. Sobolev estimate of the remainder -- 5.3. Tame estimate of the remainder -- 5.4. Hölder estimate of the remainder -- Chapter 6. New formulation and paralinearization -- 6.1. New formulation -- 6.2. Paralinearization -- Chapter 7. Estimate of the pressure -- 7.1. ² estimate of the pressure -- 7.2. Hölder estimate of the pressure -- 7.3. Sobolev estimate of the pressure -- 7.4. Estimate of -- Chapter 8. Estimate of the velocity -- 8.1. Sobolev estimate of the velocity -- 8.2. The estimate of the irrotational part -- 8.3. The estimate of the rotational part -- Chapter 9. Proof of break-down criterion -- 9.1. The ¹ energy estimate -- 9.2. Energy estimate of the trace of the velocity and the free surface -- 9.3. Energy estimate of the vorticity -- 9.4. Nonlinear estimates -- 9.5. Energy functional -- 9.6. Proof of Theorem 1.3 -- Chapter 10. Iteration scheme -- 10.1. Strategy -- 10.2. Iteration scheme -- 10.3. Existence of iteration scheme -- Chapter 11. Uniform energy estimates -- 11.1. Set-up -- 11.2. Energy functional. , 11.3. Estimate of the velocity -- 11.4. Estimate of the pressure -- 11.5. Estimates of the remainder of DN operator -- 11.6. Energy estimates -- 11.7. Nonlinear estimates -- 11.8. Completion of the uniform estimate -- Chapter 12. Cauchy sequence and the limit system -- 12.1. Set-up -- 12.2. Elliptic estimates with a parameter -- 12.3. Energy estimates -- 12.4. The limit system -- Chapter 13. From the limit system to the Euler equations -- Chapter 14. Proof of Theorem 1.1 -- 14.1. Construction of approximate smooth solution -- 14.2. Uniform estimates and existence -- 14.3. Uniqueness of the solution -- Acknowledgement -- Bibliography -- Back Cover.

Note: Intro -- Preface -- Contents -- List of Contributors, MAE 49 -- Modern Aspects of Electrochemistry -- 1 Durability of PEM Fuel Cell Membranes -- 1 Summary -- 2 Review of PEM Fuel Cell Degradation Phenomena and Mechanisms -- 3 Membrane Degradation -- 3.1. Stress in Membrane and MEAs -- 3.2. Mechanical Characterization of Membranes -- 3.3. Chemical Degradation Processes -- 3.4. Mechanical Degradation Processes -- 3.5. Interactions of Chemical and Mechanical Degradation -- 4 Accelerated Testing and Life Prediction -- 4.1. Accelerated Degradation Testing and Degradation Metrics -- 4.2. Progressive Degradation Model of Combined Effects -- 5 Mitigation -- Acknowledgments -- References -- 2 Modeling of Membrane-Electrode-Assembly Degradation in Proton-Exchange-Membrane Fuel Cells -- Local H2 Starvation and Start--Stop Induced Carbon-Support Corrosion -- 1 Introduction -- 2 Kinetic Model -- 2.1. Electrode Kinetics -- 2.2. Local H2 Starvation Model -- 2.3. Start--Stop Model -- 3 Coupled Kinetic and Transport Model -- 3.1. Model Description -- 3.2. Local H2 Starvation Simulation -- 3.3. Start--Stop Simulation -- 4 Pseudo-Capacitance Model -- 4.1. Mechanism Description -- 4.2. Model Description -- 4.3. The Pseudo-capacitive Effect -- 5 Summary and Outlook -- Acknowledgments -- List of Symbols -- References -- 3 Cold Start of Polymer Electrolyte Fuel Cells -- 1 Introduction -- 2 Equilibrium Purge Cold Start -- 2.1. Equilibrium Purge -- 2.2. Isothermal Cold Start -- 2.3. Proton Conductivity at Low Temperature -- 2.4. Effects of Key Parameters -- 2.4.1. Initial Membrane Water Content -- 2.4.2. Startup Current Density -- 2.4.3. Startup Temperature -- 2.5. ORR Kinetics at Low Temperatures -- 2.6. Short-Purge Cold Start -- 3 Water Removal During Gas Purge -- 3.1. Introduction -- 3.2. Purge Curve -- 3.3. Two Characteristic Parameters for Water Removal. , 3.4. Stages of Purge -- 3.5. Effect of Key Parameters -- 3.5.1. Purge Cell Temperature -- 3.5.2. Purge Gas Flow Rate -- 3.5.3. Matching Two Parameters -- 3.6. HFR Relaxation -- 4 Concluding Remarks -- References -- 4 Species, Temperature, and Current Distribution Mapping in Polymer Electrolyte Membrane Fuel Cells -- 1 Introduction -- 2 Species Distribution Mapping -- 2.1. Species and Properties of Interest -- 2.1.1. Hydrogen -- 2.1.2. Oxygen -- 2.1.3. Water -- 2.1.4. Contaminants and Diluents -- 2.1.5. Pressure Drop -- 2.1.6. Flow Distribution -- 2.2. Methodology and Results -- 2.2.1. Pressure Drop Measurement -- 2.2.2. Gas Composition Analysis -- 2.2.3. Neutron Imaging -- 2.2.4. Magnetic Resonance Imaging -- 2.2.5. X-ray Imaging -- 2.2.6. Optically Transparent Fuel Cells -- 2.2.7. Embedded Sensors -- 2.2.8. Other Methods -- 2.3. Design Implications -- 3 Temperature Distribution Mapping -- 3.1. Methodology and Results -- 3.1.1. IR Transparent Fuel Cells -- 3.1.2. Embedded Sensors -- 3.2. Design Implications -- 4 Current Distribution Mapping -- 4.1. Methodology and Results -- 4.1.1. Partial MEA -- 4.1.2. Segmented Cells -- 4.1.3. Other Methods -- 4.2. Design Implications -- 5 Concluding Remarks -- References -- 5 High-Resolution Neutron Radiography Analysis of Proton Exchange Membrane Fuel Cells -- 1 Introduction -- 2 Neutron Radiography Facility Layout And Detectors -- 2.1. Neutron Sources and Radiography Beamlines -- 2.2. Neutron Imaging Detectors -- 3 Water Metrology with Neutron Radiography -- 3.1. Neutron Attenuation Coefficient of Water, 0 w -- 3.2. Sources of Uncertainties in Neutron Radiography -- 3.2.1. Counting Statistics -- 3.2.2. Beam Hardening -- 3.2.3. Background Subtraction -- 3.2.4. Changes in the Total Neutron Scattering from Water Absorbed in the Membrane -- 3.2.5. Image Spatial Resolution. , 4 Recent In Situ High-Resolution Neutron Radiography Experiments of PEMFCs -- 4.1. Proof-of-Principle Experiments -- 4.2. In Situ, Steady-State Through-Plane Water Content -- 4.3. Dynamic Through-Plane Mass Transport Measurements -- 5 Conclusions -- Acknowledgments -- References -- 6 Magnetic Resonance Imaging and Tunable Diode Laser Absorption Spectroscopy for In-Situ Water Diagnostics in Polymer Electrolyte Membrane Fuel Cells -- 1 Introduction -- 2 Magnetic Resonance Imaging (MRI): As a Diagnostic Tool for In-Situ Visualization of Water Content Distribution in PEMFC s -- 2.1. Basic Principle of MRI -- 2.2. MRI System Hardware for PEMFC Visualization -- 2.3. MRI Signal Calibration for Water Content in PEM -- 2.4. In Situ Visualization of Water in PEMFC Using MRI -- 3 Tunable Diode Laser Absorption Spectroscopy (TDLAS): As a Diagnostic Tool for In-Situ Detection of Water Vapor Concentration in PEMFC s -- 3.1. Basic Principle of TDLAS -- 3.2. TDLAS System Hardware for Water Vapor Measurement -- 3.3. TDLAS Signal Calibration for Measurement of Water Vapor Concentration -- 3.4. In Situ Measurement of Water Vapor in PEMFC Using TDLAS -- 4 Summary -- References -- 7 Characterization of the Capillary Properties of Gas Diffusion Media -- 1 Introduction -- 1.1. Motivation -- 2 Basic Considerations -- 3 Measurement of Capillary Pressure Curves -- 4 Interpretation of Capillary Pressure Curves -- 4.1. Capillary Pressure Hysteresis -- 4.2. Effect of Hydrophobic Coating -- 4.3. Effect of Compression -- 4.4. Water Breakthrough Condition -- 4.5. Finite-Size Effects -- 4.6. Effect of Microporous Layer -- 5 Conclusion and Outlook -- References -- 8 Mesoscopic Modeling of Two-Phase Transport in Polymer Electrolyte Fuel Cells -- 1 Introduction -- 2 Model Description -- 2.1. Stochastic Microstructure Reconstruction Model. , 2.1.1. Catalyst Layer Structure Generation -- 2.1.2. Gas Diffusion Layer Structure Generation -- 2.2. Lattice Boltzmann Model -- 2.2.1. Two-phase LB Model Description -- 3 Two-Phase Simulation -- 3.1. Two-phase Transport Mechanism -- 3.2. Two-phase Numerical Experiments and Setup -- 4 Two-Phase Behavior and Flooding Dynamics -- 4.1. Structure-Wettability Influence -- 4.2. Effect of GDL Compression -- 4.3. Evaluation of Two-Phase Relations -- 4.4. Effect of Liquid Water on Performance -- 5 Summary and Outlook -- Acknowledgments -- References -- 9 Atomistic Modeling in Study of Polymer Electrolyte Fuel Cells -- A Review -- 1 Introduction -- 2 Fundamentals of Atomistic Modeling -- 2.1. Ab Initio Modeling of Materials -- 2.1.1. Adiabatic Approximation -- 2.1.2. Hatree--Fock Approximation and Single Electron Hamiltonian -- 2.1.3. Density Function Theory -- 2.1.4. Ab Initio Quantum Chemistry Computation -- 2.1.5. Ab Initio Molecular Dynamics -- 2.2. Classical Molecular Dynamic Modeling -- 2.3. Monte Carlo Modeling -- 2.3.1. The Metropolis Algorithm -- 2.3.2. Kinetic Monte Carlo Modeling -- 2.4. Advancement of MD Methods -- 2.4.1. Empirical Valence Bond Models -- 2.4.2. MD Modeling with Reactive Force Field -- 2.4.3. Methods for Accelerating Molecular Dynamics Simulations -- 3 Modeling of Oxygen Electroreduction Reaction Catalysts -- 3.1. The Interface Structure -- 3.1.1. Ab Initio Modeling of Interface Structure in Aqueous Solutions -- 3.1.2. MD Modeling of Interface Structure on Catalysts in Aqueous Solution -- 3.1.3. MD Modeling of Interface Structure of Polymer Electrolyte/Catalysts Interface -- 3.2. Chemsorption on Catalysts -- 3.2.1. Bond Strength of Adsorbed Oxygen Atom -- 3.2.2. Adsorption Process on Transition Metals -- 3.2.3. On Bimetallic Alloys -- 3.3. Oxygen Electroreduction Reaction with an Emphasis on Charge Transfer at Metal/Water Interface. , 4 Modeling of Oxidation of Carbon Monoxide and Methanol -- 4.1. ''Vapor Phase'' Model -- 4.2. Realistic ''Liquid Phase'' Model -- 5 Modeling of Transport Processes in Nafion Polymer Electrolytes -- 5.1. Theoretical Views of Proton Transport in Aqueous Systems and in Hydrated Nafion Membranes -- 5.1.1. In Aqueous Solution -- 5.1.2. In Hydrated Membrane (Nafion) -- 5.2. Ab Initio Models -- 5.3. Classic MD Models -- 5.4. Empirical Valence Bond and ReaXFF Models -- 6 Summarizing Remarks -- Acknowledgment -- Reference -- Index.