Gas Dynamics with Applications in Industry and Life Sciences: On Gas Kinetic/Dynamics and Life Science Seminar, March 25–26, 2021 and March 17–18, ... Proceedings in Mathematics & Statistics, 429)

This proceedings volume gathers selected contributions presented at two instances of the "JSPS/SAC Seminar: On Gas Kinetic/Dynamics and Life Science", held by the Chalmers University of Technology and University of Gothenburg, Sweden, on March 25-26, 2021 (virtual) and March 17-18, 2022 (virtual). Works in this book provide a concise approach to the theoretical and numerical analysis of kinetic type equations that arise, for example, in modeling industrial, medical, and environmental problems. Readers will find some of the most recent theoretical results, newly developed numerical methods in the field, and some open problems. Possible application areas encompass fission/fusion energy, electromagnetics, nuclear science and engineering, medical service, radiation oncology, and plants growth conditions, to name a few. The JSPS/SAC seminars are jointly organized by JSPS (Japan Society for the Promotion of Science)―Stockholm Office and the Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, Sweden. These seminars foster discussions on the mathematical theory, industrial and life science applications, and numerical analysis of non-linear hyperbolic partial differential equations modeling collision-less plasma and charged particles. Chapter 4 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. Chapter 11 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. Preface for Proceedings of JSPS/SAC Workshops at Chalmers 2021 & 2022 6 Contents 8 The History and Significance of the Klein-Nishina Formula 10 1 Prologue 10 2 Some History and the Road to the Formula 11 3 Oskar Klein, the Klein-Gordon and Dirac Equations—A Primer in Quantum Mechanics 17 4 The Klein-Nishina Formula and Its Significance 21 5 The Negative Energy States and the Nishina-Waller Correspondence 22 6 Epilogue 26 References 27 Constructions of Simple Kinetic Equations for a Dense Gas 28 1 Introduction 28 2 Previous Models 29 2.1 Outline of Previous Models 29 2.2 Fluid-Dynamic Limits and Transport Properties 32 3 Modified Models in Terms of the Ellipsoidal-Statistical (ES)-Type Collision Term 33 3.1 The First ES-Based Model 33 3.2 A Slight Limitation on the Monotonicity of the First ES-Based Model 35 3.3 The Second ES-Based Model 37 4 Preliminary Tests 40 5 Conclusion 42 Appendix 43 References 48 Double Layer Solutions of the Vlasov–Poisson System 49 1 Introduction 49 2 Review of the Study of Single Layer Solutions 52 3 The Main Theorem of Double Layer Solutions 53 4 Proof 55 References 60 Inverse Magnus Effect in a Rarefied Gas 61 1 Introduction 62 2 Problem and Formulation 62 2.1 Problem 63 2.2 Formulation 64 3 Asymptotic Analysis 67 3.1 Leading Order in ε 67 3.2 Second Order in ε 70 4 Numerical Results for hL and Discussions 74 4.1 Comments on the Computation of hL 74 4.2 Transverse Force Acting on a Rotating Sphere 75 5 Analytical Tools 76 5.1 Isotropy of mathcalL and mathcalJ 76 5.2 Symmetry Relation 78 6 Concluding Remarks and Perspectives 80 References 81 A Discontinuous Galerkin Approach for Stabilized Maxwell's Equations in Pseudo-Frequency Domain 83 1 Introduction 83 2 The Mathematical Model 84 3 The Finite Element Scheme 87 3.1 The Continuous Variational Formulation 87 3.2 The Discontinuous Finite Element Scheme 88 4 Error Analysis 92 4.1 A Priori Error Estimates 93 5 Numerical Examples 96 6 Conclusion 98 References 99 Bidomain Model for Axon Bundles with Random Geometry 101 1 Introduction 101 2 Bundles with Randomly Distributed Axons 102 3 Problem Statement and Main Result 105 4 Microscopic Problem 108 5 Proof of the Homogenization Result 112 References 123 A Posteriori Error Estimates and Adaptive Error Control for Permittivity Reconstruction in Conductive Media 125 1 Introduction 125 2 The Mathematical Model 127 3 Optimization Approach 128 4 Finite Element Method 131 5 A Posteriori Error Estimates 132 6 Adaptive Algorithms for Solution of CIP 137 7 Numerical Results 138 8 Conclusions 147 References 147 Truncated SVD for Applications in Microwave Thermometry 150 1 Introduction 151 2 The Mathematical Model 152 3 Statement of an Ill-Posed Problem 153 4 Preliminaries: SVD Decomposition for Solution of Least Squares Problem 154 5 Solution of Rank-Deficient Problem Using Truncated SVD 156 6 Numerical Results 160 6.1 The Experimental Set-up 160 6.2 Performance of TSVD 162 7 Concluding Remarks 170 References 170 Methods of Quantitative Reconstruction for Acoustic Coefficient Inverse Problem 173 1 Introduction 173 2 The Mathematical Model 175 3 Method of Analytic Reconstruction for the Solution of IP 176 3.1 Nonlinear Integro-Differential Equation 177 3.2 Finite Element Method for Reconstruction 179 3.3 Algorithms for Analytic Reconstruction 182 4 Lagrangian Approach for the Solution of IP 182 4.1 Finite Element Discretization 185 4.2 Conjugate Gradient Algorithm 186 4.3 Adaptive Finite Element Inversion Algorithms for the Solution of IP 187 5 The Adaptive Spectral Inversion for the Solution of IP 188 5.1 Description of the ASI Method 189 6 Numerical Studies 191 6.1 Generation of Data 192 6.2 Analytic Approach for Solution IP 193 6.3 Lagrangian Approach 196 6.4 Adaptive Spectral Inversion Approach 199 7 Conclusions 201 References 202 Numerical Validation of Optimization Approach for Solution of Coefficient Inverse Problem in Pseudo-Frequency Domain 205 1 Introduction 205 2 Model Problem in the Pseudo-Frequency Domain 206 3 Lagrangian Approach for CIP 208 4 Algorithm 211 5 Numerical Results 211 5.1 Test 1 212 5.2 Test 2 214 6 Noisy Data 214 7 Impulse Excitation of Wave Equation 216 8 Conclusion 218 References 219 A Multiscale Numerical Simulation of Quasi-Two-Dimensional Bacterial Turbulence Using a Regularized Stokeslet Representation 220 1 Introduction 220 2 Microswimmer Collective Dynamics with a Regularized Stokeslet Representation 222 2.1 Flow Representation 222 2.2 Modeling Interactions 224 2.3 Numerical Implementations 225 3 Numerical Results 227 3.1 Quasi-Two-Dimensional Dynamics in a Free Space 227 3.2 Quasi-Two-Dimensional Dynamics in Free-Slip Parallel Walls 228 4 Summary and Discussion 229 References 230 Visualization of 14C-labeled Gas Fixation in a Plant—Development of Real-Time Radioisotope Imaging 232 1 Introduction 232 2 Development of Real-Time RI System 233 3 14CO2 Gas Imaging [7, 9] 236 4 Conclusion 238 References 238 Numerical Study on the Self-organized Pattern Formation of Run-and-Tumble Chemotactic Bacteria 240 1 Introduction 240 2 Problem and Formulation 242 2.1 Problem 242 2.2 Basic Equation 242 2.3 Nondimensionalization 244 3 Numerical Results 245 3.1 Instability Diagram 246 3.2 Volcano Effect 247 3.3 Standing and Traveling Bands 248 4 Concluding Remarks 250 References 252 Derivation of a Generalised Replicator Equation in the Limit of Weak Selection 254 1 Introduction 254 2 The Population Dynamical Model 255 3 Analysis of the Model 256 4 Application to Hawk-Dove Game with Density-Dependent Growth 261 4.1 Numerical Comparison 262 5 Discussion 264 References 264 A Review and Case Study of Neural Network Techniques for Automated Generation of High Level-of-Detail 3D City Models 266 1 Introduction 267 1.1 Digital Twins of Cities 267 1.2 3D City Model Generation 268 1.3 Mesh Generation for Large-Scale City Modeling and Simulation 269 1.4 Outline of This paper 270 2 Rooftop Segmentation from Aerial Imagery 270 2.1 Case Study: Rooftop Segmentation Using Data from the Swedish Mapping, Cadastral and Land Registration Authority 271 3 Façade Feature Extraction from Street Level Imagery 277 3.1 Case Study: Façade Extraction Using Google Street View data 278 4 Conclusion 285 References 286