LEADER 07369nam 2200553 450 001 996466417303316 005 20231110233213.0 010 $a3-030-93302-4 035 $a(MiAaPQ)EBC6941414 035 $a(Au-PeEL)EBL6941414 035 $a(CKB)21435612700041 035 $a(PPN)261518852 035 $a(EXLCZ)9921435612700041 100 $a20221113d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aActive particles$hVolume 3 $eadvances in theory, models, and applications /$fNicola Bellomo, Jose? Antonio Carrillo, and Eitan Tadmor, editors 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2022] 210 4$dŠ2022 215 $a1 online resource (230 pages) 225 1 $aModeling and Simulation in Science, Engineering and Technology 311 08$aPrint version: Bellomo, Nicola Active Particles, Volume 3 Cham : Springer International Publishing AG,c2022 9783030933012 327 $aIntro -- Preface -- Contents -- Variability and Heterogeneity in Natural Swarms: Experiments and Modeling -- 1 Introduction -- 2 Sources of Variability in Nature -- 2.1 Development as a Source of Variation -- 2.2 Transient Changes in the Behavior of Individuals -- 2.3 Environmentally Induced Variations -- 2.4 Social Structure -- 2.5 Inherent/Intrinsic Properties and Animal Personality -- 2.6 Variability in Microorganisms -- 3 Experiments with Heterogeneous Swarms -- 3.1 Fish -- 3.2 Mammals -- 3.3 Insects -- 3.4 Microorganisms -- 4 Modeling Heterogeneous Collective Motion -- 4.1 Continuous Models -- 4.2 Agent-Based Models -- 4.3 Specific Examples: Locust -- 4.4 Specific Examples: Microorganisms and Cells -- 5 Summary and Concluding Remarks -- References -- Active Crowds -- 1 Introduction -- 2 Models for Active Particles -- 2.1 Continuous Random Walks -- 2.1.1 Excluded-Volume Interactions -- 2.2 Discrete Random Walks -- 2.3 Hybrid Random Walks -- 3 Models for Externally Activated Particles -- 3.1 Continuous Models -- 3.2 Discrete Models -- 4 General Model Structure -- 4.1 Wasserstein Gradient Flows -- 4.2 Entropy Dissipation -- 5 Boundary Effects -- 5.1 Mass Conserving Boundary Conditions -- 5.2 Flux Boundary Conditions -- 5.3 Other Boundary Conditions -- 6 Active Crowds in the Life and Social Science -- 6.1 Pedestrian Dynamics -- 6.2 Transport in Biological Systems -- 7 Numerical Simulations -- 7.1 One Spatial Dimension -- 7.2 Two Spatial Dimensions -- References -- Mathematical Modeling of Cell Collective Motion Triggered by Self-Generated Gradients -- 1 Introduction -- 2 The Keller-Segel Model and Variations -- 2.1 The Construction of Waves by Keller and Segel -- 2.2 Positivity and Stability Issues -- 2.3 Variations on the Keller-Segel Model -- 2.4 Beyond the Keller-Segel Model: Two Scenarios for SGG. 327 $a3 Scenario 1: Strongest Advection at the Back -- 4 Scenario 2: Cell Leakage Compensated by Growth -- 5 Conclusion and Perspectives -- References -- Clustering Dynamics on Graphs: From Spectral Clustering to Mean Shift Through Fokker-Planck Interpolation -- 1 Introduction -- 1.1 Mean Shift-Based Methods -- 1.1.1 Lifting the Dynamics to the Wasserstein Space -- 1.2 Spectral Methods -- 1.2.1 Normalized Versions of the Graph Laplacian -- 1.2.2 More General Spectral Embeddings -- 1.3 Outline -- 2 Mean Shift and Fokker-Planck Dynamics on Graphs -- 2.1 Dynamic Interpretation of Spectral Embeddings -- 2.2 The Mean Shift Algorithm on Graphs -- 2.2.1 Mean Shift on Graphs as Inspired by Wasserstein Gradient Flows -- 2.2.2 Quickshift and KNF -- 3 Fokker-Planck Equations on Graphs -- 3.1 Fokker-Planck Equations on Graphs via Interpolation -- 3.2 Fokker-Planck Equation on Graphs via Reweighing and Connections to Graph Mean Shift -- 4 Continuum Limits of Fokker-Planck Equations on Graphs and Implications -- 4.1 Continuum Limit of Mean Shift Dynamics on Graphs -- 4.2 Continuum Limits of Fokker-Planck Equations on Graphs -- 4.3 The Witten Laplacian and Some Implications for Data Clustering -- 5 Numerical Examples -- 5.1 Numerical Method -- 5.2 Simulations -- 5.2.1 Graph Dynamics as Density Dynamics -- 5.2.2 Comparison of Graph Dynamics and PDE Dynamics -- 5.2.3 Clustering Dynamics -- 5.2.4 Effect of the Kernel Density Estimate on Clustering -- 5.2.5 Effect of Data Distribution on Clustering -- 5.2.6 Blue Sky Problem -- 5.2.7 Density vs. Geometry -- References -- Random Batch Methods for Classical and Quantum Interacting Particle Systems and Statistical Samplings -- 1 Introduction -- 2 The Random Batch Methods -- 2.1 The RBM Algorithms -- 2.2 Convergence Analysis -- 2.3 An Illustrating Example: Wealth Evolution -- 3 The Mean-Field Limit -- 4 Molecular Dynamics. 327 $a4.1 RBM with Kernel Splitting -- 4.2 Random Batch Ewald: An Importance Sampling in the Fourier Space -- 5 Statistical Sampling -- 5.1 Random Batch Monte Carlo for Many-Body Systems -- 5.2 RBM-SVGD: A Stochastic Version of Stein Variational Gradient Descent -- 6 Agent-Based Models for Collective Dynamics -- 6.1 The Cucker-Smale Model -- 6.2 Consensus Models -- 7 Quantum Dynamics -- 7.1 A Theoretical Result on the N-Body Schrödinger Equation -- 7.1.1 Mathematical Setting and Main Result -- 7.2 Quantum Monte Carlo Methods -- 7.2.1 The Random Batch Method for VMC -- 7.2.2 The Random Batch Method for DMC -- References -- Trends in Consensus-Based Optimization -- 1 Introduction -- 1.1 Notation and Assumptions -- 1.1.1 The Weighted Average -- 2 Consensus-Based Global Optimization Methods -- 2.1 Original Statement of the Method -- 2.1.1 Particle Scheme -- 2.1.2 Mean-Field Limit -- 2.1.3 Analytical Results for the Original Scheme Without Heaviside Function -- 2.1.4 Numerical Methods -- 2.2 Variant 1: Component-Wise Diffusion and Random Batches -- 2.2.1 Component-Wise Geometric Brownian Motion -- 2.2.2 Random Batch Method -- 2.2.3 Implementation and Numerical Results -- 2.3 Variant 2: Component-Wise Common Diffusion -- 2.3.1 Analytical Results -- 2.3.2 Numerical Results -- 3 Relationship of CBO and Particle Swarm Optimization -- 3.1 Variant 4: Personal Best Information -- 3.1.1 Performance -- 4 CBO with State Constraints -- 4.1 Variant 5: Dynamics Constrained to Hyper-Surfaces -- 4.1.1 Analytical Results -- 5 Overview of Applications -- 5.1 Global Optimization Problems: Comparison to Heuristic Methods -- 5.2 Machine Learning -- 5.3 Global Optimization with Constrained State Space -- 5.4 PDE Versus SDE Simulations -- 6 Conclusion, Outlook and Open problems -- References. 410 0$aModeling and Simulation in Science, Engineering and Technology 606 $aMathematical optimization 606 $aMathematical optimization$xComputer programs 606 $aModels matemātics$2thub 606 $aOptimitzaciķ matemātica$2thub 608 $aLlibres electrōnics$2thub 615 0$aMathematical optimization. 615 0$aMathematical optimization$xComputer programs. 615 7$aModels matemātics 615 7$aOptimitzaciķ matemātica 676 $a519.3 702 $aBellomo$b N. 702 $aCarrillo$b Jose? Antonio 702 $aTadmor$b Eitan 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466417303316 996 $aActive particles$91537369 997 $aUNISA