Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Active particles . Volume 3 : advances in theory, models, and applications / / Nicola Bellomo, José Antonio Carrillo, and Eitan Tadmor, editors
| Active particles . Volume 3 : advances in theory, models, and applications / / Nicola Bellomo, José Antonio Carrillo, and Eitan Tadmor, editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2022] |
| Descrizione fisica | 1 online resource (230 pages) |
| Disciplina | 519.3 |
| Collana | Modeling and Simulation in Science, Engineering and Technology |
| Soggetto topico |
Mathematical optimization
Mathematical optimization - Computer programs Models matemàtics Optimització matemàtica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-93302-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- 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.
3 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. 4.1 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. |
| Record Nr. | UNISA-996466417303316 |
| Cham, Switzerland : , : Springer International Publishing, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Active particles . Volume 3 : advances in theory, models, and applications / / Nicola Bellomo, José Antonio Carrillo, and Eitan Tadmor, editors
| Active particles . Volume 3 : advances in theory, models, and applications / / Nicola Bellomo, José Antonio Carrillo, and Eitan Tadmor, editors |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2022] |
| Descrizione fisica | 1 online resource (230 pages) |
| Disciplina | 519.3 |
| Collana | Modeling and Simulation in Science, Engineering and Technology |
| Soggetto topico |
Mathematical optimization
Mathematical optimization - Computer programs Models matemàtics Optimització matemàtica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-93302-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- 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.
3 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. 4.1 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. |
| Record Nr. | UNINA-9910556880003321 |
| Cham, Switzerland : , : Springer International Publishing, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Complex systems and society : modeling and simulation / / Giulia Ajmone Marsan, Nicola Bellomo, Andrea Tosin
| Complex systems and society : modeling and simulation / / Giulia Ajmone Marsan, Nicola Bellomo, Andrea Tosin |
| Autore | Bellomo Nicola |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | New York : , : Springer, , 2013 |
| Descrizione fisica | 1 online resource (xii, 90 pages) : illustrations (some color) |
| Disciplina | 300.151 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Social sciences - Mathematical models
Economics - Mathematical models Social sciences - Computer simulation Economics - Computer simulation |
| ISBN | 1-4614-7242-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. The Role of Individual Behaviors in Socio-Economic Sciences -- 2. Mathematical Tools for Modeling Social Complex Systems -- 3. Modeling Cooperation and Competition in Socio-Economic Systems -- 4. Welfare Policy: Applications and Simulations -- 5. Forward Look at Research Perspectives -- References. |
| Record Nr. | UNINA-9910739411103321 |
Bellomo Nicola
|
||
| New York : , : Springer, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Crowd dynamics . Volume 3 : modeling and social applications in the time of COVID-19 / / edited by Nicola Bellomo and Livio Gibelli
| Crowd dynamics . Volume 3 : modeling and social applications in the time of COVID-19 / / edited by Nicola Bellomo and Livio Gibelli |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (259 pages) |
| Disciplina | 620.86 |
| Collana | Modeling and Simulation in Science, Engineering and Technology |
| Soggetto topico |
Human engineering
Social psychology Ergonomia Psicologia social Pandèmia de COVID-19, 2020- |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-91646-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466547803316 |
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Crowd dynamics . Volume 3 : modeling and social applications in the time of COVID-19 / / edited by Nicola Bellomo and Livio Gibelli
| Crowd dynamics . Volume 3 : modeling and social applications in the time of COVID-19 / / edited by Nicola Bellomo and Livio Gibelli |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (259 pages) |
| Disciplina | 620.86 |
| Collana | Modeling and Simulation in Science, Engineering and Technology |
| Soggetto topico |
Human engineering
Social psychology Ergonomia Psicologia social Pandèmia de COVID-19, 2020- |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-91646-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910548178303321 |
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lecture notes on the discretization of the Boltzmann equation [[electronic resource] /] / editors Nicola Bellomo, Renée Gatignol
| Lecture notes on the discretization of the Boltzmann equation [[electronic resource] /] / editors Nicola Bellomo, Renée Gatignol |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (317 p.) |
| Disciplina | 530.13/8 |
| Altri autori (Persone) |
BellomoN
GatignolRenée |
| Collana | Series on advances in mathematics for applied sciences |
| Soggetto topico |
Transport theory
Finite element method Differential equations - Asymptotic theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-94792-X
9786611947927 981-279-690-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS ; Preface ; Chapter 1. From the Boltzmann Equation to Discretized Kinetic Models ; 1.1 Introduction ; 1.2 The Nonlinear Boltzmann Equation ; 1.3 The Discrete and Semicontinuous Boltzmann Equation ; 1.4 Plan of the Lecture Notes ; 1.5 References
Chapter 2. Discrete Velocity Models for Gas Mixtures 2.1 Introduction ; 2.2 DVM for mixtures ; 2.3 Models with a finite number of velocities and the problem of spurious invariants ; 2.4 Constructing DVM with arbitrarily many velocities ; 2.5 Concluding remarks ; 2.6 References Chapter 3. Discrete Velocity Models with Multiple Collisions 3.1 Introduction ; 3.2 Discrete Models with Multiple Collisions ; 3.3 Macroscopic Description ; 3.4 Boundary Conditions for Discrete Models ; 3.5 Conclusion ; 3.6 References Chapter 4. Discretization of the Boltzmann Equation and the Semicontinuous Model 4.1 Introduction ; 4.2 Splitting and Energy Formulation ; 4.3 Working in a Finite Energy Interval ; 4.4 Energy Discretization and Kinetic Model 4.5 Conservation and Euler Equations for the Discretized Model 4.6 Energy Formulation of the Collision Dynamics ; 4.7 Concluding Remarks ; 4.8 References ; Chapter 5. Semi-continuous Extended Kinetic Theory ; 5.1 Introduction ; 5.2 Continuous Kinetic Equations 5.3 Semi-continuous Kinetic Equations |
| Record Nr. | UNINA-9910454085103321 |
| River Edge, NJ, : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lecture notes on the discretization of the Boltzmann equation [[electronic resource] /] / editors Nicola Bellomo, Renée Gatignol
| Lecture notes on the discretization of the Boltzmann equation [[electronic resource] /] / editors Nicola Bellomo, Renée Gatignol |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (317 p.) |
| Disciplina | 530.13/8 |
| Altri autori (Persone) |
BellomoN
GatignolRenée |
| Collana | Series on advances in mathematics for applied sciences |
| Soggetto topico |
Transport theory
Finite element method Differential equations - Asymptotic theory |
| ISBN |
1-281-94792-X
9786611947927 981-279-690-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS ; Preface ; Chapter 1. From the Boltzmann Equation to Discretized Kinetic Models ; 1.1 Introduction ; 1.2 The Nonlinear Boltzmann Equation ; 1.3 The Discrete and Semicontinuous Boltzmann Equation ; 1.4 Plan of the Lecture Notes ; 1.5 References
Chapter 2. Discrete Velocity Models for Gas Mixtures 2.1 Introduction ; 2.2 DVM for mixtures ; 2.3 Models with a finite number of velocities and the problem of spurious invariants ; 2.4 Constructing DVM with arbitrarily many velocities ; 2.5 Concluding remarks ; 2.6 References Chapter 3. Discrete Velocity Models with Multiple Collisions 3.1 Introduction ; 3.2 Discrete Models with Multiple Collisions ; 3.3 Macroscopic Description ; 3.4 Boundary Conditions for Discrete Models ; 3.5 Conclusion ; 3.6 References Chapter 4. Discretization of the Boltzmann Equation and the Semicontinuous Model 4.1 Introduction ; 4.2 Splitting and Energy Formulation ; 4.3 Working in a Finite Energy Interval ; 4.4 Energy Discretization and Kinetic Model 4.5 Conservation and Euler Equations for the Discretized Model 4.6 Energy Formulation of the Collision Dynamics ; 4.7 Concluding Remarks ; 4.8 References ; Chapter 5. Semi-continuous Extended Kinetic Theory ; 5.1 Introduction ; 5.2 Continuous Kinetic Equations 5.3 Semi-continuous Kinetic Equations |
| Record Nr. | UNINA-9910782280603321 |
| River Edge, NJ, : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lecture notes on the discretization of the Boltzmann equation [[electronic resource] /] / editors Nicola Bellomo, Renée Gatignol
| Lecture notes on the discretization of the Boltzmann equation [[electronic resource] /] / editors Nicola Bellomo, Renée Gatignol |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (317 p.) |
| Disciplina | 530.13/8 |
| Altri autori (Persone) |
BellomoN
GatignolRenée |
| Collana | Series on advances in mathematics for applied sciences |
| Soggetto topico |
Transport theory
Finite element method Differential equations - Asymptotic theory |
| ISBN |
1-281-94792-X
9786611947927 981-279-690-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS ; Preface ; Chapter 1. From the Boltzmann Equation to Discretized Kinetic Models ; 1.1 Introduction ; 1.2 The Nonlinear Boltzmann Equation ; 1.3 The Discrete and Semicontinuous Boltzmann Equation ; 1.4 Plan of the Lecture Notes ; 1.5 References
Chapter 2. Discrete Velocity Models for Gas Mixtures 2.1 Introduction ; 2.2 DVM for mixtures ; 2.3 Models with a finite number of velocities and the problem of spurious invariants ; 2.4 Constructing DVM with arbitrarily many velocities ; 2.5 Concluding remarks ; 2.6 References Chapter 3. Discrete Velocity Models with Multiple Collisions 3.1 Introduction ; 3.2 Discrete Models with Multiple Collisions ; 3.3 Macroscopic Description ; 3.4 Boundary Conditions for Discrete Models ; 3.5 Conclusion ; 3.6 References Chapter 4. Discretization of the Boltzmann Equation and the Semicontinuous Model 4.1 Introduction ; 4.2 Splitting and Energy Formulation ; 4.3 Working in a Finite Energy Interval ; 4.4 Energy Discretization and Kinetic Model 4.5 Conservation and Euler Equations for the Discretized Model 4.6 Energy Formulation of the Collision Dynamics ; 4.7 Concluding Remarks ; 4.8 References ; Chapter 5. Semi-continuous Extended Kinetic Theory ; 5.1 Introduction ; 5.2 Continuous Kinetic Equations 5.3 Semi-continuous Kinetic Equations |
| Record Nr. | UNINA-9910821245403321 |
| River Edge, NJ, : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Predicting pandemics in a globally connected world . Volume 1 : toward a multiscale, multidisciplinary framework through modeling and simulation / / edited by Nicola Bellomo and Mark A. J. Chaplain
| Predicting pandemics in a globally connected world . Volume 1 : toward a multiscale, multidisciplinary framework through modeling and simulation / / edited by Nicola Bellomo and Mark A. J. Chaplain |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2022] |
| Descrizione fisica | 1 online resource (314 pages) |
| Disciplina | 016.36229 |
| Collana | Modeling and Simulation in Science, Engineering and Technology |
| Soggetto topico |
Epidemiology - Mathematical models
Epidèmies COVID-19 Models matemàtics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-96562-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Modelling, Simulations, and Social Impact of Evolutionary Virus Pandemics -- 1 Aims and Plan of the Chapter -- 2 On the Contents of the Edited Book -- 3 Reasonings on Research Perspectives -- References -- Understanding COVID-19 Epidemics: A Multi-Scale ModelingApproach -- 1 Introduction -- 2 Mathematical Modeling Applied to Infectious Diseases: COVID-19 as a Case Study -- 2.1 The SIR and SHAR Models -- 2.2 The SHARUCD Modeling Framework -- 2.3 Modeling the Implementation of Control Measures -- 2.4 The Refined SHARUCD Model -- 2.4.1 Further Refinements: Detection Rate and Import -- 3 KTAP Modeling Framework -- 3.1 Modeling Contagion, Progression, and Recovery -- 3.2 Application of the KTAP Model to Selected Case Studies -- 3.2.1 Effect of Lockdown Measures and Restrictions Lifting -- 3.2.2 Effect of Heterogeneity -- 4 Discussion -- References -- Kinetic Modelling of Epidemic Dynamics: Social Contacts, Control with Uncertain Data, and Multiscale Spatial Dynamics -- 1 Introduction -- 2 Kinetic Modelling of Social Heterogeneity in Epidemic Dynamics -- 2.1 Modelling Contact Heterogeneity -- 2.1.1 Kinetic Model for Contact Formation -- 2.1.2 Quasi-Invariant Scaling and Steady States -- 2.1.3 The Macroscopic Social-SIR Dynamics -- 2.1.4 A Social-SIR Model with Saturated Incidence Rate -- 2.1.5 Extrapolation of the Shape of the Incidence Rate from Data -- 2.2 The Interplay Between Economy and the Pandemic -- 2.2.1 Wealth Exchanges in Epidemic Modelling -- 2.2.2 Fokker-Planck Scaling and Steady States -- 2.2.3 The Formation of Bimodal Wealth Distributions -- 2.2.4 The Increase of Wealth Inequalities -- 3 Social Control and Data Uncertainty -- 3.1 Control of Socially Structured Models -- 3.1.1 Optimal Control Formulation -- 3.1.2 Feedback Controlled Compartmental Models.
3.1.3 Containment in Homogeneous Social Mixing Dynamics -- 3.2 Dealing with Data Uncertainty -- 3.2.1 Feedback Controlled and Socially Structured Models with Uncertain Inputs -- 3.2.2 Application to the COVID-19 Outbreak -- 4 Multiscale Transport Models -- 4.1 Spatial Dynamics on Networks -- 4.1.1 1D Hyperbolic Compartmental Model -- 4.1.2 Macroscopic Formulation and Diffusion Limit -- 4.1.3 Extension to Multi-Compartmental Modelling -- 4.1.4 Network Modelling -- 4.1.5 Effect of Spatially Heterogeneous Environments in Hyperbolic and Parabolic Configuration -- 4.1.6 Application to the Emergence of COVID-19 in Italy -- 4.2 Realistic Geographical Settings -- 4.2.1 2D Kinetic Transport Model -- 4.2.2 Macroscopic Formulation and Diffusion Limit -- 4.2.3 Extension to Multi-Compartmental Modelling -- 4.2.4 Application to the Spatial Spread of COVID-19 in Italy in Emilia-Romagna and Lombardy Region -- 5 Concluding Remarks and Research Perspectives -- 5.1 Data sources -- References -- The COVID-19 Pandemic Evolution in Hawai`i and New Jersey: A Lesson on Infection Transmissibility and the Role of HumanBehavior -- 1 Introduction -- 2 Mathematical Models -- 2.1 Agent-Based Models -- 2.1.1 COVID-19 Agent-Based Simulator (Covasim) -- 2.2 Compartmental SEIR Models and Variants -- 2.3 Comparison of Agent-Based and Compartmental Models -- 3 Archipelagos and Islands -- 3.1 March 2020-June 2021 -- 3.1.1 CM Model Fit from March 06, 2020 to January 15, 2021 -- 3.1.2 Comparing CM and ABM Models -- 3.2 July 2021-September 2021 -- 3.3 Discussion -- 4 The Pandemic Waves in New Jersey -- 4.1 Comparing New Jersey to the US -- 4.2 Spatial and Temporal Patterns in COVID-19 Cases in New Jersey -- 4.3 Sociodemographic Variables -- 4.4 Discussion -- 5 The Use of Compartmental Models in New Jersey -- 5.1 Time-Evolution of the Basic Reproduction Number. 5.2 Infected Confirmed Cases, Hospitalizations, and Deaths -- 5.3 Discussion -- 6 Conclusion -- References -- A Novel Point Process Model for COVID-19: Multivariate Recursive Hawkes Process -- 1 Introduction -- 1.1 Hawkes Point Process Modeling of Infectious Diseases -- 1.2 Multivariate Hawkes Processes -- 1.3 Recursive Hawkes Processes -- 1.4 Outline -- 2 Theoretical Properties of Temporal Multivariate Recursive Hawkes Models -- 2.1 Existence -- 2.2 Mean -- 2.3 Variance -- 3 Parameter Fitting and Simulation Algorithms -- 3.1 Parameter Fitting Algorithms -- 3.1.1 Parametric (or Semi-parametric) Estimation -- 3.1.2 Temporal Version of Parameter Fitting Algorithms -- 3.2 Simulation Algorithm -- 4 Reconstruct Multivariate Point Process from Data with Imprecise Time -- 4.1 Time Reconstruction -- 4.2 Category Index Reconstruction -- 5 Numerical Experiments and Results -- 5.1 Synthetic Data Sets -- 5.1.1 Comparison Between Parametric Fitting and Non-parametric Fitting -- 5.1.2 Verification of the Parameter Fitting Algorithm -- 5.1.3 Experiments About Data Sets with Imprecise Time -- 5.2 Experiments on Real COVID-19 Data -- 5.2.1 Model Validation -- 5.2.2 Prediction Based on MRHP and Historical Information -- 6 Conclusion -- References -- Multiscale Aspects of Virus Dynamics -- 1 Introduction -- 1.1 On the Biology of the Virus -- 1.2 Modeling the Complexity of COVID-19 -- 2 Epistemic and Empirical Uncertainties in Compartmental and Individual-Based Models -- 2.1 SIR Model -- 2.2 Individual-Based Interpretation of λ -- 2.3 An Example of Modified SIR Model -- 2.4 Individuals Behind the Modified SIR Model -- 2.5 Time-Discretization -- 3 The Individual-Based Model of FlaLaFauciRiva -- 3.1 A Formula for the Parameter λ of Compartmental Models -- 3.2 Analysis of the Fluctuations -- 3.3 Simulations -- 3.4 Presence of Immunized Population and Virus Variants. Appendix -- References -- Productivity in Times of Covid-19: An Agent-Based Model Approach -- 1 Introduction -- 2 Model -- 3 Mean Field Approximation -- 4 Setting the Model Functions -- 5 Simulations -- 6 Conclusion -- References -- Transmission Dynamics and Quarantine Control of COVID-19 in Cluster Community -- 1 Introduction -- 2 Mathematical Modeling -- 2.1 Stage 1: SEIR-Type Model Without Quarantine -- 2.2 Stage 2: Transmission-Quarantine (TQ) Model -- 3 Analytic Results and Case Study for Emerging Stage -- 3.1 Analytic Results -- 3.2 A Real World Case Study for Stage 1 -- 4 Case Study and Sensitivity Analysis for Quarantine Stage -- 4.1 A Real World Study for Stage 2 -- 4.2 Sensitivity Analysis -- 5 Discussion -- Appendix: Proofs of Theorems -- References -- A 2D Kinetic Model for Crowd Dynamics with Disease Contagion -- 1 Introduction -- 2 A Simplified Two-Dimensional Kinetic Model -- 3 Discretization in Space and Time -- 4 Numerical Results -- 4.1 Tests with v = 0 -- 4.2 Tests with Prescribed Walking Velocity -- 5 A More Complex 2D Kinetic Model -- 6 Conclusions -- References -- Multiscale Derivation of a Time-Dependent SEIRD Reaction-Diffusion System for COVID-19 -- 1 Introduction -- 2 Phenomenological Modeling of Diffusion Population Dynamics -- 3 From Kinetic Theory Model to SEIRD Reaction-Diffusion System -- 3.1 Kinetic Theory Model -- 3.2 Micro-Macro Formulation -- 4 Numerical Method -- 4.1 Semi-Implicit Time Discretization -- 4.2 Fully Discrete Asymptotic Preserving Numerical Scheme in 1D -- 4.3 Boundary Conditions -- 5 Numerical Results -- 5.1 Test 1: Asymptotic Preserving Numerical Scheme Property -- 5.2 Test 2: Diffusion Effect -- 5.3 Test 3: Role of the Transmission Function -- 6 Conclusion and Perspectives -- References. |
| Record Nr. | UNISA-996490344003316 |
| Cham, Switzerland : , : Birkhäuser, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Predicting pandemics in a globally connected world . Volume 1 : toward a multiscale, multidisciplinary framework through modeling and simulation / / edited by Nicola Bellomo and Mark A. J. Chaplain
| Predicting pandemics in a globally connected world . Volume 1 : toward a multiscale, multidisciplinary framework through modeling and simulation / / edited by Nicola Bellomo and Mark A. J. Chaplain |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2022] |
| Descrizione fisica | 1 online resource (314 pages) |
| Disciplina | 016.36229 |
| Collana | Modeling and Simulation in Science, Engineering and Technology |
| Soggetto topico |
Epidemiology - Mathematical models
Epidèmies COVID-19 Models matemàtics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-96562-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Modelling, Simulations, and Social Impact of Evolutionary Virus Pandemics -- 1 Aims and Plan of the Chapter -- 2 On the Contents of the Edited Book -- 3 Reasonings on Research Perspectives -- References -- Understanding COVID-19 Epidemics: A Multi-Scale ModelingApproach -- 1 Introduction -- 2 Mathematical Modeling Applied to Infectious Diseases: COVID-19 as a Case Study -- 2.1 The SIR and SHAR Models -- 2.2 The SHARUCD Modeling Framework -- 2.3 Modeling the Implementation of Control Measures -- 2.4 The Refined SHARUCD Model -- 2.4.1 Further Refinements: Detection Rate and Import -- 3 KTAP Modeling Framework -- 3.1 Modeling Contagion, Progression, and Recovery -- 3.2 Application of the KTAP Model to Selected Case Studies -- 3.2.1 Effect of Lockdown Measures and Restrictions Lifting -- 3.2.2 Effect of Heterogeneity -- 4 Discussion -- References -- Kinetic Modelling of Epidemic Dynamics: Social Contacts, Control with Uncertain Data, and Multiscale Spatial Dynamics -- 1 Introduction -- 2 Kinetic Modelling of Social Heterogeneity in Epidemic Dynamics -- 2.1 Modelling Contact Heterogeneity -- 2.1.1 Kinetic Model for Contact Formation -- 2.1.2 Quasi-Invariant Scaling and Steady States -- 2.1.3 The Macroscopic Social-SIR Dynamics -- 2.1.4 A Social-SIR Model with Saturated Incidence Rate -- 2.1.5 Extrapolation of the Shape of the Incidence Rate from Data -- 2.2 The Interplay Between Economy and the Pandemic -- 2.2.1 Wealth Exchanges in Epidemic Modelling -- 2.2.2 Fokker-Planck Scaling and Steady States -- 2.2.3 The Formation of Bimodal Wealth Distributions -- 2.2.4 The Increase of Wealth Inequalities -- 3 Social Control and Data Uncertainty -- 3.1 Control of Socially Structured Models -- 3.1.1 Optimal Control Formulation -- 3.1.2 Feedback Controlled Compartmental Models.
3.1.3 Containment in Homogeneous Social Mixing Dynamics -- 3.2 Dealing with Data Uncertainty -- 3.2.1 Feedback Controlled and Socially Structured Models with Uncertain Inputs -- 3.2.2 Application to the COVID-19 Outbreak -- 4 Multiscale Transport Models -- 4.1 Spatial Dynamics on Networks -- 4.1.1 1D Hyperbolic Compartmental Model -- 4.1.2 Macroscopic Formulation and Diffusion Limit -- 4.1.3 Extension to Multi-Compartmental Modelling -- 4.1.4 Network Modelling -- 4.1.5 Effect of Spatially Heterogeneous Environments in Hyperbolic and Parabolic Configuration -- 4.1.6 Application to the Emergence of COVID-19 in Italy -- 4.2 Realistic Geographical Settings -- 4.2.1 2D Kinetic Transport Model -- 4.2.2 Macroscopic Formulation and Diffusion Limit -- 4.2.3 Extension to Multi-Compartmental Modelling -- 4.2.4 Application to the Spatial Spread of COVID-19 in Italy in Emilia-Romagna and Lombardy Region -- 5 Concluding Remarks and Research Perspectives -- 5.1 Data sources -- References -- The COVID-19 Pandemic Evolution in Hawai`i and New Jersey: A Lesson on Infection Transmissibility and the Role of HumanBehavior -- 1 Introduction -- 2 Mathematical Models -- 2.1 Agent-Based Models -- 2.1.1 COVID-19 Agent-Based Simulator (Covasim) -- 2.2 Compartmental SEIR Models and Variants -- 2.3 Comparison of Agent-Based and Compartmental Models -- 3 Archipelagos and Islands -- 3.1 March 2020-June 2021 -- 3.1.1 CM Model Fit from March 06, 2020 to January 15, 2021 -- 3.1.2 Comparing CM and ABM Models -- 3.2 July 2021-September 2021 -- 3.3 Discussion -- 4 The Pandemic Waves in New Jersey -- 4.1 Comparing New Jersey to the US -- 4.2 Spatial and Temporal Patterns in COVID-19 Cases in New Jersey -- 4.3 Sociodemographic Variables -- 4.4 Discussion -- 5 The Use of Compartmental Models in New Jersey -- 5.1 Time-Evolution of the Basic Reproduction Number. 5.2 Infected Confirmed Cases, Hospitalizations, and Deaths -- 5.3 Discussion -- 6 Conclusion -- References -- A Novel Point Process Model for COVID-19: Multivariate Recursive Hawkes Process -- 1 Introduction -- 1.1 Hawkes Point Process Modeling of Infectious Diseases -- 1.2 Multivariate Hawkes Processes -- 1.3 Recursive Hawkes Processes -- 1.4 Outline -- 2 Theoretical Properties of Temporal Multivariate Recursive Hawkes Models -- 2.1 Existence -- 2.2 Mean -- 2.3 Variance -- 3 Parameter Fitting and Simulation Algorithms -- 3.1 Parameter Fitting Algorithms -- 3.1.1 Parametric (or Semi-parametric) Estimation -- 3.1.2 Temporal Version of Parameter Fitting Algorithms -- 3.2 Simulation Algorithm -- 4 Reconstruct Multivariate Point Process from Data with Imprecise Time -- 4.1 Time Reconstruction -- 4.2 Category Index Reconstruction -- 5 Numerical Experiments and Results -- 5.1 Synthetic Data Sets -- 5.1.1 Comparison Between Parametric Fitting and Non-parametric Fitting -- 5.1.2 Verification of the Parameter Fitting Algorithm -- 5.1.3 Experiments About Data Sets with Imprecise Time -- 5.2 Experiments on Real COVID-19 Data -- 5.2.1 Model Validation -- 5.2.2 Prediction Based on MRHP and Historical Information -- 6 Conclusion -- References -- Multiscale Aspects of Virus Dynamics -- 1 Introduction -- 1.1 On the Biology of the Virus -- 1.2 Modeling the Complexity of COVID-19 -- 2 Epistemic and Empirical Uncertainties in Compartmental and Individual-Based Models -- 2.1 SIR Model -- 2.2 Individual-Based Interpretation of λ -- 2.3 An Example of Modified SIR Model -- 2.4 Individuals Behind the Modified SIR Model -- 2.5 Time-Discretization -- 3 The Individual-Based Model of FlaLaFauciRiva -- 3.1 A Formula for the Parameter λ of Compartmental Models -- 3.2 Analysis of the Fluctuations -- 3.3 Simulations -- 3.4 Presence of Immunized Population and Virus Variants. Appendix -- References -- Productivity in Times of Covid-19: An Agent-Based Model Approach -- 1 Introduction -- 2 Model -- 3 Mean Field Approximation -- 4 Setting the Model Functions -- 5 Simulations -- 6 Conclusion -- References -- Transmission Dynamics and Quarantine Control of COVID-19 in Cluster Community -- 1 Introduction -- 2 Mathematical Modeling -- 2.1 Stage 1: SEIR-Type Model Without Quarantine -- 2.2 Stage 2: Transmission-Quarantine (TQ) Model -- 3 Analytic Results and Case Study for Emerging Stage -- 3.1 Analytic Results -- 3.2 A Real World Case Study for Stage 1 -- 4 Case Study and Sensitivity Analysis for Quarantine Stage -- 4.1 A Real World Study for Stage 2 -- 4.2 Sensitivity Analysis -- 5 Discussion -- Appendix: Proofs of Theorems -- References -- A 2D Kinetic Model for Crowd Dynamics with Disease Contagion -- 1 Introduction -- 2 A Simplified Two-Dimensional Kinetic Model -- 3 Discretization in Space and Time -- 4 Numerical Results -- 4.1 Tests with v = 0 -- 4.2 Tests with Prescribed Walking Velocity -- 5 A More Complex 2D Kinetic Model -- 6 Conclusions -- References -- Multiscale Derivation of a Time-Dependent SEIRD Reaction-Diffusion System for COVID-19 -- 1 Introduction -- 2 Phenomenological Modeling of Diffusion Population Dynamics -- 3 From Kinetic Theory Model to SEIRD Reaction-Diffusion System -- 3.1 Kinetic Theory Model -- 3.2 Micro-Macro Formulation -- 4 Numerical Method -- 4.1 Semi-Implicit Time Discretization -- 4.2 Fully Discrete Asymptotic Preserving Numerical Scheme in 1D -- 4.3 Boundary Conditions -- 5 Numerical Results -- 5.1 Test 1: Asymptotic Preserving Numerical Scheme Property -- 5.2 Test 2: Diffusion Effect -- 5.3 Test 3: Role of the Transmission Function -- 6 Conclusion and Perspectives -- References. |
| Record Nr. | UNINA-9910595039903321 |
| Cham, Switzerland : , : Birkhäuser, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
