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The nonlinear world : conceptual analysis and phenomenology / / by Yoshitsugu Oono
| The nonlinear world : conceptual analysis and phenomenology / / by Yoshitsugu Oono |
| Autore | Oono Yoshitsugu |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Tokyo ; ; London, : Springer, 2012 |
| Descrizione fisica | 1 online resource (306 p.) |
| Disciplina | 570.1 |
| Collana | Springer series in synergetics |
| Soggetto topico |
Phenomenological biology
Nonlinear theories Synergetics |
| ISBN |
1-283-90996-0
4-431-54029-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Looking at the Nonlinear World -- Conceptual Analysis -- Phenomenology -- Modeling -- Toward Complexity. |
| Record Nr. | UNINA-9910438113403321 |
Oono Yoshitsugu
|
||
| Tokyo ; ; London, : Springer, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Physics of self-organization and evolution [[electronic resource] /] / Rainer Feistel and Werner Ebeling
| Physics of self-organization and evolution [[electronic resource] /] / Rainer Feistel and Werner Ebeling |
| Autore | Feistel Rainer |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Weinheim, : Wiley-VCH, c2011 |
| Descrizione fisica | 1 online resource (535 p.) |
| Disciplina | 003.7 |
| Altri autori (Persone) | EbelingWerner <1936-> |
| Soggetto topico |
Evolution (Biology)
Self-organizing systems Synergetics Thermodynamic equilibrium |
| ISBN |
3-527-63680-3
1-283-86973-X 3-527-63681-1 3-527-63679-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Physics of Self-Organization and Evolution; Contents; Preface; 1 Introduction to the Field of Self-Organization; 1.1 Basic Concepts; 1.2 History of Evolution as a Short Story; 1.3 Structure, Self-organization, and Complexity; 1.4 Entropy, Equilibrium, and Nonequilibrium; 1.5 Dynamics, Stability, and Instability; 1.6 Self-Organization of Information and Values; 2 Fundamental Laws of Equilibrium and Nonequilibrium Thermodynamics; 2.1 The Thermodynamic Way of Describing Nature - Basic Variables; 2.2 Three Fundamental Laws and the Gibbs Relation of Thermodynamics
2.3 Thermodynamic Potentials, Inequalities, and Variational Principles2.4 Irreversible Processes and Self-Organization; 2.5 Irreversible Radiation Transport; 2.6 Irreversible Processes and Fluctuations; 2.7 Toward a Thermodynamics of Small Systems Far from Equilibrium; 3 Evolution of Earth and the Terrestrial Climate; 3.1 The Photon Mill; 3.2 Black-Body Radiation Model of Earth; 3.3 Local Seasonal Response; 3.4 Atmospheric Cooling Rate; 3.5 Black-Body Model with Atmosphere; 3.6 Humidity and Latent Heat; 3.7 Greenhouse Effect; 3.8 Spatial Structure of the Planet; 3.9 Early Evolution of Earth 4 Nonlinear Dynamics, Instabilities, and Fluctuations4.1 State Space, Dynamic Systems, and Graphs; 4.2 Deterministic Dynamic Systems; 4.3 Stochastic Models for Continuous Variables and Predictability; 4.4 Graphs - Mathematical Models of Structures and Networks; 4.5 Stochastic Models for Discrete Variables; 4.6 Stochastic Processes on Networks; 5 Self-Reproduction, Multistability, and Information Transfer as Basic Mechanisms of Evolution; 5.1 The Role of Self-Reproduction and Multistability; 5.2 Deterministic Models of Self-Reproduction and Bistability 5.3 Stochastic Theory of Birth-and-Death Processes5.4 Stochastic Analysis of the Survival of the New; 5.5 Survival of the New in Bistable Systems; 5.6 Multistability, Information Storage, and Information Transfer; 6 Competition and Selection Processes; 6.1 Discussion of Basic Terms; 6.2 Extremum Principles; 6.3 Dynamical Models with Simple Competition; 6.4 Stochastic of Simple Competition Processes; 6.5 Competition in Species Networks; 6.6 Selection and Coexistence; 6.7 Hyperselection; 6.8 Selection in Ecological Systems; 6.9 Selection with Sexual Replication 6.10 Selection between Microreactors6.11 Selection in Social Systems; 7 Models of Evolution Processes; 7.1 Sequence-Evolution Models; 7.2 Evolution on Fitness Landscapes; 7.3 Evolution on Smooth Fisher-Eigen Landscapes; 7.4 Evolution on Random Fisher-Eigen Landscapes; 7.5 Evolution on Lotka-Volterra Landscapes; 7.6 Axiomatic Evolution Models; 7.7 Boolean Behavior in the Positive Cone; 7.8 Axiomatic Description of a Boolean Reaction System; 7.9 Reducible, Linear, and Ideal Boolean Reaction Systems; 7.10 Minor and Major of a Boolean Reaction System 7.11 Selection and Evolution in Boolean Reaction Systems |
| Record Nr. | UNINA-9910137998903321 |
|
Feistel Rainer
|
||
| Weinheim, : Wiley-VCH, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Physics of self-organization and evolution / / Rainer Feistel and Werner Ebeling
| Physics of self-organization and evolution / / Rainer Feistel and Werner Ebeling |
| Autore | Feistel Rainer |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Weinheim, : Wiley-VCH, c2011 |
| Descrizione fisica | 1 online resource (535 p.) |
| Disciplina | 003.7 |
| Altri autori (Persone) | EbelingWerner <1936-> |
| Soggetto topico |
Evolution (Biology)
Self-organizing systems Synergetics Thermodynamic equilibrium |
| ISBN |
9783527636808
3527636803 9781283869737 128386973X 9783527636815 3527636811 9783527636792 352763679X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Physics of Self-Organization and Evolution; Contents; Preface; 1 Introduction to the Field of Self-Organization; 1.1 Basic Concepts; 1.2 History of Evolution as a Short Story; 1.3 Structure, Self-organization, and Complexity; 1.4 Entropy, Equilibrium, and Nonequilibrium; 1.5 Dynamics, Stability, and Instability; 1.6 Self-Organization of Information and Values; 2 Fundamental Laws of Equilibrium and Nonequilibrium Thermodynamics; 2.1 The Thermodynamic Way of Describing Nature - Basic Variables; 2.2 Three Fundamental Laws and the Gibbs Relation of Thermodynamics
2.3 Thermodynamic Potentials, Inequalities, and Variational Principles2.4 Irreversible Processes and Self-Organization; 2.5 Irreversible Radiation Transport; 2.6 Irreversible Processes and Fluctuations; 2.7 Toward a Thermodynamics of Small Systems Far from Equilibrium; 3 Evolution of Earth and the Terrestrial Climate; 3.1 The Photon Mill; 3.2 Black-Body Radiation Model of Earth; 3.3 Local Seasonal Response; 3.4 Atmospheric Cooling Rate; 3.5 Black-Body Model with Atmosphere; 3.6 Humidity and Latent Heat; 3.7 Greenhouse Effect; 3.8 Spatial Structure of the Planet; 3.9 Early Evolution of Earth 4 Nonlinear Dynamics, Instabilities, and Fluctuations4.1 State Space, Dynamic Systems, and Graphs; 4.2 Deterministic Dynamic Systems; 4.3 Stochastic Models for Continuous Variables and Predictability; 4.4 Graphs - Mathematical Models of Structures and Networks; 4.5 Stochastic Models for Discrete Variables; 4.6 Stochastic Processes on Networks; 5 Self-Reproduction, Multistability, and Information Transfer as Basic Mechanisms of Evolution; 5.1 The Role of Self-Reproduction and Multistability; 5.2 Deterministic Models of Self-Reproduction and Bistability 5.3 Stochastic Theory of Birth-and-Death Processes5.4 Stochastic Analysis of the Survival of the New; 5.5 Survival of the New in Bistable Systems; 5.6 Multistability, Information Storage, and Information Transfer; 6 Competition and Selection Processes; 6.1 Discussion of Basic Terms; 6.2 Extremum Principles; 6.3 Dynamical Models with Simple Competition; 6.4 Stochastic of Simple Competition Processes; 6.5 Competition in Species Networks; 6.6 Selection and Coexistence; 6.7 Hyperselection; 6.8 Selection in Ecological Systems; 6.9 Selection with Sexual Replication 6.10 Selection between Microreactors6.11 Selection in Social Systems; 7 Models of Evolution Processes; 7.1 Sequence-Evolution Models; 7.2 Evolution on Fitness Landscapes; 7.3 Evolution on Smooth Fisher-Eigen Landscapes; 7.4 Evolution on Random Fisher-Eigen Landscapes; 7.5 Evolution on Lotka-Volterra Landscapes; 7.6 Axiomatic Evolution Models; 7.7 Boolean Behavior in the Positive Cone; 7.8 Axiomatic Description of a Boolean Reaction System; 7.9 Reducible, Linear, and Ideal Boolean Reaction Systems; 7.10 Minor and Major of a Boolean Reaction System 7.11 Selection and Evolution in Boolean Reaction Systems |
| Record Nr. | UNINA-9910827404903321 |
|
Feistel Rainer
|
||
| Weinheim, : Wiley-VCH, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Synergetics : an introduction : nonequilibrium phase transitions and self-organization in physics, chemistry, and biology / / Hermann Haken
| Synergetics : an introduction : nonequilibrium phase transitions and self-organization in physics, chemistry, and biology / / Hermann Haken |
| Autore | Haken H. |
| Edizione | [2nd ed. 1978.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer-Verlag, , [2012] |
| Descrizione fisica | 1 online resource (359 pages) : illustrations |
| Disciplina | 003.7 |
| Collana | Springer Series in Synergetics |
| Soggetto topico |
Self-organizing systems
Synergetics |
| ISBN | 3-642-96469-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Goal -- 1.1 Order and Disorder: Some Typical Phenomena -- 1.2 Some Typical Problems and Difficulties -- 1.3 How We Shall Proceed -- 2. Probability -- 2.1 Object of Our Investigations: The Sample Space -- 2.2 Random Variables -- 2.3 Probability -- 2.4 Distribution -- 2.5 Random Variables with Densities -- 2.6 Joint Probability -- 2.7 Mathematical Expectation E(X), and Moments -- 2.8 Conditional Probabilities -- 2.9 Independent and Dependent Random Variables -- 2.10*Generating Functions and Characteristic Functions -- 2.11 A Special Probability Distribution: Binomial Distribution -- 2.12 The Poisson Distribution -- 2.13 The Normal Distribution (Gaussian Distribution) -- 2.14 Stirling’s Formula -- 2.15*Central Limit Theorem -- 3. Information -- 3.1 Some Basic Ideas -- 3.2* Information Gain: An Illustrative Derivation -- 3.3 Information Entropy and Constraints -- 3.4 An Example from Physics: Thermodynamics -- 3.5* An Approach to Irreversible Thermodynamics -- 3.6 Entropy—Curse of Statistical Mechanics? -- 4. Chance -- 4.1 A Model of Brownian Movement -- 4.2 The Random Walk Model and Its Master Equation -- 4.3* Joint Probability and Paths. Markov Processes. The Chapman-Kolmogorov Equation. Path Integrals -- 4.4* How to Use Joint Probabilities. Moments. Characteristic Function. Gaussian Processes -- 4.5 The Master Equation -- 4.6 Exact Stationary Solution of the Master Equation for Systems in Detailed Balance -- 4.7* The Master Equation with Detailed Balance. Symmetrization, Eigenvalues and Eigenstates -- 4.8* Kirchhoff’s Method of Solution of the Master Equation -- 4.9* Theorems about Solutions of the Master Equation -- 4.10 The Meaning of Random Processes. Stationary State, Fluctuations, Recurrence Time -- 4.11*Master Equation and Limitations of Irreversible Thermodynamics -- 5. Necessity -- 5.1 Dynamic Processes -- 5.2* Critical Points and Trajectories in a Phase Plane. Once Again Limit Cycles -- 5.3* Stability -- 5.4 Examples and Exercises on Bifurcation and Stability -- 5.5* Classification of Static Instabilities, or an Elementary Approach to Thorn’s Theory of Catastrophes -- 6. Chance and Necessity -- 6.1 Langevin Equations: An Example -- 6.2* Reservoirs and Random Forces -- 6.3 The Fokker-Planck Equation -- 6.4 Some Properties and Stationary Solutions of the Fokker-Planck Equation -- 6.5 Time-Dependent Solutions of the Fokker-Planck Equation -- 6.6* Solution of the Fokker-Planck Equation by Path Integrals -- 6.7 Phase Transition Analogy -- 6.8 Phase Transition Analogy in Continuous Media: Space-Dependent Order Parameter -- 7. Self-Organization -- 7.1 Organization -- 7.2 Self-Organization -- 7.3 The Role of Fluctuations: Reliability or Adaptibility? Switching -- 7.4* Adiabatic Elimination of Fast Relaxing Variables from the Fokker-Planck Equation -- 7.5* Adiabatic Elimination of Fast Relaxing Variables from the Master Equation -- 7.6 Self-Organization in Continuously Extended Media. An Outline of the Mathematical Approach -- 7.7* Generalized Ginzburg-Landau Equations for Nonequilibrium Phase Transitions -- 7.8* Higher-Order Contributions to Generalized Ginzburg-Landau Equations -- 7.9* Scaling Theory of Continuously Extended Nonequilibrium Systems -- 7.10*Soft-Mode Instability -- 7.1 l*Hard-Mode Instability -- 8. Physical Systems -- 8.1 Cooperative Effects in the Laser: Self-Organization and Phase Transition -- 8.2 The Laser Equations in the Mode Picture -- 8.3 The Order Parameter Concept -- 8.4 The Single-Mode Laser -- 8.5 The Multimode Laser -- 8.6 Laser with Continuously Many Modes. Analogy with Superconductivity -- 8.7 First-Order Phase Transitions of the Single-Mode Laser -- 8.8 Hierarchy of Laser Instabilities and Ultrashort Laser Pulses -- 8.9 Instabilities in Fluid Dynamics: The Bénard and Taylor Problems -- 8.10 The Basic Equations -- 8.11 Damped and Neutral Solutions (R ? Rc) -- 8.12 Solution Near R = Rc (Nonlinear Domain). Effective Langevin Equations -- 8.13 The Fokker-Planck Equation and Its Stationary Solution -- 8.14 A Model for the Statistical Dynamics of the Gunn Instability Near Threshold -- 8.15 Elastic Stability: Outline of Some Basic Ideas -- 9. Chemical and Biochemical Systems -- 9.1 Chemical and Biochemical Reactions -- 9.2 Deterministic Processes, Without Diffusion, One Variable -- 9.3 Reaction and Diffusion Equations -- 9.4 Reaction-Diffusion Model with Two or Three Variables: The Brusselator and the Oregonator -- 9.5 Stochastic Model for a Chemical Reaction Without Diffusion. Birth and Death Processes. One Variable -- 9.6 Stochastic Model for a Chemical Reaction with Diffusion. One Variable -- 9.7* Stochastic Treatment of the Brusselator Close to Its Soft-Mode Instability -- 9.8 Chemical Networks -- 10. Applications to Biology -- 10.1 Ecology, Population-Dynamics -- 10.2 Stochastic Models for a Predator-Prey System -- 10.3 A Simple Mathematical Model for Evolutionary Processes -- 10.4 A Model for Morphogenesis -- 10.5 Order Parameters and Morphogenesis -- 10.6 Some Comments on Models of Morphogenesis -- 11. Sociology: A Stochastic Model for the Formation of Public Opinion -- 12. Chaos -- 12.1 What is Chaos? -- 12.2 The Lorenz Model. Motivation and Realization -- 12.3 How Chaos Occurs -- 12.4 Chaos and the Failure of the Slaving Principle -- 12.5 Correlation Function and Frequency Distribution -- 12.6 Further Examples of Chaotic Motion -- 13. Some Historical Remarks and Outlook -- References, Further Reading and Comments. |
| Record Nr. | UNINA-9910789216603321 |
|
Haken H.
|
||
| Berlin, Heidelberg : , : Springer-Verlag, , [2012] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Synergetics : an introduction : nonequilibrium phase transitions and self-organization in physics, chemistry, and biology / / Hermann Haken
| Synergetics : an introduction : nonequilibrium phase transitions and self-organization in physics, chemistry, and biology / / Hermann Haken |
| Autore | Haken H. |
| Edizione | [2nd ed. 1978.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer-Verlag, , [2012] |
| Descrizione fisica | 1 online resource (359 pages) : illustrations |
| Disciplina | 003.7 |
| Collana | Springer Series in Synergetics |
| Soggetto topico |
Self-organizing systems
Synergetics |
| ISBN | 3-642-96469-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Goal -- 1.1 Order and Disorder: Some Typical Phenomena -- 1.2 Some Typical Problems and Difficulties -- 1.3 How We Shall Proceed -- 2. Probability -- 2.1 Object of Our Investigations: The Sample Space -- 2.2 Random Variables -- 2.3 Probability -- 2.4 Distribution -- 2.5 Random Variables with Densities -- 2.6 Joint Probability -- 2.7 Mathematical Expectation E(X), and Moments -- 2.8 Conditional Probabilities -- 2.9 Independent and Dependent Random Variables -- 2.10*Generating Functions and Characteristic Functions -- 2.11 A Special Probability Distribution: Binomial Distribution -- 2.12 The Poisson Distribution -- 2.13 The Normal Distribution (Gaussian Distribution) -- 2.14 Stirling’s Formula -- 2.15*Central Limit Theorem -- 3. Information -- 3.1 Some Basic Ideas -- 3.2* Information Gain: An Illustrative Derivation -- 3.3 Information Entropy and Constraints -- 3.4 An Example from Physics: Thermodynamics -- 3.5* An Approach to Irreversible Thermodynamics -- 3.6 Entropy—Curse of Statistical Mechanics? -- 4. Chance -- 4.1 A Model of Brownian Movement -- 4.2 The Random Walk Model and Its Master Equation -- 4.3* Joint Probability and Paths. Markov Processes. The Chapman-Kolmogorov Equation. Path Integrals -- 4.4* How to Use Joint Probabilities. Moments. Characteristic Function. Gaussian Processes -- 4.5 The Master Equation -- 4.6 Exact Stationary Solution of the Master Equation for Systems in Detailed Balance -- 4.7* The Master Equation with Detailed Balance. Symmetrization, Eigenvalues and Eigenstates -- 4.8* Kirchhoff’s Method of Solution of the Master Equation -- 4.9* Theorems about Solutions of the Master Equation -- 4.10 The Meaning of Random Processes. Stationary State, Fluctuations, Recurrence Time -- 4.11*Master Equation and Limitations of Irreversible Thermodynamics -- 5. Necessity -- 5.1 Dynamic Processes -- 5.2* Critical Points and Trajectories in a Phase Plane. Once Again Limit Cycles -- 5.3* Stability -- 5.4 Examples and Exercises on Bifurcation and Stability -- 5.5* Classification of Static Instabilities, or an Elementary Approach to Thorn’s Theory of Catastrophes -- 6. Chance and Necessity -- 6.1 Langevin Equations: An Example -- 6.2* Reservoirs and Random Forces -- 6.3 The Fokker-Planck Equation -- 6.4 Some Properties and Stationary Solutions of the Fokker-Planck Equation -- 6.5 Time-Dependent Solutions of the Fokker-Planck Equation -- 6.6* Solution of the Fokker-Planck Equation by Path Integrals -- 6.7 Phase Transition Analogy -- 6.8 Phase Transition Analogy in Continuous Media: Space-Dependent Order Parameter -- 7. Self-Organization -- 7.1 Organization -- 7.2 Self-Organization -- 7.3 The Role of Fluctuations: Reliability or Adaptibility? Switching -- 7.4* Adiabatic Elimination of Fast Relaxing Variables from the Fokker-Planck Equation -- 7.5* Adiabatic Elimination of Fast Relaxing Variables from the Master Equation -- 7.6 Self-Organization in Continuously Extended Media. An Outline of the Mathematical Approach -- 7.7* Generalized Ginzburg-Landau Equations for Nonequilibrium Phase Transitions -- 7.8* Higher-Order Contributions to Generalized Ginzburg-Landau Equations -- 7.9* Scaling Theory of Continuously Extended Nonequilibrium Systems -- 7.10*Soft-Mode Instability -- 7.1 l*Hard-Mode Instability -- 8. Physical Systems -- 8.1 Cooperative Effects in the Laser: Self-Organization and Phase Transition -- 8.2 The Laser Equations in the Mode Picture -- 8.3 The Order Parameter Concept -- 8.4 The Single-Mode Laser -- 8.5 The Multimode Laser -- 8.6 Laser with Continuously Many Modes. Analogy with Superconductivity -- 8.7 First-Order Phase Transitions of the Single-Mode Laser -- 8.8 Hierarchy of Laser Instabilities and Ultrashort Laser Pulses -- 8.9 Instabilities in Fluid Dynamics: The Bénard and Taylor Problems -- 8.10 The Basic Equations -- 8.11 Damped and Neutral Solutions (R ? Rc) -- 8.12 Solution Near R = Rc (Nonlinear Domain). Effective Langevin Equations -- 8.13 The Fokker-Planck Equation and Its Stationary Solution -- 8.14 A Model for the Statistical Dynamics of the Gunn Instability Near Threshold -- 8.15 Elastic Stability: Outline of Some Basic Ideas -- 9. Chemical and Biochemical Systems -- 9.1 Chemical and Biochemical Reactions -- 9.2 Deterministic Processes, Without Diffusion, One Variable -- 9.3 Reaction and Diffusion Equations -- 9.4 Reaction-Diffusion Model with Two or Three Variables: The Brusselator and the Oregonator -- 9.5 Stochastic Model for a Chemical Reaction Without Diffusion. Birth and Death Processes. One Variable -- 9.6 Stochastic Model for a Chemical Reaction with Diffusion. One Variable -- 9.7* Stochastic Treatment of the Brusselator Close to Its Soft-Mode Instability -- 9.8 Chemical Networks -- 10. Applications to Biology -- 10.1 Ecology, Population-Dynamics -- 10.2 Stochastic Models for a Predator-Prey System -- 10.3 A Simple Mathematical Model for Evolutionary Processes -- 10.4 A Model for Morphogenesis -- 10.5 Order Parameters and Morphogenesis -- 10.6 Some Comments on Models of Morphogenesis -- 11. Sociology: A Stochastic Model for the Formation of Public Opinion -- 12. Chaos -- 12.1 What is Chaos? -- 12.2 The Lorenz Model. Motivation and Realization -- 12.3 How Chaos Occurs -- 12.4 Chaos and the Failure of the Slaving Principle -- 12.5 Correlation Function and Frequency Distribution -- 12.6 Further Examples of Chaotic Motion -- 13. Some Historical Remarks and Outlook -- References, Further Reading and Comments. |
| Record Nr. | UNINA-9910813107803321 |
|
Haken H.
|
||
| Berlin, Heidelberg : , : Springer-Verlag, , [2012] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Synergetics : an introduction : monequilibrium phase transitions and self-organization in physics, chemistry and biology / / Hermann Haken
| Synergetics : an introduction : monequilibrium phase transitions and self-organization in physics, chemistry and biology / / Hermann Haken |
| Autore | Haken H. |
| Edizione | [1st ed. 1977.] |
| Pubbl/distr/stampa | Berlin ; ; Heidelberg ; ; New York : , : Springer-Verlag, , 1977 |
| Descrizione fisica | 1 online resource (327 pages) : illustrations |
| Disciplina | 003.7 |
| Soggetto topico |
Self-organizing systems
Synergetics |
| ISBN | 3-642-96363-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Goal -- 1.1 Order and Disorder: Some Typical Phenomena -- 1.2 Some Typical Problems and Difficulties -- 1.3 How We Shall Proceed -- 2. Probability -- 2.1 Object of Our Investigations: The Sample Space -- 2.2 Random Variables -- 2.3 Probability -- 2.4 Distribution -- 2.5 Random Variables with Densities -- 2.6 Joint Probability -- 2.7 Mathematical Expectation E(X), and Moments -- 2.8 Conditional Probabilites -- 2.9 Independent and Dependent Random Variables -- 2.10 Generating Functions and Characteristic Functions -- 2.11 A Special Probability Distribution: Binomial Distribution -- 2.12 The Poisson Distribution -- 2.13 The Normal Distribution (Gaussian Distribution) -- 2.14 Stirling’s Formula -- 2.15 Central Limit Theorem -- 3. Information -- 3.1 Some Basic Ideas -- 3.2 Information Gain: An Illustrative Derivation -- 3.3 Information Entropy and Constraints -- 3.4 An Example from Physics: Thermodynamics -- 3.5 An Approach to Irreversible Thermodynamics -- 3.6 Entropy—Curse of Statistical Mechanics? -- 4. Chance -- 4.1 A Model of Brownian Movement -- 4.2 The Random Walk Model and Its Master Equation -- 4.3 Joint Probability and Paths. Markov Processes. The Chapman-Kolmogorov Equation. Path Integrals -- 4.4 How to Use Joint Probabilities. Moments. Characteristic Function. Gaussian Processes -- 4.5 The Master Equation -- 4.6 Exact Stationary Solution of the Master Equation for Systems in Detailed Balance -- 4.7 The Master Equation with Detailed Balance. Symmetrization, Eigenvalues and Eigenstates -- 4.8 Kirchhoff’s Method of Solution of the Master Equation -- 4.9 Theorems about Solutions of the Master Equation -- 4.10 The Meaning of Random Processes. Stationary State, Fluctuations, Recurrence Time -- 4.11 Master Equation and Limitations of Irreversible Thermodynamics -- 5. Necessity -- 5.1 Dynamic Processes -- 5.2 Critical Points and Trajectories in a Phase Plane. Once Again Limit Cycles -- 5.3 Stability -- 5.4 Examples and Exercises on Bifurcation and Stability -- 5.5 Classification of Static Instabilities, or an Elementary Approach to Thom’s Theory of Catastrophes -- 6. Chance and Necessity -- 6.1 Langevin Equations: An Example -- 6.2 Reservoirs and Random Forces -- 6.3 The Fokker-Planck Equation -- 6.4 Some Properties and Stationary Solutions of the Fokker-Planck Equation -- 6.5 Time-Dependent Solutions of the Fokker-Planck Equation -- 6.6 Solution of the Fokker-Planck Equation by Path Integrals -- 6.7 Phase Transition Analogy -- 6.8 Phase Transition Analogy in Continuous Media: Space-Dependent Order Parameter -- 7. Self-Organization -- 7.1 Organization -- 7.2 Self-Organization -- 7.3 The Role of Fluctuations: Reliability or Adaptibility? Switching -- 7.4 Adiabatic Elimination of Fast Relaxing Variables from the Fokker-Planck Equation -- 7.5 Adiabatic Elimination of Fast Relaxing Variables from the Master Equation -- 7.6 Self-Organization in Continuously Extended Media. An Outline of the Mathematical Approach -- 7.7 Generalized Ginzburg-Landau Equations for Nonequilibrium Phase Transitions -- 7.8 Higher-Order Contributions to Generalized Ginzburg-Landau Equations -- 7.9 Scaling Theory of Continuously Extended Nonequilibrium Systems -- 7.10 Soft-Mode Instability -- 7.11 Hard-Mode Instability -- 8. Physical Systems -- 8.1 Cooperative Effects in the Laser: Self-Organization and Phase Transition -- 8.2 The Laser Equations in the Mode Picture -- 8.3 The Order Parameter Concept -- 8.4 The Single-Mode Laser -- 8.5 The Multimode Laser -- 8.6 Laser with Continuously Many Modes. Analogy with Superconductivity -- 8.7 First-Order Phase Transitions of the Single-Mode Laser -- 8.8 Hierachy of Laser Instabilities and Ultrashort Laser Pulses -- 8.9 Instabilities in Fluid Dynamics: The Bénard and Taylor Problems -- 8.10 The Basic Equations -- 8.11 Damped and Neutral Solutions (R ? Rc) -- 8.12 Solution Near R = Rc (Nonlinear Domain). Effective Langevin Equations -- 8.13 The Fokker-Planck Equation and Its Stationary Solution -- 8.14 A Model for the Statistical Dynamics of the Gunn Instability Near Threshold -- 8.15 Elastic Stability: Outline of Some Basic Ideas -- 9. Chemical and Biochemical Systems -- 9.1 Chemical and Biochemical Reactions -- 9.2 Deterministic Processes, Without Diffusion, One Variable -- 9.3 Reaction and Diffusion Equations -- 9.4 Reaction-Diffusion Model with Two or Three Variables: The Brusselator and the Oregonator -- 9.5 Stochastic Model for a Chemical Reaction Without Diffusion. Birth and Death Processes. One Variable -- 9.6 Stochastic Model for a Chemical Reaction with Diffusion. One Variable -- 9.7 Stochastic Treatment ofthe Brusselator Close to Its Soft-Mode Instability -- 9.8 Chemical Networks -- 10. Applications to Biology -- 10.1 Ecology, Population-Dynamics -- 10.2 Stochastic Models for a Predator-Prey System -- 10.3 A Simple Mathematical Model for Evolutionary Processes -- 10.4 A Model for Morphogenesis -- 11. Sociology: A Stochastic Model for the Formation of Public Opinion -- 12. Some Historical Remarks and Outlook -- References, Further Reading, and Comments. |
| Record Nr. | UNINA-9910789209503321 |
|
Haken H.
|
||
| Berlin ; ; Heidelberg ; ; New York : , : Springer-Verlag, , 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Synergetics : an introduction : monequilibrium phase transitions and self-organization in physics, chemistry and biology / / Hermann Haken
| Synergetics : an introduction : monequilibrium phase transitions and self-organization in physics, chemistry and biology / / Hermann Haken |
| Autore | Haken H. |
| Edizione | [1st ed. 1977.] |
| Pubbl/distr/stampa | Berlin ; ; Heidelberg ; ; New York : , : Springer-Verlag, , 1977 |
| Descrizione fisica | 1 online resource (327 pages) : illustrations |
| Disciplina | 003.7 |
| Soggetto topico |
Self-organizing systems
Synergetics |
| ISBN | 3-642-96363-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Goal -- 1.1 Order and Disorder: Some Typical Phenomena -- 1.2 Some Typical Problems and Difficulties -- 1.3 How We Shall Proceed -- 2. Probability -- 2.1 Object of Our Investigations: The Sample Space -- 2.2 Random Variables -- 2.3 Probability -- 2.4 Distribution -- 2.5 Random Variables with Densities -- 2.6 Joint Probability -- 2.7 Mathematical Expectation E(X), and Moments -- 2.8 Conditional Probabilites -- 2.9 Independent and Dependent Random Variables -- 2.10 Generating Functions and Characteristic Functions -- 2.11 A Special Probability Distribution: Binomial Distribution -- 2.12 The Poisson Distribution -- 2.13 The Normal Distribution (Gaussian Distribution) -- 2.14 Stirling’s Formula -- 2.15 Central Limit Theorem -- 3. Information -- 3.1 Some Basic Ideas -- 3.2 Information Gain: An Illustrative Derivation -- 3.3 Information Entropy and Constraints -- 3.4 An Example from Physics: Thermodynamics -- 3.5 An Approach to Irreversible Thermodynamics -- 3.6 Entropy—Curse of Statistical Mechanics? -- 4. Chance -- 4.1 A Model of Brownian Movement -- 4.2 The Random Walk Model and Its Master Equation -- 4.3 Joint Probability and Paths. Markov Processes. The Chapman-Kolmogorov Equation. Path Integrals -- 4.4 How to Use Joint Probabilities. Moments. Characteristic Function. Gaussian Processes -- 4.5 The Master Equation -- 4.6 Exact Stationary Solution of the Master Equation for Systems in Detailed Balance -- 4.7 The Master Equation with Detailed Balance. Symmetrization, Eigenvalues and Eigenstates -- 4.8 Kirchhoff’s Method of Solution of the Master Equation -- 4.9 Theorems about Solutions of the Master Equation -- 4.10 The Meaning of Random Processes. Stationary State, Fluctuations, Recurrence Time -- 4.11 Master Equation and Limitations of Irreversible Thermodynamics -- 5. Necessity -- 5.1 Dynamic Processes -- 5.2 Critical Points and Trajectories in a Phase Plane. Once Again Limit Cycles -- 5.3 Stability -- 5.4 Examples and Exercises on Bifurcation and Stability -- 5.5 Classification of Static Instabilities, or an Elementary Approach to Thom’s Theory of Catastrophes -- 6. Chance and Necessity -- 6.1 Langevin Equations: An Example -- 6.2 Reservoirs and Random Forces -- 6.3 The Fokker-Planck Equation -- 6.4 Some Properties and Stationary Solutions of the Fokker-Planck Equation -- 6.5 Time-Dependent Solutions of the Fokker-Planck Equation -- 6.6 Solution of the Fokker-Planck Equation by Path Integrals -- 6.7 Phase Transition Analogy -- 6.8 Phase Transition Analogy in Continuous Media: Space-Dependent Order Parameter -- 7. Self-Organization -- 7.1 Organization -- 7.2 Self-Organization -- 7.3 The Role of Fluctuations: Reliability or Adaptibility? Switching -- 7.4 Adiabatic Elimination of Fast Relaxing Variables from the Fokker-Planck Equation -- 7.5 Adiabatic Elimination of Fast Relaxing Variables from the Master Equation -- 7.6 Self-Organization in Continuously Extended Media. An Outline of the Mathematical Approach -- 7.7 Generalized Ginzburg-Landau Equations for Nonequilibrium Phase Transitions -- 7.8 Higher-Order Contributions to Generalized Ginzburg-Landau Equations -- 7.9 Scaling Theory of Continuously Extended Nonequilibrium Systems -- 7.10 Soft-Mode Instability -- 7.11 Hard-Mode Instability -- 8. Physical Systems -- 8.1 Cooperative Effects in the Laser: Self-Organization and Phase Transition -- 8.2 The Laser Equations in the Mode Picture -- 8.3 The Order Parameter Concept -- 8.4 The Single-Mode Laser -- 8.5 The Multimode Laser -- 8.6 Laser with Continuously Many Modes. Analogy with Superconductivity -- 8.7 First-Order Phase Transitions of the Single-Mode Laser -- 8.8 Hierachy of Laser Instabilities and Ultrashort Laser Pulses -- 8.9 Instabilities in Fluid Dynamics: The Bénard and Taylor Problems -- 8.10 The Basic Equations -- 8.11 Damped and Neutral Solutions (R ? Rc) -- 8.12 Solution Near R = Rc (Nonlinear Domain). Effective Langevin Equations -- 8.13 The Fokker-Planck Equation and Its Stationary Solution -- 8.14 A Model for the Statistical Dynamics of the Gunn Instability Near Threshold -- 8.15 Elastic Stability: Outline of Some Basic Ideas -- 9. Chemical and Biochemical Systems -- 9.1 Chemical and Biochemical Reactions -- 9.2 Deterministic Processes, Without Diffusion, One Variable -- 9.3 Reaction and Diffusion Equations -- 9.4 Reaction-Diffusion Model with Two or Three Variables: The Brusselator and the Oregonator -- 9.5 Stochastic Model for a Chemical Reaction Without Diffusion. Birth and Death Processes. One Variable -- 9.6 Stochastic Model for a Chemical Reaction with Diffusion. One Variable -- 9.7 Stochastic Treatment ofthe Brusselator Close to Its Soft-Mode Instability -- 9.8 Chemical Networks -- 10. Applications to Biology -- 10.1 Ecology, Population-Dynamics -- 10.2 Stochastic Models for a Predator-Prey System -- 10.3 A Simple Mathematical Model for Evolutionary Processes -- 10.4 A Model for Morphogenesis -- 11. Sociology: A Stochastic Model for the Formation of Public Opinion -- 12. Some Historical Remarks and Outlook -- References, Further Reading, and Comments. |
| Record Nr. | UNINA-9910813427903321 |
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Haken H.
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| Berlin ; ; Heidelberg ; ; New York : , : Springer-Verlag, , 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Synergy
| Synergy |
| Pubbl/distr/stampa | [Amsterdam, The Netherlands] : , : Elsevier, , [2014]- |
| Descrizione fisica | 1 online resource |
| Soggetto topico |
Synergetics
Life sciences |
| Soggetto genere / forma | Periodicals. |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910249450503321 |
| [Amsterdam, The Netherlands] : , : Elsevier, , [2014]- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
