Stochastic systems with time delay : probabilistic and thermodynamic descriptions of non-Markovian processes far from equilibrium / / Sarah A.M. Loos

• Record Nr.: UNINA9910502633203321
• Autore: Loos Sarah A. M.
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2021]; ©2021
• ISBN: 3-030-80771-1
• Descrizione fisica: 1 online resource (296 pages)
• Collana: Springer Theses
• Disciplina: 003.76
• Soggetti: Stochastic systems; Time delay systems; Thermodynamics - Mathematics; Sistemes estocàstics; Termodinàmica; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Supervisor's Foreword -- Abstract -- Acknowledgements -- Publications by Sarah A. M. Loos -- Contents -- Abbreviations and Symbols -- Abbreviations -- Symbols -- 1 Introduction -- 1.1 Outline of the Thesis -- References -- Part I Theoretical Background and State of the Art -- 2 The Langevin Equation -- 2.1 The Stochastic Way of Describing Things -- 2.1.1 Brownian Motion -- 2.1.2 Colloidal Suspensions -- 2.1.3 Side Note: A More General View -- 2.2 The Markovian Langevin Equation -- 2.2.1 Gaussian White Noise -- 2.2.2 Ensemble Averages and Probability Density -- 2.2.3 Solutions of the Langevin Equation and the Overdamped Limit -- 2.2.4 Ornstein-Uhlenbeck Process -- 2.2.5 White Noise-Wiener Process-Stochastic Calculus -- 2.2.6 Path Integral Representation -- 2.3 Generalised Langevin Equations-How Stochastic Motion … -- 2.3.1 Infinite Harmonic Oscillators Bath-An Example of a Mori-Zwanzig Projection -- 2.3.2 Coarse-Graining-Forgetting Some Details -- 2.3.3 Side Node: Taking this Simplified Model Serious -- 2.3.4 The Markov Assumption ; -- 2.3.5 Real-World Complications -- 2.3.6 Time-Reversal Symmetry and Causality -- 2.4 Introduction to the Langevin Equation with Time Delay -- 2.4.1 Optical Traps-An Experimental Tool to Control -- 2.4.2 Time-Delayed Feedback -- 2.4.3 The Langevin Equation with Time Delay -- 2.4.4 Side Note: Delay Differential Equations -- 2.4.5 Linear Systems with Time Delay -- 2.5 Nonlinear Example Systems with Time Delay -- 2.5.1 Bistable System: The Doublewell Potential -- 2.5.2 Periodic System: The Washboard Potential -- 2.5.3 Scaling -- 2.6 Timescales -- 2.6.1 Kramers Escape Times -- 2.7 Delay-Induced Oscillations and Coherence Resonance -- 2.7.1 Delay-Induced Oscillations -- 2.7.2 Coherence Resonance -- 2.7.3 Bifurcation Theoretical Perspective on Delay-Induced Oscillations -- References -- 3 Fokker-Planck Equations.; 3.1 Markovian Case -- 3.1.1 Natural Boundary Conditions -- 3.1.2 Joint Probability Densities -- 3.1.3 The Probability Current and Steady States -- 3.2 Introduction to Fokker-Planck Descriptions of Systems with Time Delay -- 3.2.1 Earlier Approximation Schemes -- 3.2.2 Probability Current and Apparent Equilibrium of Time-Delayed Systems -- 3.2.3 Side Note: Delay in Ensemble-Averaged Quantities -- References -- 4 Stochastic Thermodynamics -- 4.1 Side Note: Some Historical Notes and Where Is Stochastic … -- 4.2 Stochastic Energetics -- 4.2.1 Steady States -- 4.3 Fluctuating Entropy -- 4.3.1 Thermal Equilibrium &amp -- Nonequilibrium Steady States -- 4.4 Fluctuation Theorems -- 4.4.1 Route to First Principles-Axiom of Causality -- 4.5 Information -- 4.5.1 Mutual Information and Its Generalization -- 4.5.2 Information Flow -- 4.6 Previous Results, Expectations and Apparent Problems for Systems with Time Delay -- 4.6.1 Energetics in the Presence of Delay -- 4.6.2 Entropic Description -- 4.6.3 The Acausality Issue -- 4.6.4 Short Comment on Effective Thermodynamics -- 4.7 Side Note: Active Particles &amp -- Non-reciprocal Interactions -- 4.7.1 Active Ornstein-Uhlenbeck Particles -- 4.7.2 Connection Between Active Matter and Time-Delayed Systems -- 4.7.3 Non-reciprocal Interactions -- References -- Part II Probabilistic Descriptions for Systems with Time Delay -- 5 Infinite Fokker-Planck Hierarchy -- 5.1 Derivation of Fokker-Planck Hierarchy from Novikov's Theorem -- 5.1.1 Alternative Approach with Two Time Arguments -- 5.2 Exact Probabilistic Solutions for Linear Systems with Time Delay -- 5.2.1 Derivation of the Second Member of the Fokker-Planck Hierarchy -- 5.2.2 Steady-State Solutions -- 5.2.3 The Notion of Effective Temperature -- 5.2.4 Markovian Versus Non-Markovian Two-Time Probability Density -- References.; 6 Markovian Embedding-A New Derivation of the Fokker-Planck Hierarchy -- 6.1 Markovian Embedding-A Different View on Memory -- 6.1.1 Projection, Memory Kernel &amp -- Colored Noise -- 6.1.2 Limit ntoinfty -- 6.1.3 Interpretation of the Xj Variables -- 6.1.4 Initial Condition -- 6.1.5 (n+1)-dimensional Markovian Fokker-Planck Equation -- 6.2 Derivation of First Member of Fokker-Planck Hierarchy -- 6.3 Derivation of Higher Members via Markovian Embedding -- 6.3.1 Comparison to Equation from Novikov's Theorem -- 6.4 Side Note: Discrete Versus Distributed Delay -- 6.4.1 Distributed Delay -- 6.4.2 Probability Densities in the Presence of Discrete and Distributed Delay -- References -- 7 Force-Linearization Closure -- 7.1 Details of the Approximation -- 7.1.1 Linearization of the Deterministic Forces -- 7.1.2 Analytical Probabilistic Solution for Linearized Forces -- 7.1.3 Vanishing Steady-State Probability Current -- 7.1.4 Specification to Linear Delay Force -- 7.2 Comparison to Earlier Approaches -- 7.2.1 Small Delay Expansion -- 7.2.2 Perturbation Theory -- 7.2.3 Effective Temperatures -- 7.3 Application to the Periodic Potential -- 7.3.1 ; Discussion of Results -- 7.4 Application to the Bistable Potential -- 7.4.1 Discussion of Results -- 7.5 Estimation of Escape Times -- 7.5.1 Interwell Dynamics -- 7.5.2 The Kramers-FLC Estimate -- 7.5.3 Comparison with Numerical Results -- 7.5.4 Delay-Induced Oscillations -- 7.5.5 Side Note: Normal Diffusion Despite Non-Markovianity -- References -- 8 Approximation for the Two-time Probability density -- 8.1 Application to the Bistable Delayed System -- 8.1.1 Comparison with Approaches for One-time Probability Density -- 8.2 Concluding Remarks -- References -- Part III Thermodynamic Notions for Systems with Time Delay -- 9 The Heat Flow Induced by a Discrete Delay -- 9.1 Main Idea -- 9.1.1 Polynomial Energy Landscapes.; 9.2 Mean Heat Rate &amp -- Medium Entropy Production -- 9.2.1 Linear Systems -- 9.2.2 Markovian Limits in Nonlinear Systems -- 9.2.3 Limit of Vanishing Delay Time -- 9.2.4 Influence of Inertia Term -- 9.2.5 Discussion of the Behavior for Small Delay Times -- 9.3 Application to the Bistable Potential -- 9.3.1 Low Thermal Energy-Intrawell Dynamics -- 9.3.2 High Thermal Energy-Interwell Dynamics -- 9.4 Preliminary Numerical Results for Fluctuation of Heat, Work and Internal Energy -- 9.5 Concluding Remarks -- References -- 10 Entropy, Information and Energy Flows -- 10.1 Emergence of Non-monotonic Memory -- 10.1.1 Interpretation of Xj&gt -- 0 in the Case of a Feedback Controller -- 10.2 The Role of Non-reciprocal Coupling-Connection to Active Matter -- 10.2.1 A Generic Model with Non-reciprocal Coupling -- 10.3 Non-reciprocal Coupling and Non-equilibrium -- 10.3.1 Fluctuation-Dissipation Relation -- 10.3.2 Total Entropy Production -- 10.3.3 Analytical Solutions -- 10.4 Non-reciprocal Coupling and Activity -- 10.4.1 Mapping Non-reciprocity of the Coupling to a Temperature Gradient Between the Coupled Entities -- 10.4.2 Reversed Heat Flow -- 10.5 Non-reciprocal Coupling and Information -- 10.5.1 Information Flow and Generalized Second Law -- 10.5.2 Information-Theoretic Perspective on Feedback Control -- 10.6 Total Entropy Production and Heat Flow in the Presence of Non-monotonic Memory -- 10.6.1 Limit of Discrete Delay -- 10.6.2 Impact of Measurement Errors -- 10.7 Irreversibility and Coarse-Graining -- References -- Part IV Concluding Remarks -- 11 Summary -- References -- 12 Outlook-Open Questions and Further Perspectives -- References -- Appendix Appendix -- A.1 Numerical Methods -- A.2 Derivation of Novikov's Theorem -- A.3 Green's Function Method -- A.4 Connection to Fokker-Planck Hierarchy from Novikov's Theorem.; A.5 Fluctuation-Dissipation Relation for Unidirectional Ring of Arbitrary Length n -- Appendix About the Author.

Compiler Construction : 15th International Conference, CC 2006, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2006, Vienna, Austria, March 30-31, 2006, Proceedings / / edited by Alan Mycroft, Andreas Zeller

• Record Nr.: UNINA9910484099903321
• Pubbl/distr/stampa: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2006
• ISBN: 3-540-33051-8
• Edizione: [1st ed. 2006.]
• Descrizione fisica: 1 online resource (XIII, 277 p.)
• Collana: Theoretical Computer Science and General Issues, , 2512-2029 ; ; 3923
• Altri autori (Persone): MycroftAlan; ZellerAndreas
• Disciplina: 005.4/5
• Soggetti: Computer science; Compilers (Computer programs); Operating systems (Computers); Machine theory; Software engineering; Artificial intelligence; Computer Science Logic and Foundations of Programming; Compilers and Interpreters; Operating Systems; Formal Languages and Automata Theory; Software Engineering; Artificial Intelligence
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Invited Talk -- Using Dependent Types to Port Type Systems to Low-Level Languages -- Program Analysis -- Interprocedural Dataflow Analysis in the Presence of Large Libraries -- Efficient Flow-Sensitive Interprocedural Data-Flow Analysis in the Presence of Pointers -- Path-Based Reuse Distance Analysis -- Context-Sensitive Points-to Analysis: Is It Worth It? -- Dynamic Analysis -- Selective Runtime Memory Disambiguation in a Dynamic Binary Translator -- Accurately Choosing ; Execution Runs for Software Fault Localization -- Tool Demonstrations -- Demonstration: On-Line Visualization and Analysis of Real-Time Systems with TuningFork -- Data-Flow Analysis as Model Checking Within the jABC -- The CGiS Compiler—A Tool Demonstration -- Optimization -- Loop Transformations in the Ahead-of-Time Optimization of Java Bytecode -- Hybrid Optimizations: Which Optimization Algorithm to Use? -- A Fresh Look at PRE as a Maximum Flow Problem -- Performance Characterization of the 64-bit x86 Architecture from Compiler Optimizations’ Perspective -- Code Generation -- Lightweight Lexical Closures for Legitimate Execution Stack Access -- Polyhedral Code Generation in the Real World -- Iterative Collective Loop Fusion -- Converting Intermediate Code to Assembly Code Using Declarative Machine Descriptions -- Register Allocation -- SARA: Combining Stack Allocation and Register Allocation -- Register Allocation for Programs in SSA-Form -- Enhanced Bitwidth-Aware Register Allocation.
• Sommario/riassunto: ETAPS 2006 was the ninth instance of the European Joint Conferences on Theory and Practice of Software. ETAPS is an annual federated conference that was established in 1998 by combining a number of existing and new conferences. This year it comprised ?ve conferences (CC, ESOP, FASE, FOSSACS, TACAS), 18 satellite workshops (AC- CAT, AVIS, CMCS, COCV, DCC, EAAI, FESCA, FRCSS, GT-VMT, LDTA, MBT, QAPL, SC, SLAP, SPIN, TERMGRAPH, WITS and WRLA), two tutorials, and seven invited lectures (not including those that were speci?c to the satellite events). We - ceived over 550 submissions to the ?ve conferences this year, giving an overall acc- tance rate of 23%, with acceptance rates below 30% for each conference. Congratu- tions to all the authors who made it to the ?nal programme! I hope that most of the other authorsstill founda way of participatingin this excitingevent and I hope you will continue submitting. The events that comprise ETAPS address various aspects of the system devel- ment process, including speci?cation, design, implementation, analysis and impro- ment. The languages, methodologies and tools which support these activities are all well within its scope. Di?erent blends of theory and practice are represented, with an inclination towards theory with a practical motivation on the one hand and soundly based practice on the other. Many of the issues involved in software design apply to systems in general, including hardware systems, and the emphasis on software is not intended to be exclusive.