Diversity and Non-integer Differentiation for System Dynamics

Content: Cover
 Title Page 
 Copyright
 Contents
 Acknowledgments
 Preface
 Introduction
 Chapter 1: From Diversity to Unexpected Dynamic Performances
 1.1. Introduction
 1.2. An issue raising a technological bottle-neck
 1.3. An aim liable to answer to the issue
 1.4. A strategy idea liable to reach the aim
 1.4.1. Why diversity?
 1.4.2. What does diversity imply?
 1.5. On the strategy itself
 1.5.1. The study object
 1.5.2. A pore: its model and its technological equivalent
 1.5.2.1. The model
 1.5.2.2. The technological equivalent
 1.5.3. Case of identical pores
 1.5.4. Case of different pores. 1.5.4.1. On differences coming from regional heritage1.5.4.1.1 Differences of technological origin
 1.5.4.1.2. A difference of natural origin
 1.5.4.1.3. How is difference expressed?
 1.5.4.2. Transposition to the study object
 1.6. From physics to mathematics
 1.6.1. An unusual model of the porous face
 1.6.1.1. A smoothing remarkable of simplicity: the one of crenels
 1.6.1.2. A non-integer derivative as a smoothing result
 1.6.1.3. An original heuristic verification of differentiation non-integer order
 1.6.2. A just as unusual model governing water relaxation. 1.6.3. What about a non-integer derivative which singles out these unusual models?1.6.3.1. On the sinusoidal state of the operator of order n E [0, 2]
 1.6.3.1.1. 0 d\"n d\"
 1.6.3.1.2. 1d\"n d\"2
 1.6.3.2. On the impulse state of the operator of order n E]0,1[
 1.6.3.3. An original heuristic verification of time non-integer power
 1.7. From the unusual to the unexpected
 1.7.1. Unexpected damping properties
 1.7.1.1. Relaxation damping insensitivity to the mass
 1.7.1.2. Frequency verification of the insensitivity to the mass
 1.7.2. Just as unexpected memory properties. 1.7.2.1. Taking into account the past1.7.2.2. Memory notion
 1.7.2.3. A diversion through an aspect of human memory
 1.7.2.3.1. The serial position effect
 1.7.2.3.2. A model of the primacy effect
 1.8. On the nature of diversity
 1.8.1. An action level to be defined
 1.8.2. One or several forms of diversity?
 1.8.2.1. Forms based on the invariance of the elements
 1.8.2.2. A singular form based on the time variability of an element
 1.9. From the porous dyke to the CRONE suspension
 1.10. Conclusion
 1.11. Bibliography
 Chapter 2: Damping Robustness
 2.1. Introduction. 2.2. From ladder network to a non-integer derivative as a water-dyke interface model2.2.1. On the admittance factorizing
 2.2.2. On the asymptotic diagrams at stake
 2.2.3. On the asymptotic diagram exploiting
 2.2.3.1. Step smoothing
 2.2.3.2. Crenel smoothing
 2.2.3.3. A non-integer differentiator as a smoothing result
 2.2.3.4. A non-integer derivative as a water-dyke interface model
 2.3. From a non-integer derivative to a non-integer differential equation as a model governing water relaxation
 2.3.1. Flow-pressure differential equation.