Universality of Nonclassical Nonlinearity

1. Front Matter

   Pages i-xxi

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2. The Universality of Nonclassical Nonlinearity

   1. Front Matter

      Pages 1-1

      PDF

   2. Towards a Top-Down Approach in Materials Science

      • Pier Paolo Delsanto, S. Hirsekorn

      Pages 3-13

   3. Nonlinearity and Complexity in Elastic Wave Motion

      • Franco Pastrone

      Pages 15-27

   4. Hierarchies of Waves in Nonclassical Materials

      • Jüri Engelbrecht, Franco Pastrone, Manfred Braun, Arkadi Berezovski

      Pages 29-47

   5. Nonequilibrium Nonlinear Dynamics in Solids: State of the Art

      • P. A. Johnson

      Pages 49-69

   6. Nonlinear Rock Mechanics

      • G. E. Exadaktylos

      Pages 71-90

   7. Universality in Nonlinear Structural Dynamics

      • Alberto Carpinteri, Nicola Pugno

      Pages 91-99

   8. The Evolutionary Advantage of Being Conservative: The Role of Hysteresis

      • Gian Piero Pescarmona

      Pages 101-117

   9. Cancer Growth: A Nonclassical Nonlinear Phenomenon?

      • C. A. Condat, B. F. Gregor, Y. Mansury, T. S. Deisboeck

      Pages 119-129

   10. Seasonality and Harvesting, Revisited

       • A. J. Banchio, C. A. Condat

       Pages 131-143

   11. Nonlinear Dynamical Systems in Economics

       • Paolo Patelli

       Pages 145-154

3. Applications to NDE and Ultrasonics: Models and Numerical Simulations

   1. Front Matter

      Pages 156-156

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   2. Micropotential Model for Stress–Strain Hysteresis and PM Space

      • V. Aleshin, K. Van Den Abeele

      Pages 157-175

   3. Multiscale Approach and Simulations of Wave Propagation and Resonance in Media with Localized Microdamage: 1-D and 2-D Cases

      • K. Van Den Abeele, Sigfried Vanaverbeke

      Pages 177-201

   4. Modeling and Numerical Simulation of Nonclassical Effects of Waves, Including Phase Transition Front

      • Arkadi Berezovski, Jüri Engelbrecht, Gerard A. Maugin

      Pages 203-219

   5. The Spectral Analysis of a PM Space Unit in the Context of the Classification of Nonlinear Phenomena in Ultrasonic Wave Propagation

      • Sigrun Hirsekorn

      Pages 221-230

   6. Nonlinear Ultrasonic Transmission Through Thin Bonded Interface: Theoretical Background and Numerical Simulations

      • S. Hirsekorn, M. Hirsekorn, P. P. Delsanto

      Pages 231-250

   7. A LISA Model of the Nonlinear and Hysteretic Response of Interstitial Regions to Applied Stresses

      • Antonio S. Gliozzi, Matteo Nobili, Marco Scalerandi

      Pages 251-267

   8. Numerical Analysis of the Anomalous Elastic Behavior of Hysteretic Media: Quasistatic, Dynamic, and Relaxation Experiments

      • Marco Scalerandi, Matteo Nobili, Michele Griffa, Antonio S. Gliozzi, Federico Bosia

      Pages 269-285

VarietyisperhapsthemostamazingattributeofNature,withanalmostendlessarrayof different molecules and aggregates and tens of millions of distinct forms of life. Yet, in spite of this bewildering diversity, there are some common patterns, henceforth called “phenomenological universalities,” that are found over and over again in completely different contexts. A quest for universalities is not only interesting per se, but can also yield practical applications. If several elds share a common mathematical or conceptual background, a cross-fertilization among them may lead to quick progress, even if ultimately the speci c details of any individual application must be considered independently. We all know that we live in a nonlinear world, although scientists have often tried to linearize it, sometimes as a rst step towards understanding its complexity, often because, before the advent of ubiquitous high computational power, a linear appro- mation was the only viable alternative. In this book we use the term “nonclassical n- linearity” with reference to a particularly intriguing kind of phenomenology, which has been extensively investigated in the last decade in the elds of elasticity and g- materials and whose universality has been conjectured. Its signatures are hystereticity, discrete memory, and other effects which, in the case of continuum mechanics, have been called “fast” and “slow” dynamics.

• geophysics
• nonclassical
• nonlinearity
• optics
• physics
• quantum optics
• ultrasonics

• Dip. Fisica, Torino, Italy

  Pier Paolo Delsanto

Pier Paolo Delsanto is currently a professor of Physics with a chair at the Politecnico of Torino Italy. He has also held a position as the Director of the Politecnico Research Unit in Condensed Matter Physics.

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