1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Our aim is to propose a theory which goes beyond the classical formulation of thermodynamics. This is achieved by enlarging the space of basic independent variables, through the introduction of non-equilibrium variables, such as the dissipative fluxes appearing in the balance equations. The next step is to find evolution equations for the dissipative fluxes. Whereas the evolution equations for the classical variables are given by the usual balance laws, no general criteria exist concerning the evolution equations of the dissipative fluxes, with the exception of the restrictions imposed on them by the second law of thermodynamics.

https://iopscience.iop.org/article/10.1088/0034-4885/51/8/002/pdf

Extended irreversible thermodynamics

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.

The Web of Human Sexual Contacts

We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems in continuum mechanics concern mathematical modelling of viscoelastic bodies (Sect. 1), and unsteady motion of a particle in a viscous fluid, i.e. the Basset problem (Sect. 2). In the former analysis fractional calculus leads us to introduce intermediate models of viscoelasticity which generalize the classical spring-dashpot models. The latter analysis induces us to introduce a hydrodynamic model suitable to revisit in Sect. 3 the classical theory of the Brownian motion, which is a relevant topic in statistical mechanics. By the tools of fractional calculus we explain the long tails in the velocity correlation and in the displacement variance. In Sect. 4 we consider the fractional diffusion-wave equation, which is obtained from the classical diffusion equation by replacing the first-order time derivative by a fractional derivative of order $0< \beta <2$. Led by our analysis we express the fundamental solutions (the Green functions) in terms of two interrelated auxiliary functions in the similarity variable, which turn out to be of Wright type (see Appendix), and to distinguish slow-diffusion processes ($0 < \beta < 1$) from intermediate processes ($1 < \beta < 2$).

/pdf/fractional-calculus-some-basic-problems-in-continuum-and-3cfjxwp8nw.pdf

Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics

1 Tour d'Horizon 2 Early Version of Extended Thermodynamics 1 Paradox of Heat Conduction and Shear Diffusion 1.1 Heuristic Derivation of the Laws of Fourier and Navier-Stokes 1.2 Parabolic Laws of Heat Conduction and Shear Diffusion 2 Paradox Removed 2.1 The Cattaneo Equation 2.2 Extended TIP 2.3 Finite Pulse Speeds in Extended TIP 2.4 Conclusion and Criticism 3 Kinetic Theory of Mon-atomic Gases 3.1 Boltzmann-Equation and Moments 3.2 Equations of Balance for Moments 3.3 Balance of Entropy and Possible Equilibria 3.4 The Grad Distribution 3.5 Entropy and Entropy Flux in Grad's 13-Moment Theory 3.6 Phenomenological Equations derived from the Kinetic Theory 3.7 Pulse Speeds 3.8 Conclusions 3 Formal Structure of Extended Thermodynamics 1 Field Equations 1.1 Thermodynamic Processes and Principles of the Constitutive Theory 1.2 Universal Principles of the Constitutive Theory 2 Entropy Inequality, Symmetric Hyperbolicity 2.1 Exploitation of the Entropy Inequality 2.2 Symmetric Hyperbolic Field Equations 2.3 Discussion 2.4 Characeristic Speeds 3 Main Subsystems 3.1 Constraints on the Main Field 3.2 A Main.

Rational extended thermodynamics

Relativistic thermodynamics of gases

1 Introduction.- 2 Mathematical Structure.- 3 Waves in Hyperbolic Systems.- 4 Survey of ET of Rarefied Monatomic Gases.- 5 ET Theory of Polyatomic Rarefied Gas and Dense Gas.- 6 Maximum entropy principle for rarefied polyatomic gases.- 7 Stationary heat conduction in a polyatomic gas at rest.- 8 Linear Wave in Polyatomic Gas.- 9 Shock Wave.- 10 Fluctuating hydrodynamics.- 11 Light scattering in Polyatomic Gas.- 12 ET6 Theory of Polyatomic Rarefied Gas and Dense Gas.- 13 Non linear ET6.- 14 Molecular ET Theory of Polyatomic Rarefied Gas.- 15 ET of dense gas with 6 moments.- 16 Mixture of Gases.- 17 Hyperbolic Parabolic Limit, Max wellian iteration and Objectivity.

https://www.springer.com/cda/content/document/productFlyer/productFlyer_978-3-319-13340-9.pdf?SGWID=0-0-1297-177092022-0

Rational Extended Thermodynamics beyond the Monatomic Gas

We consider a system of N balance laws compatible with an entropy principle and convex entropy density. Using the special symmetric form induced by the main field, we define the concept of principal subsystem associated with the system. We prove that the 2
 N
 −2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law. Moreover we can verify that for each principal subsystem the maximum (minimum) characteristic velocity is not larger (smaller) than the maximum (minimum) characteristic velocity of the full system. These are the subcharacteristic conditions. We present some simple examples in the case of the Euler fluid. Then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics. Finally in the moments approach to the Boltzmann equation we prove, as a consequence of the previous result, that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases.

Hyperbolic Principal Subsystems: Entropy Convexity and Subcharacteristic Conditions

© Gauthier-Villars, 1981, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A » implique l’accord avec les conditions générales d’utilisation (http://www.numdam. org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Tommaso Ruggeri

Papers

Rational extended thermodynamics

Relativistic thermodynamics of gases

Rational Extended Thermodynamics beyond the Monatomic Gas

Hyperbolic Principal Subsystems: Entropy Convexity and Subcharacteristic Conditions

Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics