Non-perturbative Renormalization Group Approach to Some Out-of-Equilibrium Systems

Diffusive Epidemic Process and Fully Developed Turbulence

Malo Tarpin (Autor)

Buch | Hardcover

XV, 207 Seiten

2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-39870-5 (ISBN)

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This thesis presents the application of non-perturbative, or functional, renormalization group to study the physics of critical stationary states in systems out-of-equilibrium. Two different systems are thereby studied. The first system is the diffusive epidemic process, a stochastic process which models the propagation of an epidemic within a population. This model exhibits a phase transition peculiar to out-of-equilibrium, between a stationary state where the epidemic is extinct and one where it survives. The present study helps to clarify subtle issues about the underlying symmetries of this process and the possible universality classes of its phase transition. The second system is fully developed homogeneous isotropic and incompressible turbulence. The stationary state of this driven-dissipative system shows an energy cascade whose phenomenology is complex, with partial scale-invariance, intertwined with what is called intermittency. In this work, analytical expressions for the space-time dependence of multi-point correlation functions of the turbulent state in 2- and 3-D are derived. This result is noteworthy in that it does not rely on phenomenological input except from the Navier-Stokes equation and that it becomes exact in the physically relevant limit of large wave-numbers. The obtained correlation functions show how scale invariance is broken in a subtle way, related to intermittency corrections.

General Introduction.- Universal Behaviors in the Diffusive Epidemic Process and in Fully Developed Turbulence.- Introduction to Non-perturbative Renormalization Group for Out-of-Equilibrium Field Theories.- Study of the Absorbing Phase Transition in DEP.- Breaking of Scale Invariance in Correlation Functions of Turbulence.- General Conclusion.- Appendices.

Erscheinungsdatum	21.03.2020
Reihe/Serie	Springer Theses
Zusatzinfo	XV, 207 p. 21 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	506 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
Schlagworte	Absorbing Phase Transition • Fully Developed Turbulence • functional renormalization group • intermittency • Non-perturbative Renormalization Group • Out-of-Equilibrium • Reaction-diffusion Process • Statistical field theory
ISBN-10	3-030-39870-6 / 3030398706
ISBN-13	978-3-030-39870-5 / 9783030398705
Zustand	Neuware