A complete theory of low-energy phase diagrams for two-dimensional turbulence steady states and equilibria

For the 2D Euler equations and related models of geophysical flows, minima of energy--Casimir variational problems are stable steady states of the equations (Arnol'd theorems). The same variational problems also describe sets of statistical equilibria of the equations. In this paper, we make use of Lyapunov--Schmidt reduction in order to study the bifurcation diagrams for these variational problems, in the limit of small energy or, equivalently, of small departure from quadratic Casimir functionals. We show a generic occurrence of phase transitions, either continuous or discontinuous. We derive the type of phase transitions for any domain geometry and any model analogous to the 2D Euler equations. The bifurcations depend crucially on a_4, the quartic coefficient in the Taylor expansion of the Casimir functional around its minima. Note that a_4 can be related to the fourth moment of the vorticity in the statistical mechanics framework. A tricritical point (bifurcation from a continuous to a discontinuous phase transition) often occurs when a_4 changes sign. The bifurcations depend also on possible constraints on the variational problems (circulation, energy). These results show that the analytical results obtained with quadratic Casimir functionals by several authors are non-generic (not robust to a small change in the parameters)

A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions

Doubly resonant semilinear elliptic problems via nonsmooth critical point theory

AbstractWe consider the existence of weak solutions for classical doubly resonant semilinear elliptic problems. We show how the main technical assumptions can be used to define appropriate metrics on the underlying function space, so that extensions of the results already known in the literature can be obtained using only basic facts from critical point theory for continuous functionals on complete metric spaces

Waste prevention action nets

Although waste prevention is considered the best possible waste management option in the European waste hierarchy model, it is unclear what constitutes waste prevention. To address this lack of clarity, this text presents an analysis of four Swedish case studies of waste prevention: a waste management company selling waste prevention services; the possibility offered to Swedish households to opt out of receiving unaddressed promotional material; a car-sharing program; and a re-use center. This analysis is informed by an action-net perspective that focuses on the way organizing emerges from connecting actions, often prior to networking between actors. In conclusion, we stress that waste prevention rests on the invention of new modes and patterns of interactions that both build and disrupt the existing institutional order and underscore the importance of physical artifacts and dedicated infrastructures for waste prevention initiatives

Servicemötet – multidisciplinära öppningar

Abstract in Undetermined Mötet mellan organisationer och kunder, det så kallade servicemötet, är av central betydelse för såväl förståelse som för ledning av tjänsteverksamheter. Att tjänster utgörs av de interaktioner som uppstår under servicemötet har sedan länge uppmärksammats, inte minst av forskare som Christian Grönroos, Evert Gummesson och Richard Normann och den Nordiska skolan inom service management. Servivemötet - Multidisciplinära öppningar tar sin utgångspunkt i denna nordiska forskningstradition, men syftar till att föra läsaren bortom några av dess nuvarande ämnesmässiga begränsningar. Genom att förena studier från olika akademiska discipliner (företagsekonomi, sociologi, etnologi, kulturgeografi) ifrågasätter boken rådande föreställningar och tillför nya infallsvinklingar om servicemötet