403 research outputs found
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 â 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 âsmoothnessâ 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 Ekelandâs variational principle extending [12, Corollary 3.4], and
deals with a function f which is, in some sense, the âuniformâ Î-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 â multidisciplinĂ€ra öppningar
Abstract in Undetermined Mötet mellan organisationer och kunder, det sÄ kallade servicemötet, Àr av central betydelse för sÄvÀl förstÄelse som för ledning av tjÀnsteverksamheter. Att tjÀnster utgörs av de interaktioner som uppstÄr under servicemötet har sedan lÀnge uppmÀrksammats, inte minst av forskare som Christian Grönroos, Evert Gummesson och Richard Normann och den Nordiska skolan inom service management. Servivemötet - MultidisciplinÀra öppningar tar sin utgÄngspunkt i denna nordiska forskningstradition, men syftar till att föra lÀsaren bortom nÄgra av dess nuvarande ÀmnesmÀssiga begrÀnsningar. Genom att förena studier frÄn olika akademiska discipliner (företagsekonomi, sociologi, etnologi, kulturgeografi) ifrÄgasÀtter boken rÄdande förestÀllningar och tillför nya infallsvinklingar om servicemötet
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