65,721 research outputs found
An exact solution method for binary equilibrium problems with compensation and the power market uplift problem
We propose a novel method to find Nash equilibria in games with binary
decision variables by including compensation payments and
incentive-compatibility constraints from non-cooperative game theory directly
into an optimization framework in lieu of using first order conditions of a
linearization, or relaxation of integrality conditions. The reformulation
offers a new approach to obtain and interpret dual variables to binary
constraints using the benefit or loss from deviation rather than marginal
relaxations. The method endogenizes the trade-off between overall (societal)
efficiency and compensation payments necessary to align incentives of
individual players. We provide existence results and conditions under which
this problem can be solved as a mixed-binary linear program.
We apply the solution approach to a stylized nodal power-market equilibrium
problem with binary on-off decisions. This illustrative example shows that our
approach yields an exact solution to the binary Nash game with compensation. We
compare different implementations of actual market rules within our model, in
particular constraints ensuring non-negative profits (no-loss rule) and
restrictions on the compensation payments to non-dispatched generators. We
discuss the resulting equilibria in terms of overall welfare, efficiency, and
allocational equity
Equilibrium and out of equilibrium phase transitions in systems with long range interactions and in 2D flows
In self-gravitating stars, two dimensional or geophysical flows and in
plasmas, long range interactions imply a lack of additivity for the energy; as
a consequence, the usual thermodynamic limit is not appropriate. However, by
contrast with many claims, the equilibrium statistical mechanics of such
systems is a well understood subject. In this proceeding, we explain briefly
the classical approach to equilibrium and non equilibrium statistical mechanics
for these systems, starting from first principles. We emphasize recent and new
results, mainly a classification of equilibrium phase transitions, new
unobserved equilibrium phase transition, and out of equilibrium phase
transitions. We briefly discuss what we consider as challenges in this field
Oceanic rings and jets as statistical equilibrium states
Equilibrium statistical mechanics of two-dimensional flows provides an
explanation and a prediction for the self-organization of large scale coherent
structures. This theory is applied in this paper to the description of oceanic
rings and jets, in the framework of a 1.5 layer quasi-geostrophic model. The
theory predicts the spontaneous formation of regions where the potential
vorticity is homogenized, with strong and localized jets at their interface.
Mesoscale rings are shown to be close to a statistical equilibrium: the theory
accounts for their shape, their drift, and their ubiquity in the ocean,
independently of the underlying generation mechanism. At basin scale, inertial
states presenting mid basin eastward jets (and then different from the
classical Fofonoff solution) are described as marginally unstable states. These
states are shown to be marginally unstable for the equilibrium statistical
theory. In that case, considering a purely inertial limit is a first step
toward more comprehensive out of equilibrium studies that would take into
account other essential aspects, such as wind forcing.Comment: 15 pages, submitted to Journal of Physical Oceanograph
Equilibrium statistical mechanics and energy partition for the shallow water model
The aim of this paper is to use large deviation theory in order to compute
the entropy of macrostates for the microcanonical measure of the shallow water
system. The main prediction of this full statistical mechanics computation is
the energy partition between a large scale vortical flow and small scale
fluctuations related to inertia-gravity waves. We introduce for that purpose a
discretized model of the continuous shallow water system, and compute the
corresponding statistical equilibria. We argue that microcanonical equilibrium
states of the discretized model in the continuous limit are equilibrium states
of the actual shallow water system. We show that the presence of small scale
fluctuations selects a subclass of equilibria among the states that were
previously computed by phenomenological approaches that were neglecting such
fluctuations. In the limit of weak height fluctuations, the equilibrium state
can be interpreted as two subsystems in thermal contact: one subsystem
corresponds to the large scale vortical flow, the other subsystem corresponds
to small scale height and velocity fluctuations. It is shown that either a
non-zero circulation or rotation and bottom topography are required to sustain
a non-zero large scale flow at equilibrium. Explicit computation of the
equilibria and their energy partition is presented in the quasi-geostrophic
limit for the energy-enstrophy ensemble. The possible role of small scale
dissipation and shocks is discussed. A geophysical application to the Zapiola
anticyclone is presented.Comment: Journal of Statistical Physics, Springer Verlag, 201
The catalytic role of beta effect in barotropization processes
The vertical structure of freely evolving, continuously stratified,
quasi-geostrophic flow is investigated. We predict the final state
organization, and in particular its vertical structure, using statistical
mechanics and these predictions are tested against numerical simulations. The
key role played by conservation laws in each layer, including the fine-grained
enstrophy, is discussed. In general, the conservation laws, and in particular
that enstrophy is conserved layer-wise, prevent complete barotropization, i.e.,
the tendency to reach the gravest vertical mode. The peculiar role of the
-effect, i.e. of the existence of planetary vorticity gradients, is
discussed. In particular, it is shown that increasing increases the
tendency toward barotropization through turbulent stirring. The effectiveness
of barotropisation may be partly parameterized using the Rhines scale . As this parameter decreases (beta increases) then
barotropization can progress further, because the beta term provides enstrophy
to each layer
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