2 research outputs found
The Valence Bond Glass phase
We show that a new glassy phase can emerge in presence of strong magnetic
frustration and quantum fluctuations. It is a Valence Bond Glass. We study its
properties solving the Hubbard-Heisenberg model on a Bethe lattice within the
large limit introduced by Affleck and Marston. We work out the phase
diagram that contains Fermi liquid, dimer and valence bond glass phases. This
new glassy phase has no electronic or spin gap (although a pseudo-gap is
observed), it is characterized by long-range critical valence bond correlations
and is not related to any magnetic ordering. As a consequence it is quite
different from both valence bond crystals and spin glasses
Message Passing for Optimization and Control of Power Grid: Model of Distribution System with Redundancy
We use a power grid model with generators and consumption units to
optimize the grid and its control. Each consumer demand is drawn from a
predefined finite-size-support distribution, thus simulating the instantaneous
load fluctuations. Each generator has a maximum power capability. A generator
is not overloaded if the sum of the loads of consumers connected to a generator
does not exceed its maximum production. In the standard grid each consumer is
connected only to its designated generator, while we consider a more general
organization of the grid allowing each consumer to select one generator
depending on the load from a pre-defined consumer-dependent and sufficiently
small set of generators which can all serve the load. The model grid is
interconnected in a graph with loops, drawn from an ensemble of random
bipartite graphs, while each allowed configuration of loaded links represent a
set of graph covering trees. Losses, the reactive character of the grid and the
transmission-level connections between generators (and many other details
relevant to realistic power grid) are ignored in this proof-of-principles
study. We focus on the asymptotic limit and we show that the interconnects
allow significant expansion of the parameter domains for which the probability
of a generator overload is asymptotically zero. Our construction explores the
formal relation between the problem of grid optimization and the modern theory
of sparse graphical models. We also design heuristic algorithms that achieve
the asymptotically optimal selection of loaded links. We conclude discussing
the ability of this approach to include other effects, such as a more realistic
modeling of the power grid and related optimization and control algorithms.Comment: 10 page