459 research outputs found
What are the Building Blocks of Our Universe?
We are told that we are living in a Golden Age of Astronomy. Cosmological
Parameters are found with un precedented accuracy. Yet, the known form of
matter forms only a small fraction of the total energy density of the universe.
Also, a mysterious dark energy dominates the universe and causes acceleration
in the rate of expansion.Comment: To be published in the Proceedings of the Interantional Conference on
COSMOLOGY;Facts and Problems (College de France, Paris, June 8-11, 2004
Noncommutative Geometry and a Discretized Version of Kaluza-Klein Theory with a Finite Field Content
We consider a four-dimensional space-time supplemented by two discrete points
assigned to a algebraic structure and develop the formalism of
noncommutative geometry. By setting up a generalised vielbein, we study the
metric structure. Metric compatible torsion free connection defines a unique
finite field content in the model and leads to a discretized version of
Kaluza-Klein theory. We study some special cases of this model that illustrate
the rich and complex structure with massive modes and the possible presence of
a cosmological constant.Comment: 21 pages, LATEX fil
A Discretized Version of Kaluza-Klein Theory with Torsion and Massive Fields
We consider an internal space of two discrete points in the fifth dimension
of the Kaluza-Klein theory by using the formalism of noncommutative geometry
developed in a previous paper \cite{VIWA} of a spacetime supplemented by two
discrete points. With the nonvanishing internal torsion 2-form there are no
constraints implied on the vielbeins. The theory contains a pair of tensor, a
pair of vector and a pair of scalar fields. Using the generalized Cartan
structure equation we are able not only to determine uniquely the hermitian and
metric compatible connection 1-forms, but also the nonvanishing internal
torsion 2-form in terms of vielbeins. The resulting action has a rich and
complex structure, a particular feature being the existence of massive modes.
Thus the nonvanishing internal torsion generates a Kaluza-Klein type model with
zero and massive modes.Comment: 24 page
Optimal Topology Design for Disturbance Minimization in Power Grids
The transient response of power grids to external disturbances influences
their stable operation. This paper studies the effect of topology in linear
time-invariant dynamics of different power grids. For a variety of objective
functions, a unified framework based on norm is presented to analyze the
robustness to ambient fluctuations. Such objectives include loss reduction,
weighted consensus of phase angle deviations, oscillations in nodal frequency,
and other graphical metrics. The framework is then used to study the problem of
optimal topology design for robust control goals of different grids. For radial
grids, the problem is shown as equivalent to the hard "optimum communication
spanning tree" problem in graph theory and a combinatorial topology
construction is presented with bounded approximation gap. Extended to loopy
(meshed) grids, a greedy topology design algorithm is discussed. The
performance of the topology design algorithms under multiple control objectives
are presented on both loopy and radial test grids. Overall, this paper analyzes
topology design algorithms on a broad class of control problems in power grid
by exploring their combinatorial and graphical properties.Comment: 6 pages, 3 figures, a version of this work will appear in ACC 201
Baryons and Mesons with Beauty
Recent experimental findings of several mesons and baryons with "beauty" and
"charm" as flavors remind us of the days when strangeness was discovered, and
how its inclusion led to SU(3)-flavor symmetry with enormous success in the
classification of the "proliferated" states into SU(3) multiplets. One of the
key elements was the successful application of the first order perturbation in
symmetry breaking, albeit what then appeared to be huge mass differences, and
the prediction of new states that were confirmed by experiments. In this note,
we venture into the past and, applying the same techniques, predict some new
"beauty-" and "charm-" flavored hadrons. If these new states are confirmed
experimentally, it may provide a useful phenomenological model for classifying
numerous states that are found to be in the PDG data and could invite further
theoretical challenges towards our understanding of symmetry breaking.Comment: 9 pages, 5 figures, plain Late
Mechanism Design for Demand Response Programs
Demand Response (DR) programs serve to reduce the consumption of electricity
at times when the supply is scarce and expensive. The utility informs the
aggregator of an anticipated DR event. The aggregator calls on a subset of its
pool of recruited agents to reduce their electricity use. Agents are paid for
reducing their energy consumption from contractually established baselines.
Baselines are counter-factual consumption estimates of the energy an agent
would have consumed if they were not participating in the DR program. Baselines
are used to determine payments to agents. This creates an incentive for agents
to inflate their baselines. We propose a novel self-reported baseline mechanism
(SRBM) where each agent reports its baseline and marginal utility. These
reports are strategic and need not be truthful. Based on the reported
information, the aggregator selects or calls on agents to meet the load
reduction target. Called agents are paid for observed reductions from their
self-reported baselines. Agents who are not called face penalties for
consumption shortfalls below their baselines. The mechanism is specified by the
probability with which agents are called, reward prices for called agents, and
penalty prices for agents who are not called. Under SRBM, we show that truthful
reporting of baseline consumption and marginal utility is a dominant strategy.
Thus, SRBM eliminates the incentive for agents to inflate baselines. SRBM is
assured to meet the load reduction target. SRBM is also nearly efficient since
it selects agents with the smallest marginal utilities, and each called agent
contributes maximally to the load reduction target. Finally, we show that SRBM
is almost optimal in the metric of average cost of DR provision faced by the
aggregator
Learning Robustness with Bounded Failure: An Iterative MPC Approach
We propose an approach to design a Model Predictive Controller (MPC) for
constrained Linear Time Invariant systems performing an iterative task. The
system is subject to an additive disturbance, and the goal is to learn to
satisfy state and input constraints robustly. Using disturbance measurements
after each iteration, we construct Confidence Support sets, which contain the
true support of the disturbance distribution with a given probability. As more
data is collected, the Confidence Supports converge to the true support of the
disturbance. This enables design of an MPC controller that avoids conservative
estimate of the disturbance support, while simultaneously bounding the
probability of constraint violation. The efficacy of the proposed approach is
then demonstrated with a detailed numerical example.Comment: Added GitHub link to all source code
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