4,460 research outputs found
Percolation on hyperbolic lattices
The percolation transitions on hyperbolic lattices are investigated
numerically using finite-size scaling methods. The existence of two distinct
percolation thresholds is verified. At the lower threshold, an unbounded
cluster appears and reaches from the middle to the boundary. This transition is
of the same type and has the same finite-size scaling properties as the
corresponding transition for the Cayley tree. At the upper threshold, on the
other hand, a single unbounded cluster forms which overwhelms all the others
and occupies a finite fraction of the volume as well as of the boundary
connections. The finite-size scaling properties for this upper threshold are
different from those of the Cayley tree and two of the critical exponents are
obtained. The results suggest that the percolation transition for the
hyperbolic lattices forms a universality class of its own.Comment: 17 pages, 18 figures, to appear in Phys. Rev.
Moving-Horizon Dynamic Power System State Estimation Using Semidefinite Relaxation
Accurate power system state estimation (PSSE) is an essential prerequisite
for reliable operation of power systems. Different from static PSSE, dynamic
PSSE can exploit past measurements based on a dynamical state evolution model,
offering improved accuracy and state predictability. A key challenge is the
nonlinear measurement model, which is often tackled using linearization,
despite divergence and local optimality issues. In this work, a moving-horizon
estimation (MHE) strategy is advocated, where model nonlinearity can be
accurately captured with strong performance guarantees. To mitigate local
optimality, a semidefinite relaxation approach is adopted, which often provides
solutions close to the global optimum. Numerical tests show that the proposed
method can markedly improve upon an extended Kalman filter (EKF)-based
alternative.Comment: Proc. of IEEE PES General Mtg., Washnigton, DC, July 27-31, 2014.
(Submitted
Anomalous response in the vicinity of spontaneous symmetry breaking
We propose a mechanism to induce negative AC permittivity in the vicinity of
a ferroelectric phase transition involved with spontaneous symmetry breaking.
This mechanism makes use of responses at low frequency, yielding a high gain
and a large phase delay, when the system jumps over the free-energy barrier
with the aid of external fields. We illustrate the mechanism by analytically
studying spin models with the Glauber-typed dynamics under periodic
perturbations. Then, we show that the scenario is supported by numerical
simulations of mean-field as well as two-dimensional spin systems.Comment: 6 pages, 5 figure
Residual discrete symmetry of the five-state clock model
It is well-known that the -state clock model can exhibit a
Kosterlitz-Thouless (KT) transition if is equal to or greater than a
certain threshold, which has been believed to be five. However, recent
numerical studies indicate that helicity modulus does not vanish in the
high-temperature phase of the five-state clock model as predicted by the KT
scenario. By performing Monte Carlo calculations under the fluctuating twist
boundary condition, we show that it is because the five-state clock model does
not have the fully continuous U(1) symmetry even in the high-temperature phase
while the six-state clock model does. We suggest that the upper transition of
the five-state clock model is actually a weaker cousin of the KT transition so
that it is that exhibits the genuine KT behavior.Comment: 13 pages, 17 figure
Radio Map Estimation: A Data-Driven Approach to Spectrum Cartography
Radio maps characterize quantities of interest in radio communication
environments, such as the received signal strength and channel attenuation, at
every point of a geographical region. Radio map estimation typically entails
interpolative inference based on spatially distributed measurements. In this
tutorial article, after presenting some representative applications of radio
maps, the most prominent radio map estimation methods are discussed. Starting
from simple regression, the exposition gradually delves into more sophisticated
algorithms, eventually touching upon state-of-the-art techniques. To gain
insight into this versatile toolkit, illustrative toy examples will also be
presented
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