26,406 research outputs found
Non-Stationary Random Process for Large-Scale Failure and Recovery of Power Distributions
A key objective of the smart grid is to improve reliability of utility
services to end users. This requires strengthening resilience of distribution
networks that lie at the edge of the grid. However, distribution networks are
exposed to external disturbances such as hurricanes and snow storms where
electricity service to customers is disrupted repeatedly. External disturbances
cause large-scale power failures that are neither well-understood, nor
formulated rigorously, nor studied systematically. This work studies resilience
of power distribution networks to large-scale disturbances in three aspects.
First, a non-stationary random process is derived to characterize an entire
life cycle of large-scale failure and recovery. Second, resilience is defined
based on the non-stationary random process. Close form analytical expressions
are derived under specific large-scale failure scenarios. Third, the
non-stationary model and the resilience metric are applied to a real life
example of large-scale disruptions due to Hurricane Ike. Real data on
large-scale failures from an operational network is used to learn time-varying
model parameters and resilience metrics.Comment: 11 pages, 8 figures, submitted to IEEE Sig. Pro
A Biased Resistor Network Model for Electromigration Failure and Related Phenomena in Metallic Lines
Electromigration phenomena in metallic lines are studied by using a biased
resistor network model. The void formation induced by the electron wind is
simulated by a stochastic process of resistor breaking, while the growth of
mechanical stress inside the line is described by an antagonist process of
recovery of the broken resistors. The model accounts for the existence of
temperature gradients due to current crowding and Joule heating. Alloying
effects are also accounted for. Monte Carlo simulations allow the study within
a unified theoretical framework of a variety of relevant features related to
the electromigration. The predictions of the model are in excellent agreement
with the experiments and in particular with the degradation towards electrical
breakdown of stressed Al-Cu thin metallic lines. Detailed investigations refer
to the damage pattern, the distribution of the times to failure (TTFs), the
generalized Black's law, the time evolution of the resistance, including the
early-stage change due to alloying effects and the electromigration saturation
appearing at low current densities or for short line lengths. The dependence of
the TTFs on the length and width of the metallic line is also well reproduced.
Finally, the model successfully describes the resistance noise properties under
steady state conditions.Comment: 39 pages + 17 figure
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Resistance and Resistance Fluctuations in Random Resistor Networks Under Biased Percolation
We consider a two-dimensional random resistor network (RRN) in the presence
of two competing biased percolations consisting of the breaking and recovering
of elementary resistors. These two processes are driven by the joint effects of
an electrical bias and of the heat exchange with a thermal bath. The electrical
bias is set up by applying a constant voltage or, alternatively, a constant
current. Monte Carlo simulations are performed to analyze the network evolution
in the full range of bias values. Depending on the bias strength, electrical
failure or steady state are achieved. Here we investigate the steady-state of
the RRN focusing on the properties of the non-Ohmic regime. In constant voltage
conditions, a scaling relation is found between and , where
is the average network resistance, the linear regime resistance
and the threshold value for the onset of nonlinearity. A similar relation
is found in constant current conditions. The relative variance of resistance
fluctuations also exhibits a strong nonlinearity whose properties are
investigated. The power spectral density of resistance fluctuations presents a
Lorentzian spectrum and the amplitude of fluctuations shows a significant
non-Gaussian behavior in the pre-breakdown region. These results compare well
with electrical breakdown measurements in thin films of composites and of other
conducting materials.Comment: 15 figures, 23 page
Modulated Branching Processes, Origins of Power Laws and Queueing Duality
Power law distributions have been repeatedly observed in a wide variety of
socioeconomic, biological and technological areas. In many of the observations,
e.g., city populations and sizes of living organisms, the objects of interest
evolve due to the replication of their many independent components, e.g.,
births-deaths of individuals and replications of cells. Furthermore, the rates
of the replication are often controlled by exogenous parameters causing periods
of expansion and contraction, e.g., baby booms and busts, economic booms and
recessions, etc. In addition, the sizes of these objects often have reflective
lower boundaries, e.g., cities do not fall bellow a certain size, low income
individuals are subsidized by the government, companies are protected by
bankruptcy laws, etc.
Hence, it is natural to propose reflected modulated branching processes as
generic models for many of the preceding observations. Indeed, our main results
show that the proposed mathematical models result in power law distributions
under quite general polynomial Gartner-Ellis conditions, the generality of
which could explain the ubiquitous nature of power law distributions. In
addition, on a logarithmic scale, we establish an asymptotic equivalence
between the reflected branching processes and the corresponding multiplicative
ones. The latter, as recognized by Goldie (1991), is known to be dual to
queueing/additive processes. We emphasize this duality further in the
generality of stationary and ergodic processes.Comment: 36 pages, 2 figures; added references; a new theorem in Subsection
4.
Distribution of Return Periods of Rare Events in Correlated Time Series
We study the effect on the distribution of return periods of rare events of
the presence in a time series of finite-term correlations with non-exponential
decay. Precisely, we analyze the auto-correlation function and the statistics
of the return intervals of extreme values of the resistance fluctuations
displayed by a resistor with granular structure in a nonequilibrium stationary
state. The resistance fluctuations, , are calculated by Monte Carlo
simulations using the SBRN model introduced some years ago by Pennetta,
Tref\'an and Reggiani and based on a resistor network approach. A rare event
occurs when overcomes a threshold value significantly higher
than the average value of the resistance. We have found that for highly
disordered networks, when the auto-correlation function displays a
non-exponential decay but yet the resistance fluctuations are characterized by
a finite correlation time, the distribution of return intervals of the extreme
values is well described by a stretched exponential, with exponent largely
independent of the threshold . We discuss this result and some of the main
open questions related to it, also in connection with very recent findings by
other authors concerning the observation of stretched exponential distributions
of return intervals of extreme events in long-term correlated time series.Comment: 10 pages, 8 figures, Procs. of 4th. Int. Conf. on Unsolved Problems
on Noise and Fluctuations in Physics, Biology and High Technology (UPoN05),
6-10 June 2005, Gallipoli (Italy), AIP Conf. Procs. (in print
Modeling the mechanics of amorphous solids at different length and time scales
We review the recent literature on the simulation of the structure and
deformation of amorphous glasses, including oxide and metallic glasses. We
consider simulations at different length and time scales. At the nanometer
scale, we review studies based on atomistic simulations, with a particular
emphasis on the role of the potential energy landscape and of the temperature.
At the micrometer scale, we present the different mesoscopic models of
amorphous plasticity and show the relation between shear banding and the type
of disorder and correlations (e.g. elastic) included in the models. At the
macroscopic range, we review the different constitutive laws used in finite
element simulations. We end the review by a critical discussion on the
opportunities and challenges offered by multiscale modeling and transfer of
information between scales to study amorphous plasticity.Comment: 58 pages, 14 figure
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