484 research outputs found
Optimal noise-canceling networks
Natural and artificial networks, from the cerebral cortex to large-scale
power grids, face the challenge of converting noisy inputs into robust signals.
The input fluctuations often exhibit complex yet statistically reproducible
correlations that reflect underlying internal or environmental processes such
as synaptic noise or atmospheric turbulence. This raises the practically and
biophysically relevant of question whether and how noise-filtering can be
hard-wired directly into a network's architecture. By considering generic phase
oscillator arrays under cost constraints, we explore here analytically and
numerically the design, efficiency and topology of noise-canceling networks.
Specifically, we find that when the input fluctuations become more correlated
in space or time, optimal network architectures become sparser and more
hierarchically organized, resembling the vasculature in plants or animals. More
broadly, our results provide concrete guiding principles for designing more
robust and efficient power grids and sensor networks.Comment: 6 pages, 3 figures, supplementary materia
Linear Optimal Power Flow Using Cycle Flows
Linear optimal power flow (LOPF) algorithms use a linearization of the
alternating current (AC) load flow equations to optimize generator dispatch in
a network subject to the loading constraints of the network branches. Common
algorithms use the voltage angles at the buses as optimization variables, but
alternatives can be computationally advantageous. In this article we provide a
review of existing methods and describe a new formulation that expresses the
loading constraints directly in terms of the flows themselves, using a
decomposition of the network graph into a spanning tree and closed cycles. We
provide a comprehensive study of the computational performance of the various
formulations, in settings that include computationally challenging applications
such as multi-period LOPF with storage dispatch and generation capacity
expansion. We show that the new formulation of the LOPF solves up to 7 times
faster than the angle formulation using a commercial linear programming solver,
while another existing cycle-based formulation solves up to 20 times faster,
with an average speed-up of factor 3 for the standard networks considered here.
If generation capacities are also optimized, the average speed-up rises to a
factor of 12, reaching up to factor 213 in a particular instance. The speed-up
is largest for networks with many buses and decentral generators throughout the
network, which is highly relevant given the rise of distributed renewable
generation and the computational challenge of operation and planning in such
networks.Comment: 11 pages, 5 figures; version 2 includes results for generation
capacity optimization; version 3 is the final accepted journal versio
Dual theory of transmission line outages
A new graph dual formalism is presented for the analysis of line outages in
electricity networks. The dual formalism is based on a consideration of the
flows around closed cycles in the network. After some exposition of the theory
is presented, a new formula for the computation of Line Outage Distribution
Factors (LODFs) is derived, which is not only computationally faster than
existing methods, but also generalizes easily for multiple line outages and
arbitrary changes to line series reactance. In addition, the dual formalism
provides new physical insight for how the effects of line outages propagate
through the network. For example, in a planar network a single line outage can
be shown to induce monotonically decreasing flow changes, which are
mathematically equivalent to an electrostatic dipole field.Comment: 8 pages, 3 figures, 1 table; Accepted at IEEE Transactions on Power
System
Spectral Design of Active Mechanical and Electrical Metamaterials
Active matter is ubiquitous in biology and becomes increasingly more
important in materials science. While numerous active systems have been
investigated in detail both experimentally and theoretically, general design
principles for functional active materials are still lacking. Building on a
recently developed linear response optimization (LRO) framework, we here
demonstrate that the spectra of nonlinear active mechanical and electric
circuits can be designed similarly to those of linear passive networks.Comment: 3 pages, 2 figures. Submitted to "14 International Congress on
Artificial Materials for Novel Wave Phenomena - Metamaterials 2020
Autonomous actuation of zero modes in mechanical networks far from equilibrium
A zero mode, or floppy mode, is a non-trivial coupling of mechanical
components yielding a degree of freedom with no resistance to deformation.
Engineered zero modes have the potential to act as microscopic motors or memory
devices, but this requires an internal actuation mechanism that can overcome
unwanted fluctuations in other modes and the dissipation inherent in real
systems. In this work, we show theoretically and experimentally that complex
zero modes in mechanical networks can be selectively mobilized by
non-equilibrium activity. We find that a correlated active bath actuates an
infinitesimal zero mode while simultaneously suppressing fluctuations in higher
modes compared to thermal fluctuations, which we experimentally mimic by high
frequency shaking of a physical network. Furthermore, self-propulsive dynamics
spontaneously mobilise finite mechanisms as exemplified by a self-propelled
topological soliton. Non-equilibrium activity thus enables autonomous actuation
of coordinated mechanisms engineered through network topology
Active topolectrical circuits
The transfer of topological concepts from the quantum world to classical
mechanical and electronic systems has opened fundamentally new approaches to
protected information transmission and wave guidance. A particularly promising
technology are recently discovered topolectrical circuits that achieve robust
electric signal transduction by mimicking edge currents in quantum Hall
systems. In parallel, modern active matter research has shown how autonomous
units driven by internal energy reservoirs can spontaneously self-organize into
collective coherent dynamics. Here, we unify key ideas from these two
previously disparate fields to develop design principles for active
topolectrical circuits (ATCs) that can self-excite topologically protected
global signal patterns. Realizing autonomous active units through nonlinear
Chua diode circuits, we theoretically predict and experimentally confirm the
emergence of self-organized protected edge oscillations in one- and
two-dimensional ATCs. The close agreement between theory, simulations and
experiments implies that nonlinear ATCs provide a robust and versatile platform
for developing high-dimensional autonomous electrical circuits with
topologically protected functionalities.Comment: 10 pages, 4 figures, includes supplementary material. This version
adds 2D experiment
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