605 research outputs found
Space-Time Sampling for Network Observability
Designing sparse sampling strategies is one of the important components in
having resilient estimation and control in networked systems as they make
network design problems more cost-effective due to their reduced sampling
requirements and less fragile to where and when samples are collected. It is
shown that under what conditions taking coarse samples from a network will
contain the same amount of information as a more finer set of samples. Our goal
is to estimate initial condition of linear time-invariant networks using a set
of noisy measurements. The observability condition is reformulated as the frame
condition, where one can easily trace location and time stamps of each sample.
We compare estimation quality of various sampling strategies using estimation
measures, which depend on spectrum of the corresponding frame operators. Using
properties of the minimal polynomial of the state matrix, deterministic and
randomized methods are suggested to construct observability frames. Intrinsic
tradeoffs assert that collecting samples from fewer subsystems dictates taking
more samples (in average) per subsystem. Three scalable algorithms are
developed to generate sparse space-time sampling strategies with explicit error
bounds.Comment: Submitted to IEEE TAC (Revised Version
Topologically protected elastic waves in phononic metamaterials
Topological states of quantum matter exhibit unique disorder-immune surface
states protected by underlying nontrivial topological invariants of the bulk.
Such immunity from backscattering makes topological surface or edge states
ideal carriers for both classical and quantum information. So far, topological
matters have been explored only in the realms of electronics and photonics,
with limited range of bulk properties and largely immutable materials. These
constraints thus impose severe performance trade-offs in experimentally
realizable topologically ordered states. In contrast, phononic metamaterials
not only provide access to a much wider range of material properties, but also
allow temporal modulation in the non-adiabatic regime. Here, from the
first-principles we demonstrate numerically the first phononic topological
metamaterial in an elastic-wave analogue of the quantum spin Hall effect. A
dual-scale phononic crystal slab is used to support two effective spins of
phonon over a broad bandwidth, and strong spin-orbit coupling is realized by
breaking spatial mirror symmetry. By preserving the spin polarization with an
external load or spatial symmetry, phononic edge states are shown to be robust
against scattering from discrete defects as well as disorders in the continuum.
Our system opens up the possibility of realizing topological materials for
phonons in both static and time-dependent regimes.Comment: 19 pages, 6 figure
Dual-carrier Floquet circulator with time-modulated optical resonators
Spatio-temporal modulation has shown great promise as a strong time-reversal
symmetry breaking mechanism that enables integrated nonreciprocal devices and
topological materials at optical frequencies. However, optical modulation has
its own constraints in terms of modulation index and frequency, which limit the
bandwidth and miniaturization of circulators and isolators, not unlike the
magneto-optical schemes that it promises to replace. Here we propose and
numerically demonstrate a Floquet circulator that leverages the untapped
degrees of freedom unique to time-modulated resonators. Excited by
sideband-selective waveguides, the system supports broadband nonreciprocal
transmission without relying on the mirror or rotational symmetries required in
conventional circulators. Cascading two resonators, we create a linear
three-port circulator that exhibits complete and frequency-independent forward
transmission between two of the ports. This approach enables wavelength-scale
circulators that can rely on a variety of modulation mechanisms
- …