7,685 research outputs found
Small gain theorems for large scale systems and construction of ISS Lyapunov functions
We consider interconnections of n nonlinear subsystems in the input-to-state
stability (ISS) framework. For each subsystem an ISS Lyapunov function is given
that treats the other subsystems as independent inputs. A gain matrix is used
to encode the mutual dependencies of the systems in the network. Under a small
gain assumption on the monotone operator induced by the gain matrix, a locally
Lipschitz continuous ISS Lyapunov function is obtained constructively for the
entire network by appropriately scaling the individual Lyapunov functions for
the subsystems. The results are obtained in a general formulation of ISS, the
cases of summation, maximization and separation with respect to external gains
are obtained as corollaries.Comment: provisionally accepted by SIAM Journal on Control and Optimizatio
Hall effect in heavy-fermion metals
The heavy fermion systems present a unique platform in which strong
electronic correlations give rise to a host of novel, and often competing,
electronic and magnetic ground states. Amongst a number of potential
experimental tools at our disposal, measurements of the Hall effect have
emerged as a particularly important one in discerning the nature and evolution
of the Fermi surfaces of these enigmatic metals. In this article, we present a
comprehensive review of Hall effect measurements in the heavy-fermion
materials, and examine the success it has had in contributing to our current
understanding of strongly correlated matter. Particular emphasis is placed on
its utility in the investigation of quantum critical phenomena which are
thought to drive many of the exotic electronic ground states in these systems.
This is achieved by the description of measurements of the Hall effect across
the putative zero-temperature instability in the archetypal heavy-fermion metal
YbRhSi. Using the CeIn (with Co, Ir) family of systems as
a paradigm, the influence of (antiferro-)magnetic fluctuations on the Hall
effect is also illustrated. This is compared to prior Hall effect measurements
in the cuprates and other strongly correlated systems to emphasize on the
generality of the unusual magnetotransport in materials with non-Fermi liquid
behavior.Comment: manuscript accepted in Adv. Phy
Unconventional superfluid order in the -band of a bipartite optical square lattice
We report on the first observation of bosons condensed into the energy minima
of an -band of a bipartite square optical lattice. Momentum spectra indicate
that a truly complex-valued staggered angular momentum superfluid order is
established. The corresponding wave function is composed of alternating local
-orbits and local -orbits residing in the deep
and shallow wells of the lattice, which are arranged as the black and white
areas of a checkerboard. A pattern of staggered vortical currents arises, which
breaks time reversal symmetry and the translational symmetry of the lattice
potential. We have measured the populations of higher order Bragg peaks in the
momentum spectra for varying relative depths of the shallow and deep lattice
wells and find remarkable agreement with band calculations.Comment: 4 pages, 3 figure
Stability Criteria for SIS Epidemiological Models under Switching Policies
We study the spread of disease in an SIS model. The model considered is a
time-varying, switched model, in which the parameters of the SIS model are
subject to abrupt change. We show that the joint spectral radius can be used as
a threshold parameter for this model in the spirit of the basic reproduction
number for time-invariant models. We also present conditions for persistence
and the existence of periodic orbits for the switched model and results for a
stochastic switched model
Ecological Observations on Predatory Coccinellidae (Coleoptera) in Southwestern Michigan
Ecological observations on habitat utilization by thirteen species of predatory Coccinellidae were made at a southern Michigan site during 1989 and 1990. Most of species were common during both years and used both agricul- tural and uncultivated habitats. Coccinella septempunctata and Coleomegilla maculata, were the most abundant in agricultural crops (alfalfa, maize, soy- bean and triticale), whereas Adalia bipunctata and Cycloneda munda, were the most abundant in deciduous and bushy habitats
Comment on "Zeeman-Driven Lifshitz Transition: A Model for the Experimentally Observed Fermi-Surface Reconstruction in YbRh2Si2"
In Phys. Rev. Lett. 106, 137002 (2011), A. Hackl and M. Vojta have proposed
to explain the quantum critical behavior of YbRh2Si2 in terms of a
Zeeman-induced Lifshitz transition of an electronic band whose width is about 6
orders of magnitude smaller than that of conventional metals. Here, we note
that the ultra-narrowness of the proposed band, as well as the proposed
scenario per se, lead to properties which are qualitatively inconsistent with
the salient features observed in YbRh2Si2 near its quantum critical point.Comment: 3 page
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