10,216 research outputs found
The complex of words and Nakaoka stability
We give a new simple proof of the exactness of the complex of injective words
and use it to prove Nakaoka's homology stability for symmetric groups. The
methods are generalized to show acyclicity in low degrees for the complex of
words in general position.Comment: 8 pages, improved notatio
A generator approach to stochastic monotonicity and propagation of order
We study stochastic monotonicity and propagation of order for Markov
processes with respect to stochastic integral orders characterized by cones of
functions satisfying for some linear operator .
We introduce a new functional analytic technique based on the generator
of a Markov process and its resolvent. We show that the existence of an
operator with positive resolvent such that is a positive
operator for a large enough class of functions implies stochastic monotonicity.
This establishes a technique for proving stochastic monotonicity and
propagation of order that can be applied in a wide range of settings including
various orders for diffusion processes with or without boundary conditions and
orders for discrete interacting particle systems
On the nature of spectral proper orthogonal decomposition and related modal decompositions
The spectral proper orthogonal decomposition (SPOD) is a newly introduced
extension of snapshot POD that recently gained attention but also brought up
controversial issues. Within the first proposition, the approach was mainly
presented in a methodological and phenomenological way. The present paper will
detail the relations between SPOD and related POD approaches from an analytical
point of view. To allow for a better grasp of the approach, an alternative
formulation is given that is based on the classic idea from Lumley that was
carried on by George. As will be shown, SPOD is closely related to POD with a
prior segmentation and Fourier transformation in time. Moreover, the SPOD is
shown to be equivalent to snapshot POD combined with time delay embedding
Real-time feedback from iterative electronic structure calculations
Real-time feedback from iterative electronic structure calculations requires
to mediate between the inherently unpredictable execution times of the
iterative algorithm employed and the necessity to provide data in fixed and
short time intervals for real-time rendering. We introduce the concept of a
mediator as a component able to deal with infrequent and unpredictable
reference data to generate reliable feedback. In the context of real-time
quantum chemistry, the mediator takes the form of a surrogate potential that
has the same local shape as the first-principles potential and can be evaluated
efficiently to deliver atomic forces as real-time feedback. The surrogate
potential is updated continuously by electronic structure calculations and
guarantees to provide a reliable response to the operator for any molecular
structure. To demonstrate the application of iterative electronic structure
methods in real-time reactivity exploration, we implement self-consistent
semi-empirical methods as the data source and apply the surrogate-potential
mediator to deliver reliable real-time feedback.Comment: 9 pages, 10 figures, 2 table
Piezo films with adjustable anisotropic strain for bending actuators with tunable bending profiles
We present a method to produce in-plane polarized piezo films with a freely
adjustable ratio of the strains in orthogonal in-plane directions. They can be
used in piezo bending actuators with a tunable curvature profile. The strains
are obtained as mean strains from a periodic polarization pattern produced by a
suitable doubly interdigitated electrode structure. This mechanism is
demonstrated for several examples using PZT sheets. We further discuss how this
tuning and the parameters of the electrode layout affect the overall magnitude
of the displacement.Comment: Presentation improved, minor fixes, appendix added. Final version
published in SMS. 15 pages, 6 figure
Topological in-plane polarized piezo actuation for compact adaptive lenses with aspherical correction
In this contribution, we investigate the effects of using in-plane polarized
piezo actuators with topological buckling displacement to drive glass-piezo
composite membranes for adaptive lenses with aspherical control. We find that
the effects on the focal power and aspherical tuning range are relatively
small, whereas the tuning speed is improved significantly with a first
resonance of 1 kHz for a 13 mm aperture lens.Comment: To be presented at ACTUATOR 2016, 15th International Conference on
New Actuators http://www.actuator.de, references correcte
Focusing Mirror with Tunable Eccentricity
We present a new kind of varifocal mirror with independently adjustable
curvatures in the major directions. For actuation we use two stacked piezo
bending actuators with crossed in-plane polarization. This mirror can be used
for example as an off-axis focusing device with tunable focal length and
compensation for a variable angle of incidence or for coma correction. We
demonstrate the prototype of such a mirror and characterize the mechanical
deflection, as well as the focusing capabilities
Recollimation boundary layers as X-ray sources in young stellar jets
Young stars accrete mass from circumstellar disks and in many cases, the
accretion coincides with a phase of massive outflows, which can be highly
collimated. Those jets emit predominantly in the optical and IR wavelength
range. However, in several cases X-ray and UV observations reveal a weak but
highly energetic component in those jets. X-rays are observed both from
stationary regions close to the star and from knots in the jet several hundred
AU from the star. In this article we show semi-analytically that a fast stellar
wind which is recollimated by the pressure from a slower, more massive disk
wind can have the right properties to power stationary X-ray emission. The size
of the shocked regions is compatible with observational constraints. Our
calculations support a wind-wind interaction scenario for the high energy
emission near the base of YSO jets. For the specific case of DG Tau, a stellar
wind with a mass loss rate of and
a wind speed of 800 km s reproduces the observed X-ray spectrum. We
conclude that a stellar wind recollimation shock is a viable scenario to power
stationary X-ray emission close to the jet launching point.Comment: accepted by ApJ, 14 pages, 9 figure
A Fidelity Study of the Superconducting Phase Diagram in the 2D Single-band Hubbard Model
Extensive numerical studies have demonstrated that the two-dimensional
single-band Hubbard model contains much of the key physics in cuprate
high-temperature superconductors. However, there is no definitive proof that
the Hubbard model truly possesses a superconducting ground state or, if it
does, of how it depends on model parameters. To answer these longstanding
questions, we study an extension of the Hubbard model including an
infinite-range d-wave pair field term, which precipitates a superconducting
state in the d-wave channel. Using exact diagonalization on 16-site square
clusters, we study the evolution of the ground state as a function of the
strength of the pairing term. This is achieved by monitoring the fidelity
metric of the ground state, as well as determining the ratio between the two
largest eigenvalues of the d-wave pair/spin/charge-density matrices. The
calculations show a d-wave superconducting ground state in doped clusters
bracketed by a strong antiferromagnetic state at half filling controlled by the
Coulomb repulsion U and a weak short-range checkerboard charge ordered state at
larger hole doping controlled by the next-nearest-neighbor hopping t'. We also
demonstrate that negative t' plays an important role in facilitating d-wave
superconductivity.Comment: 10 pages, 13 figure
Towards a comparative science of cities: using mobile traffic records in New York, London and Hong Kong
This chapter examines the possibility to analyze and compare human activities
in an urban environment based on the detection of mobile phone usage patterns.
Thanks to an unprecedented collection of counter data recording the number of
calls, SMS, and data transfers resolved both in time and space, we confirm the
connection between temporal activity profile and land usage in three global
cities: New York, London and Hong Kong. By comparing whole cities typical
patterns, we provide insights on how cultural, technological and economical
factors shape human dynamics. At a more local scale, we use clustering analysis
to identify locations with similar patterns within a city. Our research reveals
a universal structure of cities, with core financial centers all sharing
similar activity patterns and commercial or residential areas with more
city-specific patterns. These findings hint that as the economy becomes more
global, common patterns emerge in business areas of different cities across the
globe, while the impact of local conditions still remains recognizable on the
level of routine people activity.Comment: 24 pages, 9 figures, book chapter to be published in "Computational
Approaches for Urban Environments" (Springer Ed.), October 201
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