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 $\Phi f \geq 0$ for some linear operator $\Phi$. We introduce a new functional analytic technique based on the generator $A$ of a Markov process and its resolvent. We show that the existence of an operator $B$ with positive resolvent such that $\Phi A - B \Phi$ 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 $5\cdot10^{-10}\;M_{\odot}\;\mathrm{yr}^{-1}$ and a wind speed of 800 km s$^{-1}$ 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