On the 3-distortion of a path

We prove that, when a path of length n is embedded in R^2, the 3-distortion is an Omega(n^{1/2}), and that, when embedded in R^d, the 3-distortion is an O(n^{1/d-1})

Experimental investigation of outdoor propagation of finite-amplitude noise

The outdoor propagation of finite amplitude acoustic waves was investigated using a conventional electroacoustic transmitter which was mounted on the ground and pointed upward in order to avoid ground reflection effects. The propagation path was parallel to a radio tower 85 m tall, whose elevator carried the receiving microphone. The observations and conclusions are as follows: (1) At the higher source levels nonlinear propagation distortion caused a strong generation of high frequency noise over the propagation path. For example, at 70 m for a frequency 2-3 octaves above the source noise band, the measured noise was up to 30 dB higher than the linear theory prediction. (2) The generation occurred in both the nearfield and the farfield of the transmitter. (3) At no measurement point was small-signal behavior established for the high requency noise. Calculations support the contention that the nonlinearity generated high frequency noise never becomes small-signal in its behavior, regardless of distance. (4) When measured spectra are scaled in frequency and level to make them comparable with spectra of actual jet noise, they are found to be well within the jet noise range. It is therefore entirely possible that nonlinear distortion affects jet noise

SPHERE IRDIS and IFS astrometric strategy and calibration

We present the current results of the astrometric characterization of the VLT planet finder SPHERE over 2 years of on-sky operations. We first describe the criteria for the selection of the astrometric fields used for calibrating the science data: binaries, multiple systems, and stellar clusters. The analysis includes measurements of the pixel scale and the position angle with respect to the North for both near-infrared subsystems, the camera IRDIS and the integral field spectrometer IFS, as well as the distortion for the IRDIS camera. The IRDIS distortion is shown to be dominated by an anamorphism of 0.60+/-0.02% between the horizontal and vertical directions of the detector, i.e. 6 mas at 1". The anamorphism is produced by the cylindrical mirrors in the common path structure hence common to all three SPHERE science subsystems (IRDIS, IFS, and ZIMPOL), except for the relative orientation of their field of view. The current estimates of the pixel scale and North angle for IRDIS are 12.255+/-0.009 milliarcseconds/pixel for H2 coronagraphic images and -1.75+/-0.08 deg. Analyses of the IFS data indicate a pixel scale of 7.46+/-0.02 milliarcseconds/pixel and a North angle of -102.18+/-0.13 deg. We finally discuss plans for providing astrometric calibration to the SPHERE users outside the instrument consortium.Comment: 12 pages, 6 figures, 3 table

In-plane thermal conductivity of large single crystals of Sm-substituted (Y1−x_{1-x}Smx_{x})Ba2_{2}Cu3_{3}O7−δ_{7-\delta}

We have investigated the in-plane thermal conductivity $\kappa_{ab}(T,H)$ of large single crystals of optimally oxygen-doped (Y$_{1-x}$,Sm$_{x}$)Ba$_{2}$Cu$_{3}$O$_{7-\delta}$ ($x$=0, 0.1, 0.2 and 1.0) and YBa$_{2}$(Cu$_{1-y}$Zn$_{y}$)$_{3}$O$_{7-\delta}$($y$=0.0071) as functions of temperature and magnetic field (along the c axis). For comparison, the temperature dependence of $\kappa_{ab}$ for as-grown crystals with the corresponding compositions are presented. The nonlinear field dependence of $\kappa_{ab}$ for all crystals was observed at relatively low fields near a half of $T_{c}$. We make fits of the $\kappa(H)$ data to an electron contribution model, providing both the mean free path of quasiparticles $\ell_{0}$ and the electronic thermal conductivity $\kappa_{e}$, in the absence of field. The local lattice distortion due to the Sm substitution for Y suppresses both the phonon and electron contributions. On the other hand, the light Zn doping into the CuO $_{2}$ planes affects solely the electron component below $T_{c}$, resulting in a substantial decrease in $\ell_{0}$ .Comment: 7 pages,4 figures,1 tabl

Influence of an electric field on the topological stability of the neutral lithium dimer

The Hunan Natural Science Foundation of China project gratefully acknowledged approval number: 2022JJ30029. The One Hundred Talents Foundation of Hunan Province is also gratefully acknowledged for the support of S.J. and S.R.K.In this investigation, we seek to understand the role of non-nuclear attractors (NNAs) of the neutral Li2 dimer subjected to an electric (± E ) field that is directed parallel ( ±E x ) and perpendicular ( ±E y ) to the bond-path. The ±E x -fields and ±E y -fields are separately applied to the Li2 molecular graph until the bond ruptures. The next generation quantum theory of atoms in molecules (NG-QTAIM) interpretation of bonding was constructed with the stress tensor σ ( r ) eigenvectors on the Hessian of ρ( r ) molecular graph. The asymmetry induced by both the ±E y -field and ±E x -field was detected in terms of the rotation of the orthogonal triad of stress tensor σ ( r ) eigenvectors { e 1σ , e 2σ , e 3σ } relative to the Cartesian coordinate frame. The orthogonal triad of Hessian of ρ( r ) eigenvectors { e 1 , e 2 , e 3 } however, were only able to detect rotation induced by the high degree of asymmetry present for bent bond-paths induced by the ±E y -fields. Larger movement of the NNAs along the bond-path correlated with greater bond critical point (BCP) bond metallicity ξ( r b). The effect of applying the ±E x -field was compared with unpublished results on neutral Li2 subject to a stretching distortion. The lack of NNA motion along the bond-path for the stretching distortion correlated with a lower degree of bond metallicity ξ( r b). The stress tensor σ ( r ) eigenvectors have a unique ability to detect rotation relative to the Cartesian coordinate frame for high bond-path symmetry occurring for the bond-stretching distortion and application of the ±E x -field. Suggestions for future work are provided.PostprintPostprintPeer reviewe

FPT-Algorithms for Computing Gromov-Hausdorff and Interleaving Distances Between Trees

The Gromov-Hausdorff distance is a natural way to measure the distortion between two metric spaces. However, there has been only limited algorithmic development to compute or approximate this distance. We focus on computing the Gromov-Hausdorff distance between two metric trees. Roughly speaking, a metric tree is a metric space that can be realized by the shortest path metric on a tree. Any finite tree with positive edge weight can be viewed as a metric tree where the weight is treated as edge length and the metric is the induced shortest path metric in the tree. Previously, Agarwal et al. showed that even for trees with unit edge length, it is NP-hard to approximate the Gromov-Hausdorff distance between them within a factor of 3. In this paper, we present a fixed-parameter tractable (FPT) algorithm that can approximate the Gromov-Hausdorff distance between two general metric trees within a multiplicative factor of 14. Interestingly, the development of our algorithm is made possible by a connection between the Gromov-Hausdorff distance for metric trees and the interleaving distance for the so-called merge trees. The merge trees arise in practice naturally as a simple yet meaningful topological summary (it is a variant of the Reeb graphs and contour trees), and are of independent interest. It turns out that an exact or approximation algorithm for the interleaving distance leads to an approximation algorithm for the Gromov-Hausdorff distance. One of the key contributions of our work is that we re-define the interleaving distance in a way that makes it easier to develop dynamic programming approaches to compute it. We then present a fixed-parameter tractable algorithm to compute the interleaving distance between two merge trees exactly, which ultimately leads to an FPT-algorithm to approximate the Gromov-Hausdorff distance between two metric trees. This exact FPT-algorithm to compute the interleaving distance between merge trees is of interest itself, as it is known that it is NP-hard to approximate it within a factor of 3, and previously the best known algorithm has an approximation factor of O(sqrt{n}) even for trees with unit edge length

Tuning of crystal structure and magnetic properties by exceptionally large epitaxial strains

Huge deformations of the crystal lattice can be achieved in materials with inherent structural instability by epitaxial straining. By coherent growth on seven different substrates the in-plane lattice constants of 50 nm thick Fe70Pd30 films are continuously varied. The maximum epitaxial strain reaches 8,3 % relative to the fcc lattice. The in-plane lattice strain results in a remarkable tetragonal distortion ranging from c/abct = 1.09 to 1.39, covering most of the Bain transformation path from fcc to bcc crystal structure. This has dramatic consequences for the magnetic key properties. Magnetometry and X-ray circular dichroism (XMCD) measurements show that Curie temperature, orbital magnetic moment, and magnetocrystalline anisotropy are tuned over broad ranges.Comment: manuscript, 3 figures, auxiliary materia

Uncovering the magnetic environment of our solar system

Since its formation 4.6 billion years ago, our solar system has most likely crossed numerous magnetized interstellar clouds and bubbles of different sizes and contents on its path through the Milky Way. Having a reference model for how the heliosphere and interstellar winds interact is critical for understanding our current Galactic environment, and it requires untangling the roles of two major actors: the time-variable solar wind and the local interstellar magnetic field. Numerical simulations predict a distortion of the heliosphere caused by both solar wind anisotropy and interstellar magnetic field orientation. However, model comparison to deep space probes' measurements led to contradictory reports by Voyager 1 and Voyager 2 of both several crossings of the solar wind's termination shock and of the strength of the local interstellar field, with values ranging from 1.8 to 5.7 {\mu}G. Here, we show that Voyager 1 & 2 plasma, fields, and Lyman-{\alpha} sky background measurements, as well as space observations of high-energy particles of heliospheric origin, may all be explained by a rather weak interstellar field 2.2 +/- 0.1 {\mu}G pointing from Galactic coordinates (l,b) \sim (28, 52)+/- 3{\deg}. For the 2000 epoch Ulysses-based helium parameters assumed thus far, the interstellar bow shock must exist. By contrast, using the 2010 epoch IBEX-based He parameters and a stronger magnetic field leads to a plasma configuration that is not consistent with the Voyagers TS crossings. For the newly proposed interstellar He parameters, more simulations are required before one may determine whether the interstellar bow shock truly does disappear under those assumptions.Comment: 5 pages, 5 figures, in press in Astron. & Astrophy