Combinatorics of tight geodesics and stable lengths

We give an algorithm to compute the stable lengths of pseudo-Anosovs on the curve graph, answering a question of Bowditch. We also give a procedure to compute all invariant tight geodesic axes of pseudo-Anosovs. Along the way we show that there are constants $1<a_1<a_2$ such that the minimal upper bound on `slices' of tight geodesics is bounded below and above by $a_1^{\xi(S)}$ and $a_2^{\xi(S)}$, where $\xi(S)$ is the complexity of the surface. As a consequence, we give the first computable bounds on the asymptotic dimension of curve graphs and mapping class groups. Our techniques involve a generalization of Masur--Minsky's tight geodesics and a new class of paths on which their tightening procedure works.Comment: 19 pages, 2 figure

Contractible, hyperbolic but non-CAT(0) complexes

From Springer Nature via Jisc Publications RouterHistory: received 2020-04-26, rev-recd 2020-09-15, accepted 2020-09-16, pub-print 2020-10, registration 2020-10-01, pub-electronic 2020-10-26, online 2020-10-26Publication status: PublishedFunder: University of ManchesterAbstract: We prove that almost all arc complexes do not admit a CAT(0) metric with finitely many shapes, in particular any finite-index subgroup of the mapping class group does not preserve such a metric on the arc complex. We also show the analogous statement for all but finitely many disc complexes of handlebodies and free splitting complexes of free groups. The obstruction is combinatorial. These complexes are all hyperbolic and contractible but despite this we show that they satisfy no combinatorial isoperimetric inequality: for any n there is a loop of length 4 that only bounds discs consisting of at least n triangles. On the other hand we show that the curve complexes satisfy a linear combinatorial isoperimetric inequality, which answers a question of Andrew Putman

Universal scaling of nonlocal and local resistance fluctuations in small wires

Resistance fluctuations in small metal samples result from coherent transport of the carriers. The wave functions of the carriers extend into regions which are not accessible classically. We have directly measured the length dependence of the nonlocal magnetoresistance fluctuations in Sb and Au wires by studying regions of our samples separated from the classical current path by a distance L which varied from 3Lcphi down to 0.2Lcphi (where Lcphi is the phase coherence length for the carriers in the metal). These fluctuations decay exponentially with L/Lcphi. Measurements along the classical current paths scale more slowly with L/Lcphi than predicted by the analytical theory but are in agreement with numerical simulations. We have also studied the length dependence of the magnetic field correlation scale BC, and we find that it is in qualitative agreement with a recent model calculation that accounts for the voltage probes

Absence of Size Dependence of the Kondo Resistivity

We have measured the low temperature resistivity of AuFe wires in the dilute magnetic impurity limit as a function of wire width, temperature, and magnetic field. When the width dependence of the electron-electron interaction contribution to the resistivity is taken into account, the temperature dependence of the remaining Kondo contribution to the resistivity of all samples with the same impurity concentration is identical. Similar behavior is observed for the magnetic field dependent resistivity. Thus, the Kondo contribution to the resistivity is independent of width down to 38 nm, much smaller than the Kondo length ξK=ħvF/kBTK≊10 μm

An empirical approach to modeling ion production rates in Titan's ionosphere II: Ion production rates on the nightside

Ionization of neutrals by precipitating electrons and ions is the main source of Titan's nightside ionosphere. This paper has two goals: (1) characterization of the role of electron impact ionization on the nightside ionosphere for different magnetospheric conditions and (2) presentation of empirical ion production rates determined using densities measured by the Cassini Ion and Neutral Mass Spectrometer on the nightside. The ionosphere between 1000 and 1400 km is emphasized. We adopt electron fluxes measured by the Cassini Plasma Spectrometer-Electron Spectrometer and the Magnetospheric Imaging Instrument as classified by Rymer et al. (2009). The current paper follows an earlier paper (Paper I), in which we investigated sources of Titan's dayside ionosphere and demonstrated that the photoionization process is well understood. The current paper (Paper II) demonstrates that modeled and empirical ionization rates on the nightside are in agreement with an electron precipitation source above 1100 km. Ion production rate profiles appropriate for different Saturnian magnetospheric conditions, as outlined by Rymer et al., are constructed for various magnetic field topologies. Empirical production rate profiles are generated for deep nightside flybys of Titan. The results also suggest that at lower altitudes (below 1100 km) another source, such as ion precipitation, is probably needed

An empirical approach to modeling ion production rates in Titan’s ionosphere I: Ion production rates on the dayside and globally

Titan's ionosphere is created when solar photons, energetic magnetospheric electrons or ions, and cosmic rays ionize the neutral atmosphere. Electron densities generated by current theoretical models are much larger than densities measured by instruments on board the Cassini orbiter. This model density overabundance must result either from overproduction or from insufficient loss of ions. This is the first of two papers that examines ion production rates in Titan's ionosphere, for the dayside and nightside ionosphere, respectively. The first (current) paper focuses on dayside ion production rates which are computed using solar ionization sources (photoionization and electron impact ionization by photoelectrons) between 1000 and 1400 km. In addition to theoretical ion production rates, empirical ion production rates are derived from CH4, CH3+, and CH4+ densities measured by the INMS (Ion Neutral Mass Spectrometer) for many Titan passes. The modeled and empirical production rate profiles from measured densities of N2+ and CH4+ are found to be in good agreement (to within 20%) for solar zenith angles between 15 and 90°. This suggests that the overabundance of electrons in theoretical models of Titan's dayside ionosphere is not due to overproduction but to insufficient ion losses

Captive reptile mortality rates in the home and implications for the wildlife trade

The trade in wildlife and keeping of exotic pets is subject to varying levels of national and international regulation and is a topic often attracting controversy. Reptiles are popular exotic pets and comprise a substantial component of the live animal trade. High mortality of traded animals raises welfare concerns, and also has implications for conservation if collection from the wild is required to meet demand. Mortality of reptiles can occur at any stage of the trade chain from collector to consumer. However, there is limited information on mortality rates of reptiles across trade chains, particularly amongst final consumers in the home. We investigated mortality rates of reptiles amongst consumers using a specialised technique for asking sensitive questions, additive Randomised Response Technique (aRRT), as well as direct questioning (DQ). Overall, 3.6% of snakes, chelonians and lizards died within one year of acquisition. Boas and pythons had the lowest reported mortality rates of 1.9% and chameleons had the highest at 28.2%. More than 97% of snakes, 87% of lizards and 69% of chelonians acquired by respondents over five years were reported to be captive bred and results suggest that mortality rates may be lowest for captive bred individuals. Estimates of mortality from aRRT and DQ did not differ significantly which is in line with our findings that respondents did not find questions about reptile mortality to be sensitive. This research suggests that captive reptile mortality in the home is rather low, and identifies those taxa where further effort could be made to reduce mortality rate