Force-Extension Relation and Plateau Modulus for Wormlike Chains

We derive the linear force-extension relation for a wormlike chain of arbitrary stiffness including entropy elasticity, bending and thermodynamic buckling. From this we infer the plateau modulus $G^0$ of an isotropic entangled solution of wormlike chains. The entanglement length $L_e$ is expressed in terms of the characteristic network parameters for three different scaling regimes in the entangled phase. The entanglement transition and the concentration dependence of $G^0$ are analyzed. Finally we compare our findings with experimental data.Comment: 5 pages, 1 eps-figure, to appear in PR

Statistical mechanics of triangulated ribbons

We use computer simulations and scaling arguments to investigate statistical and structural properties of a semiflexible ribbon composed of isosceles triangles. We study two different models, one where the bending energy is calculated from the angles between the normal vectors of adjacent triangles, the second where the edges are viewed as semiflexible polymers so that the bending energy is related to the angles between the tangent vectors of next-nearest neighbor triangles. The first model can be solved exactly whereas the second is more involved. It was recently introduced by Liverpool and Golestanian Phys.Rev.Lett. 80, 405 (1998), Phys.Rev.E 62, 5488 (2000) as a model for double-stranded biopolymers such as DNA. Comparing observables such as the autocorrelation functions of the tangent vectors and the bond-director field, the probability distribution functions of the end-to-end distance, and the mean squared twist we confirm the existence of local twist correlation, but find no indications for other predicted features such as twist-stretch coupling, kinks, or oscillations in the autocorrelation function of the bond-director field.Comment: 10 pages, 13 figures. submitted to PRE, revised versio

Life path analysis: scaling indicates priming effects of social and habitat factors on dispersal distances

1. Movements of many animals along a life-path can be separated into repetitive ones within home ranges and transitions between home ranges. We sought relationships of social and environmental factors with initiation and distance of transition movements in 114 buzzards Buteo buteo that were marked as nestlings with long-life radio tags. 2. Ex-natal dispersal movements of 51 buzzards in autumn were longer than for 30 later in their first year and than 35 extra-natal movements between home ranges after leaving nest areas. In the second and third springs, distances moved from winter focal points by birds that paired were the same or less than for unpaired birds. No post-nuptial movement exceeded 2 km. 3. Initiation of early ex-natal dispersal was enhanced by presence of many sibs, but also by lack of worm-rich loam soils. Distances travelled were greatest for birds from small broods and with relatively little short grass-feeding habitat near the nest. Later movements were generally enhanced by the absence of loam soils and short grassland, especially with abundance of other buzzards and probable poor feeding habitats (heathland, long grass). 4. Buzzards tended to persist in their first autumn where arable land was abundant, but subsequently showed a strong tendency to move from this habitat. 5. Factors that acted most strongly in ½-km buffers round nests, or round subsequent focal points, usually promoted movement compared with factors acting at a larger scale. Strong relationships between movement distances and environmental characteristics in ½-km buffers, especially during early ex-natal dispersal, suggested that buzzards became primed by these factors to travel far. 6. Movements were also farthest for buzzards that had already moved far from their natal nests, perhaps reflecting genetic predisposition, long-term priming or poor habitat beyond the study area

Selective Dynamical Imaging of Interferometric Data

Recent developments in very long baseline interferometry (VLBI) have made it possible for the Event Horizon Telescope (EHT) to resolve the innermost accretion flows of the largest supermassive black holes on the sky. The sparse nature of the EHT's (u, v)-coverage presents a challenge when attempting to resolve highly time-variable sources. We demonstrate that the changing (u, v)-coverage of the EHT can contain regions of time over the course of a single observation that facilitate dynamical imaging. These optimal time regions typically have projected baseline distributions that are approximately angularly isotropic and radially homogeneous. We derive a metric of coverage quality based on baseline isotropy and density that is capable of ranking array configurations by their ability to produce accurate dynamical reconstructions. We compare this metric to existing metrics in the literature and investigate their utility by performing dynamical reconstructions on synthetic data from simulated EHT observations of sources with simple orbital variability. We then use these results to make recommendations for imaging the 2017 EHT Sgr A* data set

The Variability of the Black Hole Image in M87 at the Dynamical Timescale

The black hole images obtained with the Event Horizon Telescope (EHT) are expected to be variable at the dynamical timescale near their horizons. For the black hole at the center of the M87 galaxy, this timescale (5-61 days) is comparable to the 6 day extent of the 2017 EHT observations. Closure phases along baseline triangles are robust interferometric observables that are sensitive to the expected structural changes of the images but are free of station-based atmospheric and instrumental errors. We explored the day-to-day variability in closure-phase measurements on all six linearly independent nontrivial baseline triangles that can be formed from the 2017 observations. We showed that three triangles exhibit very low day-to-day variability, with a dispersion of similar to 3 degrees-5 degrees. The only triangles that exhibit substantially higher variability (similar to 90 degrees-180 degrees) are the ones with baselines that cross the visibility amplitude minima on the u-v plane, as expected from theoretical modeling. We used two sets of general relativistic magnetohydrodynamic simulations to explore the dependence of the predicted variability on various black hole and accretion-flow parameters. We found that changing the magnetic field configuration, electron temperature model, or black hole spin has a marginal effect on the model consistency with the observed level of variability. On the other hand, the most discriminating image characteristic of models is the fractional width of the bright ring of emission. Models that best reproduce the observed small level of variability are characterized by thin ring-like images with structures dominated by gravitational lensing effects and thus least affected by turbulence in the accreting plasmas

The variability of the black hole image in M87 at the dynamical timescale

The black hole images obtained with the Event Horizon Telescope (EHT) are expected to be variable at the dynamical timescale near their horizons. For the black hole at the center of the M87 galaxy, this timescale (5–61 days) is comparable to the 6 day extent of the 2017 EHT observations. Closure phases along baseline triangles are robust interferometric observables that are sensitive to the expected structural changes of the images but are free of station-based atmospheric and instrumental errors. We explored the day-to-day variability in closure-phase measurements on all six linearly independent nontrivial baseline triangles that can be formed from the 2017 observations. We showed that three triangles exhibit very low day-to-day variability, with a dispersion of ∼3°–5°. The only triangles that exhibit substantially higher variability (∼90°–180°) are the ones with baselines that cross the visibility amplitude minima on the u–v plane, as expected from theoretical modeling. We used two sets of general relativistic magnetohydrodynamic simulations to explore the dependence of the predicted variability on various black hole and accretion-flow parameters. We found that changing the magnetic field configuration, electron temperature model, or black hole spin has a marginal effect on the model consistency with the observed level of variability. On the other hand, the most discriminating image characteristic of models is the fractional width of the bright ring of emission. Models that best reproduce the observed small level of variability are characterized by thin ring-like images with structures dominated by gravitational lensing effects and thus least affected by turbulence in the accreting plasmas.https://iopscience.iop.org/article/10.3847/1538-4357/ac332e/pdfPublished versio

First M87 Event Horizon Telescope Results. II. Array and Instrumentation

The Event Horizon Telescope (EHT) is a very long baseline interferometry (VLBI) array that comprises millimeter- and submillimeter-wavelength telescopes separated by distances comparable to the diameter of the Earth. At a nominal operating wavelength of ~1.3 mm, EHT angular resolution (λ/D) is ~25 μas, which is sufficient to resolve nearby supermassive black hole candidates on spatial and temporal scales that correspond to their event horizons. With this capability, the EHT scientific goals are to probe general relativistic effects in the strong-field regime and to study accretion and relativistic jet formation near the black hole boundary. In this Letter we describe the system design of the EHT, detail the technology and instrumentation that enable observations, and provide measures of its performance. Meeting the EHT science objectives has required several key developments that have facilitated the robust extension of the VLBI technique to EHT observing wavelengths and the production of instrumentation that can be deployed on a heterogeneous array of existing telescopes and facilities. To meet sensitivity requirements, high-bandwidth digital systems were developed that process data at rates of 64 gigabit s−1, exceeding those of currently operating cm-wavelength VLBI arrays by more than an order of magnitude. Associated improvements include the development of phasing systems at array facilities, new receiver installation at several sites, and the deployment of hydrogen maser frequency standards to ensure coherent data capture across the array. These efforts led to the coordination and execution of the first Global EHT observations in 2017 April, and to event-horizon-scale imaging of the supermassive black hole candidate in M87