Constraining population synthesis models via the binary neutron star population

The observed sample of double neutron-star (NS-NS) binaries presents a challenge to population-synthesis models of compact object formation: the parameters entering into these models must be carefully chosen so as to match (i) the observed star formation rate and (ii) the formation rate of NS-NS binaries, which can be estimated from the observed sample and the selection effects related to the discoveries with radio-pulsar surveys. In this paper, we select from an extremely broad family of possible population synthesis models those few (2%) which are consistent with the observed sample of NS-NS binaries. To further sharpen the constraints the observed NS-NS population places upon our understanding of compact-object formation processes, we separate the observed NS-NS population into two channels: (i) merging NS-NS binaries, which will inspiral and merge through the action of gravitational waves within $10$ Gyr, and (ii) wide NS-NS binaries, consisting of all the rest. With the subset of astrophysically consistent models, we explore the implications for the rates at which double black hole (BH-BH), black hole-neutron star (BH-NS), and NS-NS binaries will merge through the emission of gravitational waves.Comment: (v1) Submitted to ApJ. Uses emulateapj.cls. 8 pages, 7 figures. (v2) Minor textual changes in response to referee queries. Substantial additions in appendicies, including a detailed discussion of sample multidimensional population synthesis fit

Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution

The nonlinear diffusion equation $\frac{\partial \rho}{\partial t}=D \tilde{\Delta} \rho^\nu$ is analyzed here, where $\tilde{\Delta}\equiv \frac{1}{r^{d-1}}\frac{\partial}{\partial r} r^{d-1-\theta} \frac{\partial}{\partial r}$, and $d$, $\theta$ and $\nu$ are real parameters. This equation unifies the anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). Exact point-source solution is obtained, enabling us to describe a large class of subdiffusion ($\theta > (1-\nu)d$), normal diffusion ($\theta= (1-\nu)d$) and superdiffusion ($\theta < (1-\nu)d$). Furthermore, a thermostatistical basis for this solution is given from the maximum entropic principle applied to the Tsallis entropy.Comment: 3 pages, 2 eps figure

Irreversibility and Polymer Adsorption

Physisorption or chemisorption from dilute polymer solutions often entails irreversible polymer-surface bonding. We present a theory of the non-equilibrium layers which result. While the density profile and loop distribution are the same as for equilibrium layers, the final layer comprises a tightly bound inner part plus an outer part whose chains make only fN surface contacts where N is chain length. The contact fractions f follow a broad distribution, P(f) ~ f^{-4/5}, in rather close agreement with strong physisorption experiments [H. M. Schneider et al, Langmuir v.12, p.994 (1996)].Comment: 4 pages, submitted to Phys. Rev. Let

The Ultrasensitivity of Living Polymers

Synthetic and biological living polymers are self-assembling chains whose chain length distributions (CLDs) are dynamic. We show these dynamics are ultrasensitive: even a small perturbation (e.g. temperature jump) non-linearly distorts the CLD, eliminating or massively augmenting short chains. The origin is fast relaxation of mass variables (mean chain length, monomer concentration) which perturbs CLD shape variables before these can relax via slow chain growth rate fluctuations. Viscosity relaxation predictions agree with experiments on the best-studied synthetic system, alpha-methylstyrene.Comment: 4 pages, submitted to Phys. Rev. Let

Efficacy of eribulin for metastatic breast cancer based on localization of specific secondary metastases: a post hoc analysis

Prior pooled analysis of eribulin studies (301 and 305) indicated eribulin prolonged overall survival (OS) in patients with locally advanced/metastatic breast cancer (MBC) regardless of visceral or nonvisceral disease. This hypothesis-generating post hoc analysis examined the efficacy of eribulin according to the location of metastatic sites at baseline in 1864 pretreated patients with locally advanced/MBC from studies 301 and 305. Analyses included OS, progression-free survival (PFS), and objective response rate; OS and PFS were also analyzed according to estrogen-receptor status. Eribulin appeared efficacious in patients with locally advanced/MBC, irrespective of the location of metastases at baseline. A nominally significant difference in OS in favor of patients randomized to eribulin compared with control in patients with bone, lymph node, and chest wall/breast/skin metastases at baseline was observed. Additionally, a difference in OS was also seen in patients with liver metastases randomized to eribulin versus control (median: 13.4 versus 11.3 months, respectively; hazard ratio, 0.84 [95% CI: 0.72, 0.97]). Results of this exploratory analysis suggest that eribulin may be efficacious for the treatment of locally advanced/MBC for patients with bone, liver, lung, lymph node, and chest wall/breast/skin metastases

Transition from inspiral to plunge for eccentric equatorial Kerr orbits

Ori and Thorne have discussed the duration and observability (with LISA) of the transition from circular, equatorial inspiral to plunge for stellar-mass objects into supermassive ($10^{5}-10^{8}M_{\odot}$) Kerr black holes. We extend their computation to eccentric Kerr equatorial orbits. Even with orbital parameters near-exactly determined, we find that there is no universal length for the transition; rather, the length of the transition depends sensitively -- essentially randomly -- on initial conditions. Still, Ori and Thorne's zero-eccentricity results are essentially an upper bound on the length of eccentric transitions involving similar bodies (e.g., $a$ fixed). Hence the implications for observations are no better: if the massive body is $M=10^{6}M_{\odot}$, the captured body has mass $m$, and the process occurs at distance $d$ from LISA, then $S/N \lesssim (m/10 M_{\odot})(1\text{Gpc}/d)\times O(1)$, with the precise constant depending on the black hole spin. For low-mass bodies ($m \lesssim 7 M_\odot$) for which the event rate is at least vaguely understood, we expect little chance (probably [much] less than 10%, depending strongly on the astrophysical assumptions) of LISA detecting a transition event with $S/N>5$ during its run; however, even a small infusion of higher-mass bodies or a slight improvement in LISA's noise curve could potentially produce $S/N>5$ transition events during LISA's lifetime.Comment: Submitted to PR

Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized gaussian solution

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the $N$-dimensional nonlinear diffusion equation $\partial\rho /\partial{t}={\bf \nabla} \cdot (K{\bf \nabla} \rho^{\nu})-{\bf \nabla}\cdot(\mu{\bf F} \rho)-\alpha \rho ,$ where $K=D r^{-\theta}$, $\nu$, $\theta$, $\mu$ and $D$ are real parameters and $\alpha$ is a time-dependent source. This equation unifies the O'Shaugnessy-Procaccia anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.Comment: Latex, 6 pages. To appear in Phys. Rev.

Factors affecting the local distribution of <i>Polystigma rubrum</i> stromata on <i>Prunus spinosa</i>

Background and aims – Polystigma rubrum forms orange-red stromata on the surface of living leaves of Prunus spinosa and P. domestica. Records suggests that this fungus now has a much more limited distribution in Britain than recorded in the 19th and early 20th century. Methods – We studied the local distribution of the fungus in the Burren Hills of western Ireland where it remains very common. Key results – Assessment of the local distribution of the fungus over two years found stromata to occur more frequently on P. spinosa leaves in hedgerows than woodlands. On individual trees in areas of open limestone pavement, the frequency of stromata was ten times higher in 2016 than 2015, possibly related to interannual rainfall differences. On hedgerow trees subjected to winter flooding, stromata were much less abundant, whereas stromata were more abundant on leaves also infected by the gall mite Eriophyes prunispinosae. The identity of Po. rubrum was confirmed by ITS sequencing.Conclusion – At a field location where Po. rubrum stromata are present in unusually high abundance, the distribution of stromata on trees in different habitats showed high levels of variation linked to both habitat and the presence of gall mites. Further work is required to determine whether variation in leaf surface and soil moisture are the key determinants of the observed distribution. Such investigations may reveal why Po. rubrum, once common in northern Europe is now restricted mainly to westerly, coastal locations

Effects of chiropractic spinal manipulation on laser-evoked pain and brain activity

The aim of this study was to examine the mechanisms underlying hypoalgesia induced by spinal manipulation (SM). Eighty-two healthy volunteers were assigned to one of the four intervention groups: no intervention, SM at T4 (homosegmental to pain), SM at T8 (heterosegmental to pain) or light mechanical stimulus at T4 (placebo). Eighty laser stimuli were applied on back skin at T4 to evoke pain and brain activity related to Aδ- and C-fibers activation. The intervention was performed after 40 stimuli. Laser pain was decreased by SM at T4 (p = 0.028) but not T8 (p = 0.13), compared with placebo. However, brain activity related to Aδ-fibers activation was not significantly modulated (all p > 0.05), while C-fiber activity could not be measured reliably. This indicates that SM produces segmental hypoalgesia through inhibition of nociceptive processes that are independent of Aδ fibers. It remains to be clarified whether the effect is mediated by the inhibition of C-fiber activity. [Figure not available: see fulltext.]. © 2021, The Author(s)

Mechanical response of plectonemic DNA: an analytical solution

We consider an elastic rod model for twisted DNA in the plectonemic regime. The molecule is treated as an impenetrable tube with an effective, adjustable radius. The model is solved analytically and we derive formulas for the contact pressure, twisting moment and geometrical parameters of the supercoiled region. We apply our model to magnetic tweezer experiments of a DNA molecule subjected to a tensile force and a torque, and extract mechanical and geometrical quantities from the linear part of the experimental response curve. These reconstructed values are derived in a self-contained manner, and are found to be consistent with those available in the literature.Comment: 14 pages, 4 figure