Convergence of a collocation scheme for a retarded potential integral equation

Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations (RPIEs). Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability and convergence. We shall describe some new stable collocation schemes and use Fourier methods and techniques from the analysis of one dimensional Volterra integral equations of the first kind to demonstrate that such stable schemes are convergent

Reporting suspected abuse or neglect in research involving children.

In this article, we explore the ethical issues related to the reporting of suspected abuse or neglect in research involving children. Ethical dilemmas related to reporting child maltreatment are often complex because the rights of children and their adult caregivers may conflict and determinations of abuse or neglect are socially constructed judgments that depend on particular circumstances. We argue that when reporting is legally mandated, investigators must follow the law and report their suspicions to Child Protective Services. When reporting is not legally mandated, investigators still have an ethical obligation to report to help prevent additional maltreatment and allow children to obtain access to services needed to recover from abuse or neglect. We also argue that investigators should include plans and procedures in the research protocol for making reports and training research staff in recognising evidence of child abuse or neglect. Although investigators should report evidence of abuse or neglect that is discovered incidentally, they have no mandate to actively search for such evidence when it is not related to the study's objectives. Investigators should also inform parents and children about their obligations to report suspected abuse or neglect

The Bandwidth of Transient Yaw Effects on Vehicle Aerodynamics

A vehicle on the road encounters an unsteady flow due to turbulence in the natural wind, the unsteady wakes from other vehicles and as a result of traversing through the stationary wakes of road side obstacles. There is increasing concern about potential differences in aerodynamic behaviour measured in steady flow wind tunnel conditions and that which occurs for vehicles on the road. It is possible to introduce turbulence into the wind tunnel environment (e.g. by developing active turbulence generators) but on-road turbulence is wide ranging in terms of both its intensity and frequency and it would be beneficial to better understand what aspects of the turbulence are of greatest importance to the aerodynamic performance of vehicles. There has been significant recent work on the characterisation of turbulent airflow relevant to road vehicles. The simulation of this time-varying airflow is now becoming possible in wind tunnels and in CFD. Less is known about the range of turbulence length scales and intensities that are significant to the performance of vehicles. It is only necessary to simulate (experimentally or computationally) the Venn intersection of the range of conditions experienced and the range that are important to the vehicle's performance. The focus of this work is on transient yaw fluctuations. Time-resolved simulations of simple two dimensional parametric geometries subjected to yaw transients at a range of different time scales were conducted using Exa Powerflow. The effects of model geometry, Reynolds number yaw fluctuation amplitude and superposition were investigated. It was found that, in general, the flow could be treated as quasi-steady for reduced frequencies below 0.3 (based on model length and freestream velocity), which is consistent with theory. The most significant changes were observed in a critical reduced frequency range between ω R = 0.3 and ω R = 1.5 (scales of 4-20 vehicle lengths, or periods of 0.6 to 3s for a vehicle at 30 m/s). Higher frequencies will have significant effects, but these were observed to show little sensitivity to frequency above the critical range. Small physical features on real vehicles will add importance to smaller, but not larger, scales. The dynamic effects were largely independent of Reynolds number, including for near-inviscid conditions, indicating that the sources of the non-quasi-steady response were not viscous in origin. Increasing yaw amplitude or combining multiple frequency components did not have a summative impact suggesting that it may not be possible to describe vehicle response to transient conditions using linear concepts such as transfer or admittance functions

Assessing the nutritional quality of stored grain legume fodders: Correlations among farmers’ perceptions, sheep preferences, leaf-stem ratios and laboratory analyses

Open Access Article; Published online: 16 Mar 2022Crop residues have the potential to alleviate annual feed shortages and nutrient deficiencies experienced in the dry season in the savanna zones of West Africa. Farmers in West Africa especially value the residues of grain legumes, also known as grain legume fodders (GLFs), as animal feed. In this study, therefore, we assessed the nutritional quality of GLFs as affected by storage conditions using four different methods: farmers’ perception score (FPS), sheep preference score (SPS), leaf-to-stem ratio (LSR), and laboratory analysis of organic matter digestibility (OMD), crude protein content, neutral detergent fibre (NDF) and acid detergent fibre (ADF). We also determined correlations among these variables. The fodder of cowpea, groundnut and soybean were stored separately in three locations (rooftop, room and treefork) and with two packaging types (polythene sacks or tied with ropes) for 60, 90 and 120 days. FPS was determined by scoring the perceived quality of GLFs on a scale of 1–10 (1 = bad and 10 = good) based on physical characteristics by a group of farmers. SPS was assessed by a cafeteria feeding trial based on dry matter intake of GLFs by a flock of 12 sheep per village during a 14 hr period. LSR was determined based on the mass of the botanical fractions, i.e. leaf (leaf blade only) and stem (stem and petioles) of 200 g samples separated carefully by the hand. Laboratory analysis was done by near-infrared spectroscopy (NIRS). Results showed that all quality assessment methods successfully discriminated GLF quality differences among crops. Only farmers and sheep could distinguish quality differences among all storage conditions and packing types, whereas laboratory analyses methods could not. These findings could be due to the fact that farmers use LSR to evaluate feed quality, though colour, texture and smell of the fodder could also contribute. We also found significant correlations (ranging from 0.35 to 0.88) between all the quality assessment methods across all treatments. There were few within crop correlations between the fodder quality assessment methods, i.e. only FPS and LSR for groundnut and cowpea, FPS and CP for groundnut and all laboratory analyses parameters among each other for all crops. Hence, the differences among crops were the important determinants of the correlations. From this study, we conclude that farmers have experience and knowledge about nutritional quality of feed and livestock preference for feed. Development programmes and projects could benefit from using such knowledge when formulating and implementing interventions

Two-soliton collisions in a near-integrable lattice system

We examine collisions between identical solitons in a weakly perturbed Ablowitz-Ladik (AL) model, augmented by either onsite cubic nonlinearity (which corresponds to the Salerno model, and may be realized as an array of strongly overlapping nonlinear optical waveguides), or a quintic perturbation, or both. Complex dependences of the outcomes of the collisions on the initial phase difference between the solitons and location of the collision point are observed. Large changes of amplitudes and velocities of the colliding solitons are generated by weak perturbations, showing that the elasticity of soliton collisions in the AL model is fragile (for instance, the Salerno's perturbation with the relative strength of 0.08 can give rise to a change of the solitons' amplitudes by a factor exceeding 2). Exact and approximate conservation laws in the perturbed system are examined, with a conclusion that the small perturbations very weakly affect the norm and energy conservation, but completely destroy the conservation of the lattice momentum, which is explained by the absence of the translational symmetry in generic nonintegrable lattice models. Data collected for a very large number of collisions correlate with this conclusion. Asymmetry of the collisions (which is explained by the dependence on the location of the central point of the collision relative to the lattice, and on the phase difference between the solitons) is investigated too, showing that the nonintegrability-induced effects grow almost linearly with the perturbation strength. Different perturbations (cubic and quintic ones) produce virtually identical collision-induced effects, which makes it possible to compensate them, thus finding a special perturbed system with almost elastic soliton collisions.Comment: Phys. Rev. E, in pres

Nonlinear Modulation of Multi-Dimensional Lattice Waves

The equations governing weakly nonlinear modulations of $N$-dimensional lattices are considered using a quasi-discrete multiple-scale approach. It is found that the evolution of a short wave packet for a lattice system with cubic and quartic interatomic potentials is governed by generalized Davey-Stewartson (GDS) equations, which include mean motion induced by the oscillatory wave packet through cubic interatomic interaction. The GDS equations derived here are more general than those known in the theory of water waves because of the anisotropy inherent in lattices. Generalized Kadomtsev-Petviashvili equations describing the evolution of long wavelength acoustic modes in two and three dimensional lattices are also presented. Then the modulational instability of a $N$-dimensional Stokes lattice wave is discussed based on the $N$-dimensional GDS equations obtained. Finally, the one- and two-soliton solutions of two-dimensional GDS equations are provided by means of Hirota's bilinear transformation method.Comment: Submitted to PR

Short Gamma Ray Bursts as possible electromagnetic counterpart of coalescing binary systems

Coalescing binary systems, consisting of two collapsed objects, are among the most promising sources of high frequency gravitational waves signals detectable, in principle, by ground-based interferometers. Binary systems of Neutron Star or Black Hole/Neutron Star mergers should also give rise to short Gamma Ray Bursts, a subclass of Gamma Ray Bursts. Short-hard-Gamma Ray Bursts might thus provide a powerful way to infer the merger rate of two-collapsed object binaries. Under the hypothesis that most short Gamma Ray Bursts originate from binaries of Neutron Star or Black Hole/Neutron Star mergers, we outline here the possibility to associate short Gamma Ray Bursts as electromagnetic counterpart of coalescing binary systems.Comment: 4 pages, 1 figur

Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

Causal categories: relativistically interacting processes

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a `causal category'. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.Comment: 43 pages, lots of figure

Sialic acid-to-urea ratio as a measure of airway surface hydration

Although airway mucus dehydration is key to pathophysiology of cystic fibrosis (CF) and other airways diseases, measuring mucus hydration is challenging. We explored a robust method to estimate mucus hydration using sialic acid as a marker for mucin content. Terminal sialic acid residues from mucins were cleaved by acid hydrolysis from airway samples, and concentrations of sialic acid, urea, and other biomarkers were analyzed by mass spectrometry. In mucins purified from human airway epithelial (HAE), sialic acid concentrations after acid hydrolysis correlated with mucin concentrations (r2 = 0.92). Sialic acid-to-urea ratios measured from filters applied to the apical surface of cultured HAE correlated to percent solids and were elevated in samples from CF HAEs relative to controls (2.2 ± 1.1 vs. 0.93 ± 1.8, P < 0.01). Sialic acid-to-urea ratios were elevated in bronchoalveolar lavage fluid (BALF) from β-epithelial sodium channel (ENaC) transgenic mice, known to have reduced mucus hydration, and mice sensitized to house dust mite allergen. In a translational application, elevated sialic acid-to-urea ratios were measured in BALF from young children with CF who had airway infection relative to those who did not (5.5 ± 3.7 vs. 1.9 ± 1.4, P < 0.02) and could be assessed simultaneously with established biomarkers of inflammation. The sialic acid-to-urea ratio performed similarly to percent solids, the gold standard measure of mucus hydration. The method proved robust and has potential to serve as flexible techniques to assess mucin hydration, particularly in samples like BALF in which established methods such as percent solids cannot be utilized