Accurate boundary conditions for exterior problems in gas dynamics

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory

Far field expansion for anisotropic wave equations

A necessary ingredient for the numerical simulation of many time dependent phenomena in acoustics and aerodynamics is the imposition of accurate radiation conditions at artificial boundaries. The asymptotic analysis of propagating waves provides a rational approach to the development of such conditions. A far field asymptotic expansion of solutions of anisotropic wave equations is derived. This generalizes the well known Friedlander expansion for the standard wave operator. The expansion is used to derive a hierarchy of radiation conditions of increasing accuracy. Two numerical experiments are given to illustrate the utility of this approach. The first application is the study of unsteady vortical disturbances impinging on a flat plate; the second is the simulation of inviscid flow past an impulsively started cylinder

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds

Comparative Analysis Of Zebrafish And Planarian Model Systems For Developmental Neurotoxicity Screens Using An 87-Compound Library

There is a clear need to establish and validate new methodologies to more quickly and efficiently screen chemicals for potential toxic effects, particularly on development. The emergence of alternative animal systems for rapid toxicology screens presents valuable opportunities to evaluate how systems complement each other. In this article, we compare a chemical library of 87-compounds in two such systems, developing zebrafish and freshwater planarians, by screening for developmental neurotoxic effects. We show that the systems’ toxicological profiles are complementary to each other, with zebrafish yielding more detailed morphological endpoints and planarians more behavioral endpoints. Overall, zebrafish was more sensitive to this chemical library, yielding 86/87 hits, compared to 50/87 hits in planarians. The difference in sensitivity could not be attributed to molecular weight, Log Kow or the bioconcentration factor. Of the 87 chemicals, 28 had previously been evaluated in mammalian developmental neuro- (DNT), neuro- or developmental toxicity studies. Of the 28, 20 were hits in the planarian, and 27 were hits in zebrafish. Eighteen of the 28 had previously been identified as DNT hits in mammals and were highly associated with activity in zebrafish and planarian behavioral assays in this study. Only 1 chemical (out of 28) was a false negative in both zebrafish and planarian systems. Differences in endpoint coverage and system sensitivity illustrate the value of a dual systems approach to rapidly query a large chemical-bioactivity space and provide weight-of-evidence for prioritization of chemicals for further testing

Multi-Behavioral Endpoint Testing Of An 87-Chemical Compound Library In Freshwater Planarians

There is an increased recognition in the field of toxicology of the value of medium-to-high-throughput screening methods using in vitro and alternative animal models. We have previously introduced the asexual freshwater planarian Dugesia japonica as a new alternative animal model and proposed that it is particularly well-suited for the study of developmental neurotoxicology. In this paper, we discuss how we have expanded and automated our screening methodology to allow for fast screening of multiple behavioral endpoints, developmental toxicity, and mortality. Using an 87-compound library provided by the National Toxicology Program (NTP), consisting of known and suspected neurotoxicants, including drugs, flame retardants, industrial chemicals, polycyclic aromatic hydrocarbons (PAHs), pesticides and presumptive negative controls, we further evaluate the benefits and limitations of the system for medium-throughput screening, focusing on the technical aspects of the system. We show that, in the context of this library, planarians are the most sensitive to pesticides with 16/16 compounds causing toxicity and the least sensitive to PAHs, with only 5/17 causing toxicity. Furthermore, while none of the presumptive negative controls were bioactive in adult planarians, 2/5, acetaminophen and acetylsalicylic acid, were bioactive in regenerating worms. Notably, these compounds were previously reported as developmentally toxic in mammalian studies. Through parallel screening of adults and developing animals, planarians are thus a useful model to detect such developmental-specific effects, which was observed for 13 chemicals in this library. We use the data and experience gained from this screen to propose guidelines for best practices when using planarians for toxicology screens

Studying Planarian Regeneration Aboard The International Space Station Within The Student Space Flight Experimental Program

The growing possibilities of space travel are quickly moving from science fiction to reality. However, to realize the dream of long-term space travel, we must understand how these conditions affect biological and physiological processes. Planarians are master regenerators, famous for their ability to regenerate from very small parts of the original animal. Understanding how this self-repair works may inspire regenerative therapies in humans. Two studies conducted aboard the International Space Station (ISS) showed that planarian regeneration is possible in microgravity. One study reported no regenerative defects, whereas the other study reported behavioral and microbiome alterations post-space travel and found that 1 of 15 planarians regenerated a Janus head, suggesting that microgravity exposure may not be without consequences. Given the limited number of studies and specimens, further microgravity experiments are necessary to evaluate the effects of microgravity on planarian regeneration. Such studies, however, are generally difficult and expensive to conduct. We were fortunate to be sponsored by the Student Spaceflight Experiment Program (SSEP) to investigate how microgravity affects regeneration of the planarian species Dugesia japonica on the ISS. While we were unable to successfully study planarian regeneration within the experimental constraints of our SSEP Mission, we systematically analyzed the cause for the failed experiment, leading us to propose a modified protocol. This work thus opens the door for future experiments on the effects of microgravity on planarian regeneration on SSEP Missions as well as for more advanced experiments by professional researchers

Progressive wave expansions and open boundary problems

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory

Hyperboloidal evolution of test fields in three spatial dimensions

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.Comment: 10 pages, 8 figure

A nonstationary form of the range refraction parabolic equation and its application as an artificial boundary condition for the wave equation in a waveguide

The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundary condition for the wave equation in a waveguide. The numerical comparison with Higdon's absorbing boundary conditions shows sufficiently good quality of the new boundary condition at low computational cost.Comment: 12 pages, 9 figure

Null infinity waveforms from extreme-mass-ratio inspirals in Kerr spacetime

We describe the hyperboloidal compactification for Teukolsky equations in Kerr spacetime. We include null infinity on the numerical grid by attaching a hyperboloidal layer to a compact domain surrounding the rotating black hole and the orbit of an inspiralling point particle. This technique allows us to study, for the first time, gravitational waveforms from large- and extreme-mass-ratio inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons of our results with previous calculations establish the accuracy and efficiency of the hyperboloidal layer method.Comment: 14 pages, 7 figure