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

Treatability Variance Petition for SRS Raschig Ring Packing Material

The Department of Energy's Savannah River Site (SRS) is a vital component in the nation's nuclear weapons complex. When in full operation, SRS produced nuclear material by manufacturing fuel and target components that were then irradiated in nuclear reactors

Savannah River Site sample and analysis plan for Clemson Technical Center waste

The purpose of this sampling and analysis plan is to determine the chemical, physical and radiological properties of the SRS radioactive Polychlorinated Biphenyl (PCB) liquid waste stream, to verify that it conforms to Waste Acceptance Criteria of the Department of Energy (DOE) East Tennessee Technology Park (ETTP) Toxic Substance Control Act (TSCA) Incineration Facility. Waste being sent to the ETTP TSCA Incinerator for treatment must be sufficiently characterized to ensure that the waste stream meets the waste acceptance criteria to ensure proper handling, classification, and processing of incoming waste to meet the Waste Storage and Treatment Facility`s Operating Permits. This sampling and analysis plan is limited to WSRC container(s) of homogeneous or multiphasic radioactive PCB contaminated liquids generated in association with a treatability study at Clemson Technical Center (CTC) and currently stored at the WSRC Solid Waste Division Mixed Waste Storage Facility (MWSF)

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

Would You Choose to be Happy? Tradeoffs Between Happiness and the Other Dimensions of Life in a Large Population Survey

A large literature documents the correlates and causes of subjective well-being, or happiness. But few studies have investigated whether people choose happiness. Is happiness all that people want from life, or are they willing to sacrifice it for other attributes, such as income and health? Tackling this question has largely been the preserve of philosophers. In this article, we find out just how much happiness matters to ordinary citizens. Our sample consists of nearly 13,000 members of the UK and US general populations. We ask them to choose between, and make judgments over, lives that are high (or low) in different types of happiness and low (or high) in income, physical health, family, career success, or education. We find that people by and large choose the life that is highest in happiness but health is by far the most important other concern, with considerable numbers of people choosing to be healthy rather than happy. We discuss some possible reasons for this preference

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

Mode signature and stability for a Hamiltonian model of electron temperature gradient turbulence

Stability properties and mode signature for equilibria of a model of electron temperature gradient (ETG) driven turbulence are investigated by Hamiltonian techniques. After deriving the infinite families of Casimir invariants, associated with the noncanonical Poisson bracket of the model, a sufficient condition for stability is obtained by means of the Energy-Casimir method. Mode signature is then investigated for linear motions about homogeneous equilibria. Depending on the sign of the equilibrium "translated" pressure gradient, stable equilibria can either be energy stable, i.e.\ possess definite linearized perturbation energy (Hamiltonian), or spectrally stable with the existence of negative energy modes (NEMs). The ETG instability is then shown to arise through a Kre\u{\i}n-type bifurcation, due to the merging of a positive and a negative energy mode, corresponding to two modified drift waves admitted by the system. The Hamiltonian of the linearized system is then explicitly transformed into normal form, which unambiguously defines mode signature. In particular, the fast mode turns out to always be a positive energy mode (PEM), whereas the energy of the slow mode can have either positive or negative sign

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation

Ultrasensitive immuno-detection using viral nanoparticles with modular assembly using genetically-directed biotinylation

We report a novel, modular approach to immuno-detection based on antibody recognition and PCR read-out that employs antibody-conjugated bacteriophage, easily-manipulated nonpathogenic viruses, as affinity agents. Our platform employs phage genetically tagged for in vivo biotinylation during phage maturation that can easily be linked, through avidin, to any biotinylatable affinity agent, including full-length antibodies, peptides, lectins or aptamers. The presence of analyte is reported with high sensitivity through real-time PCR. This approach avoids the need to clone antibody-encoding DNA fragments, allows the use of full-length, high affinity antibodies and, by having DNA reporters naturally encapsulated inside the bacteriophage, greatly reduces nonspecific binding of DNA. We validate the efficacy of this new approach through the detection of VEGF (Vascular Endothelial Growth Factor), a known angiogenic cancer biomarker protein, at attomolar concentrations in bronchoalveolar lavage (BAL) fluid