1,096 research outputs found
Two-path subsets: Efficient counting and applications to performability analysis
The problem of computing performability probabilities in stochastic PERT and flow networks is studied when the network is minimally designed to withstand any two component failures. Polynomial-time algorithms to compute performability when the network is planar - the nonplanar versions being NP-hard - solve related two-path subset problems. Given an acyclic graph with weights on the arcs, the algorithms compute the total weight of all subsets of arcs that are contained in (1) two source-sink paths, or (2) two are-disjoint source-sink paths. A polynomial algorithm is given for (1), and for (2) in the case where the graph is a source-sink planar k-flow graph, that is, cdge-minimal with respect to supporting k units of flow
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
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
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
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
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