Extending the range of error estimates for radial approximation in Euclidean space and on spheres

We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of R^d and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.Comment: 10 page

Phonons in random alloys: the itinerant coherent-potential approximation

We present the itinerant coherent-potential approximation(ICPA), an analytic, translationally invariant and tractable form of augmented-space-based, multiple-scattering theory in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni_{55} Pd_{45} and Ni_{50} Pt_{50} alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation(CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.Comment: 19 pages, 12 eps figures, uses RevTex

A First Comparison of the responses of a He4-based fast-neutron detector and a NE-213 liquid-scintillator reference detector

A first comparison has been made between the pulse-shape discrimination characteristics of a novel $^{4}$He-based pressurized scintillation detector and a NE-213 liquid-scintillator reference detector using an Am/Be mixed-field neutron and gamma-ray source and a high-resolution scintillation-pulse digitizer. In particular, the capabilities of the two fast neutron detectors to discriminate between neutrons and gamma-rays were investigated. The NE-213 liquid-scintillator reference cell produced a wide range of scintillation-light yields in response to the gamma-ray field of the source. In stark contrast, due to the size and pressure of the $^{4}$He gas volume, the $^{4}$He-based detector registered a maximum scintillation-light yield of 750~keV$_{ee}$ to the same gamma-ray field. Pulse-shape discrimination for particles with scintillation-light yields of more than 750~keV$_{ee}$ was excellent in the case of the $^{4}$He-based detector. Above 750~keV$_{ee}$ its signal was unambiguously neutron, enabling particle identification based entirely upon the amount of scintillation light produced.Comment: 23 pages, 7 figures, Nuclear Instruments and Methods in Physics Research Section A review addresse

Towards a first principles description of phonons in Ni50_{50}Pt50_{50} disordered alloys: the role of relaxation

Using a combination of density-functional perturbation theory and the itinerant coherent potential approximation, we study the effects of atomic relaxation on the inelastic incoherent neutron scattering cross sections of disordered Ni$_{50}$Pt$_{50}$ alloys. We build on previous work, where empirical force constants were adjusted {\it ad hoc} to agree with experiment. After first relaxing all structural parameters within the local-density approximation for ordered NiPt compounds, density-functional perturbation theory is then used to compute phonon spectra, densities of states, and the force constants. The resulting nearest-neighbor force constants are first compared to those of other ordered structures of different stoichiometry, and then used to generate the inelastic scattering cross sections within the itinerant coherent potential approximation. We find that structural relaxation substantially affects the computed force constants and resulting inelastic cross sections, and that the effect is much more pronounced in random alloys than in ordered alloys.Comment: 8 pages, 3 eps figures, uses revtex

Electromagnetic Cascades and Cascade Nucleosynthesis in the Early Universe

We describe a calculation of electromagnetic cascading in radiation and matter in the early universe initiated by the decay of massive particles or by some other process. We have used a combination of Monte Carlo and numerical techniques which enables us to use exact cross sections, where known, for all the relevant processes. In cascades initiated after the epoch of big bang nucleosynthesis $\gamma$-rays in the cascades will photodisintegrate $^4$He, producing $^3$He and deuterium. Using the observed $^3$He and deuterium abundances we are able to place constraints on the cascade energy deposition as a function of cosmic time. In the case of the decay of massive primordial particles, we place limits on the density of massive primordial particles as a function of their mean decay time, and on the expected intensity of decay neutrinos.Comment: compressed and uuencoded postscript. We now include a comparison with previous work of the photon spectrum in the cascade and the limits we calculate for the density of massive particles. The method of calculation of photon spectra at low energies has been improved. Most figures are revised. Our conclusions are substantially unchange

Self-Organized Criticality in Compact Plasmas

Compact plasmas, that exist near black-hole candidates and in gamma ray burst sources, commonly exhibit self-organized non-linear behavior. A model that simulates the non-linear behavior of compact radiative plasmas is constructed directly from the observed luminosity and variability. The simulation shows that such plasmas self organize, and that the degree of non-linearity as well as the slope of the power density spectrum increase with compactness. The simulation is based on a cellular automaton table that includes the properties of the hot (relativistic) plasmas, and the magnitude of the energy perturbations. The plasmas cool or heat up, depending on whether they release more or less than the energy of a single perturbation. The energy release depends on the plasmas densities and temperatures, and the perturbations energy. Strong perturbations may cool the previously heated plasma through shocks and/or pair creation. New observations of some active galactic nuclei and gamma ray bursters are consistent with the simulationComment: 9 pages, 5 figures, AASTeX, Submitted to ApJ

Coulomb correlation effects in zinc monochalcogenides

Electronic structure and band characteristics for zinc monochalcogenides with zinc-blende- and wurtzite-type structures are studied by first-principles density-functional-theory calculations with different approximations. It is shown that the local-density approximation underestimates the band gap and energy splitting between the states at the top of the valence band, misplaces the energy levels of the Zn-3d states, and overestimates the crystal-field-splitting energy. Regardless of the structure type considered, the spin-orbit-coupling energy is found to be overestimated for ZnO and underestimated for ZnS with wurtzite-type structure, and more or less correct for ZnSe and ZnTe with zinc-blende-type structure. The order of the states at the top of the valence band is found to be anomalous for ZnO in both zinc-blende- and wurtzite-type structure, but is normal for the other zinc monochalcogenides considered. It is shown that the Zn-3d electrons and their interference with the O-2p electrons are responsible for the anomalous order. The typical errors in the calculated band gaps and related parameters for ZnO originate from strong Coulomb correlations, which are found to be highly significant for this compound. The LDA+U approach is by and large found to correct the strong correlation of the Zn-3d electrons, and thus to improve the agreement with the experimentally established location of the Zn-3d levels compared with that derived from pure LDA calculations

Electronic structure and optical properties of ZnX (X=O, S, Se, Te)

Electronic band structure and optical properties of zinc monochalcogenides with zinc-blende- and wurtzite-type structures were studied using the ab initio density functional method within the LDA, GGA, and LDA+U approaches. Calculations of the optical spectra have been performed for the energy range 0-20 eV, with and without including spin-orbit coupling. Reflectivity, absorption and extinction coefficients, and refractive index have been computed from the imaginary part of the dielectric function using the Kramers--Kronig transformations. A rigid shift of the calculated optical spectra is found to provide a good first approximation to reproduce experimental observations for almost all the zinc monochalcogenide phases considered. By inspection of the calculated and experimentally determined band-gap values for the zinc monochalcogenide series, the band gap of ZnO with zinc-blende structure has been estimated.Comment: 17 pages, 10 figure

Testing Consumer Rationality using Perfect Graphs and Oriented Discs

Given a consumer data-set, the axioms of revealed preference proffer a binary test for rational behaviour. A natural (non-binary) measure of the degree of rationality exhibited by the consumer is the minimum number of data points whose removal induces a rationalisable data-set.We study the computational complexity of the resultant consumer rationality problem in this paper. This problem is, in the worst case, equivalent (in terms of approximation) to the directed feedback vertex set problem. Our main result is to obtain an exact threshold on the number of commodities that separates easy cases and hard cases. Specifically, for two-commodity markets the consumer rationality problem is polynomial time solvable; we prove this via a reduction to the vertex cover problem on perfect graphs. For three-commodity markets, however, the problem is NP-complete; we prove thisusing a reduction from planar 3-SAT that is based upon oriented-disc drawings