Error of truncated Chebyshev series and other near minimax polynomial approximations

AbstractIt is well known that a near minimax polynomial approximation p is obtained by truncating the Chebyshev series of a function ƒ; after n + 1 terms. It is shown that if ƒ; ϵ C(n + 1)[−1, 1], then ∥ƒ; − p ∥ may be expressed in terms of ƒ;(n + 1) in the same manner as the error of minimax approximation. The result is extended to other types of near minimax approximation

Fine structure of excitons in Cu2_2O

Three experimental observations on 1s-excitons in Cu$_2$O are not consistent with the picture of the exciton as a simple hydrogenic bound state: the energies of the 1s-excitons deviate from the Rydberg formula, the total exciton mass exceeds the sum of the electron and hole effective masses, and the triplet-state excitons lie above the singlet. Incorporating the band structure of the material, we calculate the corrections to this simple picture arising from the fact that the exciton Bohr radius is comparable to the lattice constant. By means of a self-consistent variational calculation of the total exciton mass as well as the ground-state energy of the singlet and the triplet-state excitons, we find excellent agreement with experiment.Comment: Revised abstract; 10 pages, revtex, 3 figures available from G. Kavoulakis, Physics Department, University of Illinois, Urban

Binding of Polarons and Atoms at Threshold

If the polaron coupling constant $\alpha$ is large enough, bipolarons or multi-polarons will form. When passing through the critical $\alpha_c$ from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explodes? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at $\alpha_c$. Similarly, we show that the same phenomenon occurs for atoms, e.g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schr\"odinger equation, and are very general. They use the fact that the Coulomb repulsion decays like $1/r$, while `uncertainty principle' localization energies decay more rapidly, as $1/r^2$.Comment: 19 page

Auger decay of degenerate and Bose-condensed excitons in Cu2_2O

We study the non-radiative Auger decay of excitons in Cu$_2$O, in which two excitons scatter to an excited electron and hole. The exciton decay rate for the direct and the phonon-assisted processes is calculated from first principles; incorporating the band structure of the material leads to a relatively shorter lifetime of the triplet state ortho excitons. We compare our results with the Auger decay rate extracted from data on highly degenerate triplet excitons and Bose-condensed singlet excitons in Cu$_2$O.Comment: 15 pages, revtex, figures available from G. Kavoulaki

ASTEC -- the Aarhus STellar Evolution Code

The Aarhus code is the result of a long development, starting in 1974, and still ongoing. A novel feature is the integration of the computation of adiabatic oscillations for specified models as part of the code. It offers substantial flexibility in terms of microphysics and has been carefully tested for the computation of solar models. However, considerable development is still required in the treatment of nuclear reactions, diffusion and convective mixing.Comment: Astrophys. Space Sci, in the pres

Origin of depleted basalts during subduction initiation and early development of the Izu-Bonin-Mariana island arc: Evidence from IODP expedition 351 site U1438, Amami-Sankaku basin

The Izu-Bonin-Mariana (IBM) island arc formed following initiation of subduction of the Pacific plate beneath the Philippine Sea plate at about 52 Ma. Site U1438 of IODP Expedition 351 was drilled to sample the oceanic basement on which the IBM arc was constructed, to better understand magmatism prior to and during the subduction initiation event. Site U1438 igneous basement Unit 1 (150 m) was drilled beneath 1460 m of primarily volcaniclastic sediments and sedimentary rock. Basement basalts are microcrystalline to fine-grained flows and form several distinct subunits (1a-1f), all relatively mafic (MgO = 6.5–13.8%; Mg# = 52–83), with Cr = 71–506 ppm and Ni = 62–342 ppm. All subunits are depleted in non-fluid mobile incompatible trace elements. Ratios such as Sm/Nd (0.35–0.44), Lu/Hf (0.19–0.37), and Zr/Nb (55–106) reach the highest values found in MORB, while La/Yb (0.31–0.92), La/Sm (0.43–0.91) and Nb/La (0.39–0.59) reach the lowest values. Abundances of fluid-mobile incompatible elements, K, Rb, Cs and U, vary with rock physical properties, indicating control by post-eruptive seawater alteration, but lowest abundances are typical of fresh, highly depleted MORBs. Mantle sources for the different subunits define a trend of progressive incompatible element depletion. Inferred pressures of magma segregation are 0.6–2.1 GPa with temperatures of 1280–1470 °C. New 40Ar/39Ar dates for Site U1438 basalts averaging 48.7 Ma (Ishizuka et al., 2018) are younger that the inferred age of IBM subduction initiation based on the oldest ages (52 Ma) of IBM forearc basalts (FAB) from the eastern margin of the Philippine Sea plate. FAB are hypothesized to be the first magma type erupted as the Pacific plate subsided, followed by boninites, and ultimately typical arc magmas over a period of about 10 Ma. Site U1438 basalts and IBM FABs are similar, but Site U1438 basalts have lower V contents, higher Ti/V and little geochemical evidence for involvement of slab-derived fluids. We hypothesize that the asthenospheric upwelling and extension expected during subduction initiation occurred over a broad expanse of the upper plate, even as hydrous fluids were introduced near the plate edge to produce FABs and boninites. Site U1438 basalts formed by decompression melting during the first 3 Ma of subduction initiation, and were stranded behind the early IBM arc as mantle conditions shifted to flux melting beneath a well-defined volcanic front

The Korringa-Kohn-Rostoker Non-Local Coherent Potential Approximation (KKR-NLCPA)

We introduce the Korringa-Kohn-Rostocker non-local coherent potential approximation (KKR-NLCPA) for describing the electronic structure of disordered systems. The KKR-NLCPA systematically provides a hierarchy of improvements upon the widely used KKR-CPA approach and includes non-local correlations in the disorder configurations by means of a self-consistently embedded cluster. The KKR-NLCPA method satisfies all of the requirements for a successful cluster generalization of the KKR-CPA; it remains fully causal, becomes exact in the limit of large cluster sizes, reduces to the KKR-CPA for a single-site cluster, is straightforward to implement numerically, and enables the effects of short-range order upon the electronic structure to be investigated. In particular, it is suitable for combination with electronic density functional theory to give an ab-initio description of disordered systems. Future applications to charge correlation and lattice displacement effects in alloys and spin fluctuations in magnets amongst others are very promising. We illustrate the method by application to a simple one-dimensional model.Comment: Revised versio

Origins of the Ambient Solar Wind: Implications for Space Weather

The Sun's outer atmosphere is heated to temperatures of millions of degrees, and solar plasma flows out into interplanetary space at supersonic speeds. This paper reviews our current understanding of these interrelated problems: coronal heating and the acceleration of the ambient solar wind. We also discuss where the community stands in its ability to forecast how variations in the solar wind (i.e., fast and slow wind streams) impact the Earth. Although the last few decades have seen significant progress in observations and modeling, we still do not have a complete understanding of the relevant physical processes, nor do we have a quantitatively precise census of which coronal structures contribute to specific types of solar wind. Fast streams are known to be connected to the central regions of large coronal holes. Slow streams, however, appear to come from a wide range of sources, including streamers, pseudostreamers, coronal loops, active regions, and coronal hole boundaries. Complicating our understanding even more is the fact that processes such as turbulence, stream-stream interactions, and Coulomb collisions can make it difficult to unambiguously map a parcel measured at 1 AU back down to its coronal source. We also review recent progress -- in theoretical modeling, observational data analysis, and forecasting techniques that sit at the interface between data and theory -- that gives us hope that the above problems are indeed solvable.Comment: Accepted for publication in Space Science Reviews. Special issue connected with a 2016 ISSI workshop on "The Scientific Foundations of Space Weather." 44 pages, 9 figure

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters