Deformation of LeBrun's ALE metrics with negative mass

In this article we investigate deformations of a scalar-flat K\"ahler metric on the total space of complex line bundles over CP^1 constructed by C. LeBrun. In particular, we find that the metric is included in a one-dimensional family of such metrics on the four-manifold, where the complex structure in the deformation is not the standard one.Comment: 20 pages, no figure. V2: added two references, filled a gap in the proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family of a Hirzebruch surface stated in the last paragraph in the proof of Theorem 1.2, and fixed a relevant error in the proof. Also added a reference [24] about Kuranishi family of Hirzebruch surface

Fractal boundary basins in spherically symmetric ϕ4\phi^4 theory

Results are presented from numerical simulations of the flat-space nonlinear Klein-Gordon equa- tion with an asymmetric double-well potential in spherical symmetry. Exit criteria are defined for the simulations that are used to help understand the boundaries of the basins of attraction for Gaussian "bubble" initial data. The first exit criteria, based on the immediate collapse or expan- sion of bubble radius, is used to observe the departure of the scalar field from a static intermediate attractor solution. The boundary separating these two behaviors in parameter space is smooth and demonstrates a time-scaling law with an exponent that depends on the asymmetry of the potential. The second exit criteria differentiates between the creation of an expanding true-vacuum bubble and dispersion of the field leaving the false vacuum; the boundary separating these basins of attraction is shown to demonstrate fractal behavior. The basins are defined by the number of bounces that the field undergoes before inducing a phase transition. A third, hybrid exit criteria is used to determine the location of the boundary to arbitrary precision and to characterize the threshold behavior. The possible effects this behavior might have on cosmological phase transitions are briefly discussed.Comment: 10 pages, 13 figures, 1 movie, resubmitted with additional paragraph. Matches published versio

Extreme Enhancements of r-process Elements in the Cool Metal-Poor Main-Sequence Star SDSS J2357-0052

We report the discovery of a cool metal-poor, main-sequence star exhibiting large excesses of r-process elements. This star is one of two newly discovered cool subdwarfs (effective temperatures of 5000 K) with extremely low metallicity ([Fe/H]<-3) identified from follow-up high-resolution spectroscopy of metal-poor candidates from the Sloan Digital Sky Survey. SDSS J2357-0052 has [Fe/H]=-3.4 and [Eu/Fe]=+1.9, and exhibits a scaled solar r-process abundance pattern of heavy neutron-capture elements. This is the first example of an extremely metal-poor, main-sequence star showing large excesses of r-process elements; all previous examples of the large r-process-enhancement phenomena have been associated with metal-poor giants. The metallicity of this object is the lowest, and the excess of Eu ([Eu/Fe]) is the highest, among the r-process-enhanced stars found so far. We consider possible scenarios to account for the detection of such a star, and discuss techniques to enable searches for similar stars in the future.Comment: 16 pages, 3 figures, 2 tables, ApJL in pres

Double solid twistor spaces: the case of arbitrary signature

In a recent paper (math.DG/0701278) we constructed a series of new Moishezon twistor spaces which is a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon twistor spaces on nCP^2 for arbitrary n>2, which can be regarded as a generalization of the twistor spaces of a 'double solid type' on 3CP^2 studied by Kreussler, Kurke, Poon and the author. Similarly to the twistor spaces of 'double solid type' on 3CP^2, projective models of present twistor spaces have a natural structure of double covering of a CP^2-bundle over CP^1. We explicitly give a defining polynomial of the branch divisor of the double covering whose restriction to fibers are degree four. If n>3 these are new twistor spaces, to the best of the author's knowledge. We also compute the dimension of the moduli space of these twistor spaces. Differently from math.DG/0701278, the present investigation is based on analysis of pluri-(half-)anticanonical systems of the twistor spaces.Comment: 30 pages, 3 figures; v2: title changed (the original title was "Explicit construction of new Moishezon twistor spaces, II".

Observation of a Transient Magnetization Plateau in a Quantum Antiferromagnet on the Kagome Lattice

The magnetization process of an S=1/2 antiferromagnet on the kagome lattice, [Cu_3(titmb)_2(OCOCH_3)_6]H_2O {titmb= 1,3,5-tris(imidazol-1-ylmethyl)-2,4,6 trimethylbenzene} has been measured at very low temperatures in both pulsed and steady fields. We have found a new dynamical behavior in the magnetization process: a plateau at one third of the saturation magnetization appears in the pulsed field experiments for intermediate sweep rates of the magnetic field and disappears in the steady field experiments. A theoretical analysis using exact diagonalization yields J_1=-19K and J_2=6K, for the nearest neighbor and second nearest neighbor interactions, respectively. This set of exchange parameters explains the very low saturation field and the absence of the plateau in the thermodynamic equilibrium as well as the two-peak feature in the magnetic heat capacity. Supported by numerical results we argue that a dynamical order by disorder phenomenon could explain the transient appearance of the 1/3 plateau in pulsed field experiments.Comment: 7 pages, 5 figure

Transitive X-ray spectrum and PeV gamma-ray cutoff in the M87 jet: Electron "Pevatron"

We propose a modified version of the X-ray spectral index and an intrinsic cutoff frequency of inverse Compton radiation from the brightest knot of the M87 jet, in conjunction with an application of the new conceptions of injection and diffusive shock acceleration (DSA) of electrons in magnetized filamentary plasma to the specified source. The drop of the X-ray flux density in a transitive frequency region is associated with the interplay of ordinary synchrotron cooling and weaker magnetic fields concomitant with the smaller scale filaments that allow the electron injection, while the radio-optical synchrotron continuum is dominantly established by the major electrons that are quasi-secularly bound to larger filaments. With reference to, particularly, the updated external Compton model, we demonstrate that in the Klein-Nishina regime fading inverse Comptonization, the injected electrons can be stochastically energized up to a Lorentz factor as high as $5\times 10^{10}$ in the temporal competition with diffuse synchrotron cooling; this value is larger than that attainable for a simple DSA scenario based on the resonant scattering diffusion of the gyrating electrons bound to a supposed magnetic field homogeneously pervading the entire knot. The upper limits of the photon frequency boosted via conceivable inverse Compton processes are predicted to be of the common order of $\sim 10^{30}$ Hz. The variability of the broadband spectrum is also discussed in comparison to the features of a blazar light curve. The present scenario of a peta-eV (PeV; $10^{15}$ eV) electron accelerator, the "Pevatron," might provide some guidance for exploring untrod hard X-ray and gamma-ray bands in forthcoming observations.Comment: 34 pages, 6 figures, matches version published in Ap

Degenerations of LeBrun twistor spaces

We investigate various limits of the twistor spaces associated to the self-dual metrics on n CP ^2, the connected sum of the complex projective planes, constructed by C. LeBrun. In particular, we explicitly present the following 3 kinds of degenerations whose limits of the metrics are: (a) LeBrun metrics on (n-1) CP ^2$, (b) (Another) LeBrun metrics on the total space of the line bundle O(-n) over CP ^1 (c) The hyper-Kaehler metrics on the small resolution of rational double points of type A_{n-1}, constructed by Gibbons and Hawking.Comment: 21 pages, 7 figures. V2: A new section added at the end of the article. V3: Reference slightly update

A Modular Toolkit for Distributed Interactions

We discuss the design, architecture, and implementation of a toolkit which supports some theories for distributed interactions. The main design principles of our architecture are flexibility and modularity. Our main goal is to provide an easily extensible workbench to encompass current algorithms and incorporate future developments of the theories. With the help of some examples, we illustrate the main features of our toolkit.Comment: In Proceedings PLACES 2010, arXiv:1110.385

Field-induced 3- and 2-dimensional freezing in a quantum spin liquid

Field-induced commensurate transverse magnetic ordering is observed in the Haldane-gap compound \nd by means of neutron diffraction. Depending on the direction of applied field, the high-field phase is shown to be either a 3-dimensional ordered N\'{e}el state or a short-range ordered state with dominant 2-dimensional spin correlations. The structure of the high-field phase is determined, and properties of the observed quantum phase transition are discussed.Comment: 4 pages 3 figure