Power Laws and the Cosmic Ray Energy Spectrum

Two separate statistical tests are applied to the AGASA and preliminary Auger Cosmic Ray Energy spectra in an attempt to find deviation from a pure power-law. The first test is constructed from the probability distribution for the maximum event of a sample drawn from a power-law. The second employs the TP-statistic, a function defined to deviate from zero when the sample deviates from the power-law form, regardless of the value of the power index. The AGASA data show no significant deviation from a power-law when subjected to both tests. Applying these tests to the Auger spectrum suggests deviation from a power-law. However, potentially large systematics on the relative energy scale prevent us from drawing definite conclusions at this time.Comment: 21 pages, 18 figures, submitted to Astro. Part. Phy

Influence of the halo upon angular distributions for elastic scattering and breakup

The angular distributions for elastic scattering and breakup of halo nuclei are analysed using a near-side/far-side decomposition within the framework of the dynamical eikonal approximation. This analysis is performed for 11Be impinging on Pb at 69 MeV/nucleon. These distributions exhibit very similar features. In particular they are both near-side dominated, as expected from Coulomb-dominated reactions. The general shape of these distributions is sensitive mostly to the projectile-target interactions, but is also affected by the extension of the halo. This suggests the elastic scattering not to be affected by a loss of flux towards the breakup channel.Comment: 11 pages, 3 figures, accepted for publication in Phys. Lett.

Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte

Evaluation of Automated Fermi GBM Localizations of Gamma-Ray Bursts

The capability of the Fermi Gamma-ray Burst Monitor (GBM) to localize gamma-ray bursts (GRBs) is evaluated for two different automate algorithms: the GBM Team's RoboBA algorithm and the independentl developed BALROG algorithm. Through a systematic study utilizing ove 500 GRBs with known locations from instruments like Swift and the Ferm LAT, we directly compare the effectiveness of, and accurately estimat the systematic uncertainty for, both algorithms. We show simpl adjustments to the GBM Team's RoboBA, in operation since early 2016 yields significant improvement in the systematic uncertainty, removin the long tail identified in the systematic, and improves the overal accuracy. The systematic uncertainty for the updated RoboB localizations is 1.8^\\circ for 52% of GRBs and 4.1^\\circ for th remaining 48%. Both from public reporting by BALROG and our systemati study, we find the systematic uncertainty of 1-2^\\circ quoted in GC circulars for bright GRBs localized by BALROG is an underestimate of th true magnitude of the systematic, which we find to be 2.7^\\circ fo 74% of GRBs and 33^\\circ for the remaining 26%. We show that, once th systematic uncertainty is considered, the RoboBA 90% localizatio confidence regions can be more than an order of magnitude smaller i area than those produced by BALROG

Gravitational Wave Spectrum in Inflation with Nonclassical States

The initial quantum state during inflation may evolve to a highly squeezed quantum state due to the amplification of the time-dependent parameter, $\omega_{phys}(k/a)$, which may be the modified dispersion relation in trans-Planckian physics. This squeezed quantum state is a nonclassical state that has no counterpart in the classical theory. We have considered the nonclassical states such as squeezed, squeezed coherent, and squeezed thermal states, and calculated the power spectrum of the gravitational wave perturbation when the mode leaves the horizon.Comment: 21 page

Half-metallic antiferromagnets in thiospinels

We have theoretically designed the half-metallic (HM) antiferromagnets (AFMs) in thiospinel systems, $\rm Mn(CrV)S_{4}$ and $\rm Fe_{0.5}Cu_{0.5}(V_{0.5}Ti_{1.5})S_{4}$, based on the electronic structure studies in the local-spin-density approximation (LSDA). We have also explored electronic and magnetic properties of parent spinel compounds of the above systems; $\rm CuV_{2}S_{4}$ and $\rm CuTi_{2}S_{4}$ are found to be HM ferromagnets in their cubic spinel structures, while $\rm MnCr_{2}S_{4}$ is a ferrimagnetic insulator. We have discussed the feasibility of material synthesis of HM-AFM thiospinel systems.Comment: 4 pages, 5 figure

Solar Neutrino Constraints on the BBN Production of Li

Using the recent WMAP determination of the baryon-to-photon ratio, 10^{10} \eta = 6.14 to within a few percent, big bang nucleosynthesis (BBN) calculations can make relatively accurate predictions of the abundances of the light element isotopes which can be tested against observational abundance determinations. At this value of \eta, the Li7 abundance is predicted to be significantly higher than that observed in low metallicity halo dwarf stars. Among the possible resolutions to this discrepancy are 1) Li7 depletion in the atmosphere of stars; 2) systematic errors originating from the choice of stellar parameters - most notably the surface temperature; and 3) systematic errors in the nuclear cross sections used in the nucleosynthesis calculations. Here, we explore the last possibility, and focus on possible systematic errors in the He3(\alpha,\gamma)Be7 reaction, which is the only important Li7 production channel in BBN. The absolute value of the cross section for this key reaction is known relatively poorly both experimentally and theoretically. The agreement between the standard solar model and solar neutrino data thus provides additional constraints on variations in the cross section (S_{34}). Using the standard solar model of Bahcall, and recent solar neutrino data, we can exclude systematic S_{34} variations of the magnitude needed to resolve the BBN Li7 problem at > 95% CL. Additional laboratory data on He3(\alpha,\gamma)Be7 will sharpen our understanding of both BBN and solar neutrinos, particularly if care is taken in determining the absolute cross section and its uncertainties. Nevertheless, it already seems that this ``nuclear fix'' to the Li7 BBN problem is unlikely; other possible solutions are briefly discussed.Comment: 21 pages, 3 ps figure

Stein's method on Wiener chaos

We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. We also prove results concerning random variables admitting a possibly infinite Wiener chaotic decomposition. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener-It\^o integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre, Peccati and Tudor. We apply our techniques to prove Berry-Ess\'een bounds in the Breuer-Major CLT for subordinated functionals of fractional Brownian motion. By using the well-known Mehler's formula for Ornstein-Uhlenbeck semigroups, we also recover a technical result recently proved by Chatterjee, concerning the Gaussian approximation of functionals of finite-dimensional Gaussian vectors.Comment: 39 pages; Two sections added; To appear in PTR

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe