Perturbative tests of non-perturbative counting

We observe that a class of quarter-BPS dyons in N=4 theories with charge vector (Q, P) and with nontrivial values of the arithmetic duality invariant I := gcd (Q wedge P) are nonperturbative in one frame but perturbative in another frame. This observation suggests a test of the recently computed nonperturbative partition functions for dyons with nontrivial values of the arithmetic invariant. For all values of I, we show that the nonperturbative counting yields vanishing indexed degeneracy for this class of states everywhere in the moduli space in precise agreement with the perturbative result.Comment: 10 pages, 0 figure

Dynamics of Inflation and Dark Energy from F(R,G)F(R, \mathcal{G}) Gravity

In this work we study certain classes of $F(R,{\cal G})$ gravity which have appealing phenomenological features, with respect to the successful realization of the dark energy and of the inflationary era. Particularly, we discuss the general formalism and we demonstrate how several inflationary and dark energy evolutions can be described in the context of $F(R,{\cal G})$ gravity. Also we propose a unified model, in the context of which the early and late-time dynamics are controlled by the $F(R,{\cal G})$ gravity, thus producing inflation and the dark energy era, while the intermediate era is approximately identical with standard Einstein-Hilbert gravity. Also we calculate the power spectrum of the primordial curvature perturbations corresponding to the unified $F(R,{\cal G})$ gravity model we propose, which as we demonstrate is nearly scale invariant and compatible with the latest observational data constraints

Turbulence and its effect on protostellar disk formation

We analyse simulations of turbulent, magnetised molecular cloud cores focussing on the formation of Class 0 stage protostellar discs and the physical conditions in their surroundings. We show that for a wide range of initial conditions Keplerian discs are formed in the Class 0 stage already. Furthermore, we show that the accretion of mass and angular momentum in the surroundings of protostellar discs occurs in a highly anisotropic manner, by means of a few narrow accretion channels. The magnetic field structure in the vicinity of the discs is highly disordered, revealing field reversals up to distances of 1000 AU. These findings demonstrate that as soon as even mild turbulent motions are included, the classical disc formation scenario of a coherently rotating environment and a well-ordered magnetic field breaks down.Comment: Invited contribution to the NIC proceedings 2016 for the John von Neumann-Institut f\"ur Computing (NIC) Symposium 201

Oscillations in active region fan loops: Observations from EIS/{\it Hinode} and AIA/SDO

Active region fan loops in AR 11076 were studied, in search of oscillations, using high cadence spectroscopic observations from EIS on board Hinode combined with imaging sequences from the AIA on board SDO. Spectra from EIS were analyzed in two spectral windows, \FeXII 195.12 \AA and \FeXIII 202.04 \AA along with the images from AIA in 171 \AA and 193 \AA channels. We find short ($<$3 min) and long ($\approx$9 min) periods at two different locations. Shorter periods show oscillations in all the three line parameters and the longer ones only in intensity and Doppler shift but not in line width. Line profiles at both these locations do not show any visible blue-shifted component and can be fitted well with a single Gaussian function along with a polynomial background. Results using co-spatial and co-temporal data from AIA/SDO do not show any significant peak corresponding to shorter periods, but longer periods are clearly observed in both 171 \AA and 193 \AA channels. Space-time analysis in these fan loops using images from AIA/SDO show alternate slanted ridges of positive slope, indicative of outward propagating disturbances. The apparent propagation speeds were estimated to be 83.5 $\pm$ 1.8 \kms and 100.5 $\pm$ 4.2 \kms, respectively, in the 171 \AA and 193 \AA channels. Observed short period oscillations are suggested to be caused by the simultaneous presence of more than one MHD mode whereas the long periods are suggested as signatures of slow magneto-acoustic waves. In case of shorter periods, the amplitude of oscillation is found to be higher in EIS lines with relatively higher temperature of formation. Longer periods, when observed from AIA, show a decrease of amplitude in hotter AIA channels which might indicate damping due to thermal conduction owing to their acoustic nature.Comment: Accepted for publication in Solar Physic

A spectral scheme for Kohn-Sham density functional theory of clusters

Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn-Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.Comment: Manuscript submitted (with revisions) to Journal of Computational Physic