Accelerating moderately stiff chemical kinetics in reactive-flow simulations using GPUs

The chemical kinetics ODEs arising from operator-split reactive-flow simulations were solved on GPUs using explicit integration algorithms. Nonstiff chemical kinetics of a hydrogen oxidation mechanism (9 species and 38 irreversible reactions) were computed using the explicit fifth-order Runge-Kutta-Cash-Karp method, and the GPU-accelerated version performed faster than single- and six-core CPU versions by factors of 126 and 25, respectively, for 524,288 ODEs. Moderately stiff kinetics, represented with mechanisms for hydrogen/carbon-monoxide (13 species and 54 irreversible reactions) and methane (53 species and 634 irreversible reactions) oxidation, were computed using the stabilized explicit second-order Runge-Kutta-Chebyshev (RKC) algorithm. The GPU-based RKC implementation demonstrated an increase in performance of nearly 59 and 10 times, for problem sizes consisting of 262,144 ODEs and larger, than the single- and six-core CPU-based RKC algorithms using the hydrogen/carbon-monoxide mechanism. With the methane mechanism, RKC-GPU performed more than 65 and 11 times faster, for problem sizes consisting of 131,072 ODEs and larger, than the single- and six-core RKC-CPU versions, and up to 57 times faster than the six-core CPU-based implicit VODE algorithm on 65,536 ODEs. In the presence of more severe stiffness, such as ethylene oxidation (111 species and 1566 irreversible reactions), RKC-GPU performed more than 17 times faster than RKC-CPU on six cores for 32,768 ODEs and larger, and at best 4.5 times faster than VODE on six CPU cores for 65,536 ODEs. With a larger time step size, RKC-GPU performed at best 2.5 times slower than six-core VODE for 8192 ODEs and larger. Therefore, the need for developing new strategies for integrating stiff chemistry on GPUs was discussed.Comment: 27 pages, LaTeX; corrected typos in Appendix equations A.10 and A.1

Hybrid chiral condensate in the external magnetic field

We study the phase diagram of the Nambu-Jona-Lasinio model in the external magnetic field within the mean-field approximation, taking into account the inhomogeneous chiral condensate. It is shown that there appears a new type of the chiral condensate, endowed with two features of real kink crystal and dual chiral density wave, in the magnetic field. We also show that there are first order phase transitions between different inhomogeneous phases in the presence of magnetic field.Comment: 14 pages, 24 figure

The improved Ginzburg-Landau technique

We discuss an innovative method for the description of inhomogeneous phases designed to improve the standard Ginzburg-Landau expansion. The method is characterized by two key ingredients. The first one is a moving average of the order parameter designed to account for the long-wavelength modulations of the condensate. The second one is a sum of the high frequency modes, to improve the description of the phase transition to the restored phase. The method is applied to compare the free energies of 1D and 2D inhomogeneous structures arising in the chirally symmetric broken phase.Comment: 7 pages, 5 figures. Presented at QCD@Work - International Workshop on QCD Theory and Experiment 25-28 June 2018, Matera, Ital

Capacity Region of the Symmetric Injective K-User Deterministic Interference Channel

We characterize the capacity region of the symmetric injective K-user Deterministic Interference Channel (DIC) for all channel parameters. The achievable rate region is derived by first projecting the achievable rate region of Han-Kobayashi (HK) scheme, which is in terms of common and private rates for each user, along the direction of aggregate rates for each user (i.e., the sum of common and private rates). We then show that the projected region is characterized by only the projection of those facets in the HK region for which the coefficient of common rate and private rate are the same for all users, hence simplifying the region. Furthermore, we derive a tight converse for each facet of the simplified achievable rate region.Comment: A shorter version of this paper to appear in International Symposium on Information Theory (ISIT) 201

Inhomogeneous chiral symmetry breaking in dense neutron-star matter

An increasing number of model results suggests that chiral symmetry is broken inhomogeneously in a certain window at intermediate densities in the QCD phase diagram. This could have significant effects on the properties of compact stars, possibly leading to new astrophysical signatures. In this contribution we discuss this idea by reviewing recent results on inhomogeneous chiral symmetry breaking under an astrophysics-oriented perspective. After introducing two commonly studied spatial modulations of the chiral condensate, the chiral density wave and the real kink crystal, we focus on their properties and their effect on the equation of state of quark matter. We also describe how these crystalline phases are affected by different elements which are required for a realistic description of a compact star, such as charge neutrality, the presence of magnetic fields, vector interactions and the interplay with color-superconductivity. Finally, we discuss possible signatures of inhomogeneous chiral symmetry breaking in the core of compact stars, considering the cases of mass-radius relations and neutrino emissivity explicitly.Comment: Invited contribution to the EPJA Topical Issue "Exotic Matter in Neutron Stars". v2: extended discussion on strange quarks, updated mass-radius section, other small changes; matches published version. 16 pages, 14 figure

Chiral spiral induced by a strong magnetic field

We study the modification of the chiral phase structure of QCD due to an external magnetic field. We first demonstrate how the effect of magnetic field can systematically be incorporated into a generalized Ginzburg-Landau framework. We then analyze the phase structure in the vicinity of the chiral critical point. In the chiral limit, the effect is found to be so drastic that it totally washes the tricritical point out of the phase diagram, bringing the continent for the chiral spiral. This is the case no matter how small is the intensity of the magnetic field. On the other hand, the current quark mass protects the chiral critical point from a weak magnetic field. However the critical point will eventually be covered by the chiral spiral phase as the magnetic field grows.Comment: 6 pages, 6 eps figures. Presented at QCD@Work 2016: International Workshop on QCD - Theory and Experiment, June 27-30, Martina-Franca (Italy

Globular Clusters as Tracers of Stellar Bimodality in Elliptical Galaxies: The Case of NGC 1399

Globular cluster systems (GCS) frequently show a bi-modal distribution of the cluster integrated colours. This work explores the arguments to support the idea that the same feature is shared by the diffuse stellar population of the galaxy they are associated with. In the particular case of NGC 1399 the results show that the galaxy brightness profile and colour gradient as well as the behaviour of the cumulative globular cluster specific frequency, are compatible with the presence of two dominant stellar populations, associated with the so called "blue" and "red" globular cluster families. These globular families are characterized by different intrinsic specific frequencies (defined in terms of each stellar population): Sn=3.3 +/- 0.3 in the case of the red globulars and Sn=14.3 +/- 2.5 for the blue ones. We stress that this result is not necessarily conflicting with recent works that point out a clear difference between the metallicity distribution of (resolved) halo stars and globulars when comparing their number statistics. The inferred specific frequencies imply that, in terms of their associated stellar populations, the formation of the blue globulars took place with an efficiency about 6 times higher than that corresponding to their red counterparts. The similarity of the spatial distribution of the blue globulars with that inferred for dark matter, as well as with that of the X ray emiting hot gas associated with NGC 1399, is emphasized. The impact of a relatively unconspicuous low metallicity population, that shares the properties of the blue globulars, as a possible source of chemical enrichment early in the formation history of the galaxy is also briefly discussed.Comment: 15 pages; MNRAS (accepted; October 2004