Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups

Let $\Phi$ be a classical root system and $k$ be a field of sufficiently large characteristic. Let $G$ be the classical group over $k$ with the root system $\Phi$, $U$ be its maximal unipotent subgroup and $\mathfrak{u}$ be the Lie algebra of $U$. Let $D$ be an orthogonal subset of $\Phi$ and $\Omega$ be a coadjoint orbit of $U$ associated with $D$. We construct a polarization of $\mathfrak{u}$ at the canonical form on $\Omega$. We also find the dimension of $\Omega$ in terms of the Weyl group of $\Phi$. As a corollary, we determine all possible dimensions of irreducible complex represenations of the group $U$ for the case of finite field $k$.Comment: 11 page

Lattice Model for water-solute mixtures

A lattice model for the study of mixtures of associating liquids is proposed. Solvent and solute are modeled by adapting the associating lattice gas (ALG) model. The nature of interaction solute/solvent is controlled by tuning the energy interactions between the patches of ALG model. We have studied three set of parameters, resulting on, hydrophilic, inert and hydrophobic interactions. Extensive Monte Carlo simulations were carried out and the behavior of pure components and the excess properties of the mixtures have been studied. The pure components: water (solvent) and solute, have quite similar phase diagrams, presenting: gas, low density liquid, and high density liquid phases. In the case of solute, the regions of coexistence are substantially reduced when compared with both the water and the standard ALG models. A numerical procedure has been developed in order to attain series of results at constant pressure from simulations of the lattice gas model in the grand canonical ensemble. The excess properties of the mixtures: volume and enthalpy as the function of the solute fraction have been studied for different interaction parameters of the model. Our model is able to reproduce qualitatively well the excess volume and enthalpy for different aqueous solutions. For the hydrophilic case, we show that the model is able to reproduce the excess volume and enthalpy of mixtures of small alcohols and amines. The inert case reproduces the behavior of large alcohols such as, propanol, butanol and pentanol. For last case (hydrophobic), the excess properties reproduce the behavior of ionic liquids in aqueous solution.Comment: 28 pages, 13 figure

Energy dependence of Ti/Fe ratio in the Galactic cosmic rays measured by the ATIC-2 experiment

Titanium is a rare, secondary nucleus among Galactic cosmic rays. Using the Silicon matrix in the ATIC experiment, Titanium has been separated. The energy dependence of the Ti to Fe flux ratio in the energy region from 5 GeV per nucleon to about 500 GeV per nucleon is presented.Comment: 8 pages, 4 figures, accepted for publication in Astronomy Letter

The Role of Fission in Neutron Star Mergers and Its Impact on the r-Process Peaks

Comparing observational abundance features with nucleosynthesis predictions of stellar evolution or explosion simulations, we can scrutinize two aspects: (a) the conditions in the astrophysical production site and (b) the quality of the nuclear physics input utilized. We test the abundance features of r-process nucleosynthesis calculations for the dynamical ejecta of neutron star merger simulations based on three different nuclear mass models: The Finite Range Droplet Model, the (quenched version of the) Extended Thomas Fermi Model with Strutinsky Integral, and the Hartree-Fock-Bogoliubov mass model. We make use of corresponding fission barrier heights and compare the impact of four different fission fragment distribution models on the final r-process abundance distribution. In particular, we explore the abundance distribution in the second r-process peak and the rare-earth sub-peak as a function of mass models and fission fragment distributions, as well as the origin of a shift in the third r-process peak position. The latter has been noticed in a number of merger nucleosynthesis predictions. We show that the shift occurs during the r-process freeze-out when neutron captures and β-decays compete and an (n,γ)-(γ,n) equilibrium is no longer maintained. During this phase neutrons originate mainly from fission of material above A = 240. We also investigate the role of β-decay half-lives from recent theoretical advances, which lead either to a smaller amount of fissioning nuclei during freeze-out or a faster (and thus earlier) release of fission neutrons, which can (partially) prevent this shift and has an impact on the second and rare-earth peak as well.Peer reviewe

Nucleosynthesis in neutrino heated matter: The vp-process and the r-process

This manuscript reviews recent progress in our understanding of the nucleosynthesis of medium and heavy elements in supernovae. Recent hydrodynamical models of core-collapse supernovae show that a large amount of proton rich matter is ejected under strong neutrino fluxes. This matter constitutes the site of the vp-process where antineutrino absorption reactions catalyze the nucleosynthesis of nuclei with A > 64. Supernovae are also associated with the r-process responsible for the synthesis of the heaviest elements in nature. Fission during the r-process can play a major role in determining the final abundance patter and in explaining the almost universal features seen in metal-poor r-process-rich stars.Comment: 10 pages, 3 figures, invited talk at NIC-IX, International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX, CERN, Geneva, Switzerland, 25-30 June, 200

Exact Solution of Photon Equation in Stationary G\"{o}del-type and G\"{o}del Space-Times

In this work the photon equation (massless Duffin-Kemmer-Petiau equation) is written expilicitly for general type of stationary G\"{o}del space-times and is solved exactly for G\"{o}del-type and G\"{o}del space-times. Harmonic oscillator behaviour of the solutions is discussed and energy spectrum of photon is obtained.Comment: 9 pages,RevTeX, no figure, revised for publicatio

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

Possible structure in the cosmic ray electron spectrum measured by the ATIC-2 and ATIC-4 experiments

A strong excess in a form of a wide peak in the energy range of 300-800 GeV was discovered in the first measurements of the electron spectrum in the energy range from 20 GeV to 3 TeV by the balloon-borne experiment ATIC (J. Chang et al. Nature, 2008). The experimental data processing and analysis of the electron spectrum with different criteria for selection of electrons, completely independent of the results reported in (J. Chang et al. Nature, 2008) is employed in the present paper. The new independent analysis generally confirms the results of (J. Chang et al. Nature, 2008), but shows that the spectrum in the region of the excess is represented by a number of narrow peaks. The measured spectrum is compared to the spectrum of (J. Chang et al. Nature, 2008) and to the spectrum of the Fermi/LAT experiment.Comment: LaTeX2e, 10 pages, 4 figures, a paper for ECRS 2010 (Turku, Finland); http://www.astrophys-space-sci-trans.net/7/119/2011

Upturn observed in heavy nuclei to iron ratios by the ATIC-2 experiment

The ratios of fluxes of heavy nuclei from sulfur (Z=16) to chromium (Z=24) to the flux of iron were measured by the ATIC-2 experiment. The ratios are decreasing functions of energy from 5 GeV/n to approximately 80 GeV/n, as expected. However, an unexpected sharp upturn in the ratios are observed for energies above 100 GeV/n for all elements from Z=16 to Z=24. Similar upturn but with lower amplitude was also discovered in the ATIC-2 data for the ratio of fluxes of abundant even nuclei (C, O, Ne, Mg, Si) to the flux of iron. Therefore the spectrum of iron is significantly different from the spectra of other abundant even nuclei.Comment: 4 pages, LaTeX2e, a paper for 23rd European Cosmic Ray Symposium (2012