B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations

A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.Comment: 27 pages, 30 figure

Real-Time Evolution of Soft Gluon Field Dynamics in Ultra-Relativistic Heavy-Ion Collisions

The dynamics of gluons and quarks in a relativistic nuclear collision are described, within the framework of a classical mean-field transport theory, by the coupled equations for the Yang-Mills field and a collection of colored point particles. The particles are used to represent color source effects of the valence quarks in the colliding nuclei. The possibilities of this approach are studied to describe the real time evolution of small $x$ modes in the classical effective theory in a non-perturbative coherent manner. The time evolution of the color fields is explored in a numerical simulation of the collision of two Lorentz-boosted clouds of color charged particles on a long three-dimensional gauge lattice. We report results on soft gluon scattering and coherent gluon radiation obtained in SU(2) gauge symmetry.Comment: 16 pages and 17 postscript figure

Contribution of fungi to primary biogenic aerosols in the atmosphere: wet and dry discharged spores, carbohydrates, and inorganic ions

Biogenic aerosols play important roles in atmospheric chemistry physics, the biosphere, climate, and public health. Here, we show that fungi which actively discharge their spores with liquids into the air, in particular actively wet spore discharging Ascomycota (AAM) and actively wet spore discharging Basidiomycota (ABM), are a major source of primary biogenic aerosol particles and components. We present the first estimates for the global average emission rates of fungal spores. Measurement results and budget calculations based on investigations in Amazonia (Balbina, Brazil, July 2001) indicate that the spores of AAM and ABM may account for a large proportion of coarse particulate matter in tropical rainforest regions during the wet season (0.7–2.3 μg m^−3). For the particle diameter range of 1–10 μm, the estimated proportions are ~25% during day-time, ~45% at night, and ~35% on average. For the sugar alcohol mannitol, the budget calculations indicate that it is suitable for use as a molecular tracer for actively wet discharged basidiospores (ABS). ABM emissions seem to account for most of the atmospheric abundance of mannitol (10–68 ng m^−3), and can explain the observed diurnal cycle (higher abundance at night). ABM emissions of hexose carbohydrates might also account for a significant proportion of glucose and fructose in air particulate matter (7–49 ng m^−3), but the literature-derived ratios are not consistent with the observed diurnal cycle (lower abundance at night). AAM emissions appear to account for a large proportion of potassium in air particulate matter over tropical rainforest regions during the wet season (17–43 ng m^−3), and they can also explain the observed diurnal cycle (higher abundance at night). The results of our investigations and budget calculations for tropical rainforest aerosols are consistent with measurements performed at other locations. Based on the average abundance of mannitol reported for extratropical continental boundary layer air (~25 ng m^−3), we have also calculated a value of ~17 Tg yr^−1 as a first estimate for the global average emission rate of ABS over land surfaces, which is consistent with the typically observed concentrations of ABS (~10³–10^4 m^−3; ~0.1–1 μg m^−3). The global average atmospheric abundance and emission rate of total fungal spores, including wet and dry discharged species, are estimated to be higher by a factor of about three, i.e. 1 μg m^−3 and ~50 Tg yr^−1. Comparisons with estimated rates of emission and formation of other major types of organic aerosol (~47 Tg yr^−1 of anthropogenic primary organic aerosol; 12–70 Tg yr^−1 of secondary organic aerosol) indicate that emissions from fungi should be taken into account as a significant global source of organic aerosol. The effects of fungal spores and related chemical components might be particularly important in tropical regions, where both physicochemical processes in the atmosphere and biological activity at the Earth's surface are particularly intense, and where the abundance of fungal spores and related chemical compounds are typically higher than in extratropical regions

Relativistic Hartree-Bogoliubov theory with finite range pairing forces in coordinate space: Neutron halo in light nuclei

The Relativistic Hartree Bogoliubov (RHB) model is applied in the self-consistent mean-field approximation to the description of the neutron halo in the mass region above the s-d shell. Pairing correlations and the coupling to particle continuum states are described by finite range two-body forces. Finite element methods are used in the coordinate space discretization of the coupled system of Dirac-Hartree-Bogoliubov integro-differential eigenvalue equations, and Klein-Gordon equations for the meson fields. Calculations are performed for the isotopic chains of Ne and C nuclei. We find evidence for the occurrence of neutron halo in heavier Ne isotopes. The properties of the 1f-2p orbitals near the Fermi level and the neutron pairing interaction play a crucial role in the formation of the halo. Our calculations display no evidence for the neutron halo phenomenon in C isotopes.Comment: 7 pages, Latex, 5 P.S. Figures, To appear in Phys. Rev. Let

Relativistic Hartree-Bogoliubov description of ground-state properties of Ni and Sn isotopes

The Relativistic Hartree Bogoliubov (RHB) theory is applied in the description of ground-state properties of Ni and Sn isotopes. The NL3 parameter set is used for the effective mean-field Lagrangian, and pairing correlations are described by the pairing part of the finite range Gogny interaction D1S. Fully self-consistent RHB solutions are calculated for the Ni ($28\leq N\leq 50$) and Sn ($50\leq N\leq 82$) isotopes. Binding energies, neutron separation energies, and proton and neutron $rms$ radii are compared with experimental data. The model predicts a reduction of the spin-orbit potential with the increase of the number of neutrons. The resulting energy splittings between spin-orbit partners are discussed, as well as pairing properties calculated with the finite range effective interaction in the $pp$ channel.Comment: 11 pages, RevTex, 12 p.s figures, submitted to Phys. Rev.

Proton drip-line nuclei in Relativistic Hartree-Bogoliubov theory

Ground-state properties of spherical even-even nuclei $14\leq Z \leq 28$ and $N=18,20,22$ are described in the framework of Relativistic Hartree Bogoliubov (RHB) theory. The model uses the NL3 effective interaction in the mean-field Lagrangian, and describes pairing correlations by the pairing part of the finite range Gogny interaction D1S. Binding energies, two-proton separation energies, and proton $rms$ radii that result from fully self-consistent RHB solutions are compared with experimental data. The model predicts the location of the proton drip-line. The isospin dependence of the effective spin-orbit potential is discussed, as well as pairing properties that result from the finite range interaction in the $pp$ channel.Comment: 12 pages, RevTex, 10 p.s figures, submitted to Phys. Rev.

Spherical Relativistic Hartree theory in a Woods-Saxon basis

The Woods-Saxon basis has been suggested to replace the widely used harmonic oscillator basis for solving the relativistic mean field (RMF) theory in order to generalize it to study exotic nuclei. As examples, relativistic Hartree theory is solved for spherical nuclei in a Woods-Saxon basis obtained by solving either the Schr\"odinger equation or the Dirac equation (labelled as SRHSWS and SRHDWS, respectively and SRHWS for both). In SRHDWS, the negative levels in the Dirac Sea must be properly included. The basis in SRHDWS could be smaller than that in SRHSWS which will simplify the deformed problem. The results from SRHWS are compared in detail with those from solving the spherical relativistic Hartree theory in the harmonic oscillator basis (SRHHO) and those in the coordinate space (SRHR). All of these approaches give identical nuclear properties such as total binding energies and root mean square radii for stable nuclei. For exotic nuclei, e.g., $^{72}$Ca, SRHWS satisfactorily reproduces the neutron density distribution from SRHR, while SRHHO fails. It is shown that the Woods-Saxon basis can be extended to more complicated situations for exotic nuclei where both deformation and pairing have to be taken into account.Comment: 12 pages, 9 figure