Tradable SO-2-permits in the European Union: a practicable scheme for public utilities

In this paper, a practicable scheme of SO2-emission permits for European power producers is developed. Background is the second UN-ECE Sulphur Protocol from 1994 (Protocol of Oslo). After discussing some theoretical models of spatially differentiated permit schemes, evaluating the U.S. Acid Rain and RECLAIM Program, and considering the setting in the EU-15 countries, a scheme of locally undifferentiated emission permits is proposed which is distinguished by a high degree of both economic efficiency and market functioning. However, as our model simulations indicate, national deposition targets will be violated in all probability due to the scheme?s missing differentiation regarding the receptors. The risk of hot spots is addressed adequately by a differentiated bundle of countermeasures. The general economic impact of an EU-wide permit scheme is low, and, in terms of change in GDP, lower compared to a non-coordinated SO2 policy. The proposed mode of the initial permit allocation allows for early price signals and guarantees maximum static and dynamic efficiency. Balancing the interests of existing and new emitters, a long-term transition from the grandfathering to the free auction procedure is chosen. --

Spin-orbit coupling in nuclei and realistic nucleon-nucleon potentials

We analyze the spin-orbit coupling term in the nuclear energy density functional in terms of a zero-range NN-contact interaction and finite-range contributions from two-pion exchange. We show that the strength of the spin-orbit contact interaction as extracted from high-precision nucleon-nucleon potentials is in perfect agreement with that of phenomenological Skyrme forces employed in non-relativistic nuclear structure calculations. Additional long-range contributions from chiral two-pion exchange turn out to be relatively small. These explicitly density-dependent contributions reduce the ratio of the isovector to the isoscalar spin-orbit strength significantly below the Skyrme value 1/3. We perform a similar analysis for the strength function of the $(\vec \nabla \rho)^2$-term and find values not far from those of phenomenological Skyrme parameterizations.Comment: 10 pages, 3 figures, accepted for publication in Physical Review C70 (2004

Levy flights and Levy -Schroedinger semigroups

We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.Comment: To appear in Cent. Eur. J. Phys. (2010

Tradable SO2-Permits in the European Union: A Practicable Scheme for Public Utilities

In this paper, a practicable scheme of SO2-emission permits for European power producers is developed. Background is the second UN-ECE Sulphur Protocol from 1994 (Protocol of Oslo). After discussing some theoretical models of spatially differentiated permit schemes, evaluating the U.S. Acid Rain and RECLAIM Program, and considering the setting in the EU-15 countries, a scheme of locally undifferentiated emission permits is proposed which is distinguished by a high degree of both economic efficiency and market functioning. However, as our model simulations indicate, national deposition targets will be violated in all probability due to the scheme’s missing differentiation regarding the receptors. The risk of hot spots is addressed adequately by a differentiated bundle of countermeasures. The general economic impact of an EU-wide permit scheme is low, and, in terms of change in GDP, lower compared to a non-coordinated SO2 policy. The proposed mode of the initial permit allocation allows for early price signals and guarantees maximum static and dynamic efficiency. Balancing the interests of existing and new emitters, a long-term transition from the grandfathering to the free auction procedure is chosen

Nuclear spin-orbit interaction from chiral pion-nucleon dynamics

Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent nuclear spin-orbit strength $U_{ls}(p,k_f)$. This quantity is derived from the spin-dependent part of the interaction energy $\Sigma_{spin} = {i\over 2} \vec \sigma \cdot (\vec q \times\vec p) U_{ls}(p,k_f)$ of a nucleon scattering off weakly inhomogeneous isospin symmetric nuclear matter. We find that iterated $1\pi$-exchange generates at saturation density, $k_{f0}=272.7$MeV, a spin-orbit strength at $p=0$ of $U_{ls}(0,k_{f0})\simeq 35$ MeVfm$^2$ in perfect agreement with the empirical value used in the shell model. This novel spin-orbit strength is neither of relativistic nor of short range origin. The potential $V_{ls}$ underlying the empirical spin-orbit strength $\widetilde U_{ls}= V_{ls} r_{ls}^2$ becomes a rather weak one, $V_{ls}\simeq 17$ MeV, after the identification $r_{ls}= m_\pi^{-1}$ as suggested by the present calculation. We observe however a strong $p$-dependence of $U_{ls}(p,k_{f0})$ leading even to a sign change above $p=200$MeV. This and other features of the emerging spin-orbit Hamiltonian which go beyond the usual shell model parametrization leave questions about the ultimate relevance of the spin-orbit interaction generated by $2\pi$-exchange for a finite nucleus. We also calculate the complex-valued isovector single-particle potential $U_I(p,k_f)+ i W_I(p,k_f)$ in isospin asymmetric nuclear matter proportional to $\tau_3 (N-Z)/(N+Z)$. For the real part we find reasonable agreement with empirical values and the imaginary part vanishes at the Fermi-surface $p=k_f$.Comment: 20 pages, 10 Figures, Accepted for publication in Nuclear Physics

In-medium chiral SU(3) dynamics and hypernuclear structure

A previously introduced relativistic energy density functional, successfully applied to ordinary nuclei, is extended to hypernuclei. The density-dependent mean field and the spin-orbit potential are consistently calculated for a $\Lambda$ hyperon in the nucleus using the SU(3) extension of in-medium chiral perturbation theory. The leading long range $\Lambda N$ interaction arises from kaon-exchange and $2\pi$-exchange with $\Sigma$ hyperon in the intermediate state. Scalar and vector mean fields reflecting in-medium changes of the quark condensates are constrained by QCD sum rules. The model, applied to oxygen as a test case, describes spectroscopic data in good agreement with experiment. In particular, the smallness of the $\Lambda$ spin-orbit interaction finds a natural explanation in terms of an almost complete cancellation between scalar-vector background contributions and long-range terms generated by two-pion exchange.Comment: 10 pages, 2 figures, elsart class. Minor revision

Neutron star properties and the equation of state of neutron-rich matter

We calculate total masses and radii of neutron stars (NS) for pure neutron matter and nuclear matter in beta-equilibrium. We apply a relativistic nuclear matter equation of state (EOS) derived from Dirac-Brueckner-Hartree-Fock (DBHF) calculations. We use realistic nucleon-nucleon (NN) interactions defined in the framework of the meson exchange potential models. Our results are compared with other theoretical predictions and recent observational data. Suggestions for further study are discussed.Comment: 13 pages, 9 figures, 1 table; Revised version, accepted for publication in Physical Review

Scales in nuclear matter: Chiral dynamics with pion nucleon form factors

A systematic calculation of nuclear matter is performed which includes the long-range correlations between nucleons arising from one- and two-pion exchange. Three-body effects from $2\pi$-exchange with excitations of virtual $\Delta(1232)$-isobars are also taken into account in our diagrammatic calculation of the energy per particle $\bar E(k_f)$. In order to eliminate possible high-momentum components from the interactions we introduce at each pion-baryon vertex a form factor of monopole type. The empirical nuclear matter saturation point, $\rho_0 \simeq 0.16$fm$^{-3}$, $\bar E_0\simeq -16$MeV, is well reproduced with a monopole mass of $\Lambda \simeq 4\pi f_\pi \simeq 1.16$GeV. As in the recent approach based on the universal low-momentum $NN$-potential $V_{\rm low-k}$, the inclusion of three-body effects is crucial in order to achieve saturation of nuclear matter. We demonstrate that the dependence of the pion-exchange contributions to $\bar E(k_f)$ on the ''resolution'' scale $\Lambda$ can be compensated over a wide range of $\Lambda$ by counterterms with two ''running'' contact-couplings. As a further application we study the in-medium chiral condensate $(\rho)$ beyond the linear density approximation. For $\rho \leq 1.5 \rho_0$ we find small corrections from the derivative $d \bar E(k_f)/d m_\pi$, which are stable against variations of the monopole regulator mass $\Lambda$.Comment: 13 pages, 6 figure

Patterns of Individual Shopping Behavior

Much of economic theory is built on observations of aggregate, rather than individual, behavior. Here, we present novel findings on human shopping patterns at the resolution of a single purchase. Our results suggest that much of our seemingly elective activity is actually driven by simple routines. While the interleaving of shopping events creates randomness at the small scale, on the whole consumer behavior is largely predictable. We also examine income-dependent differences in how people shop, and find that wealthy individuals are more likely to bundle shopping trips. These results validate previous work on mobility from cell phone data, while describing the unpredictability of behavior at higher resolution.Comment: 4 pages, 5 figure

Equation of state for nuclear matter based on density dependent effective interaction

An interesting method of obtaining equation of state for nuclear matter, from a density dependent M3Y interaction, by minimizing the energy per nucleon is described. The density dependence parameters of the interaction are obtained by reproducing the saturation energy per nucleon and the saturation density of spin and isospin symmetric cold infinite nuclear matter. The nuclear matter equation of state thus obtained is then used to calculate the pressure, the energy density, the nuclear incompressibility and the velocity of sound in nuclear medium. The results obtained are in good agreement with experimental data and provide a unified description of radioactivity, scattering and nuclear matter.Comment: 10 pages including 2 figure