Effective order strong stability preserving Runge–Kutta methods

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of effective order methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods—like classical order five methods—require the use of non-positive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge–Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice

Strong stability preserving explicit Runge-Kutta methods of maximal effective order

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge-Kutta methods. Relative to classical Runge-Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods - like classical order five methods - require the use of non-positive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge-Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.Comment: 17 pages, 3 figures, 8 table

Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?

In cavity quantum electrodynamics (QED), the interaction between an atomic transition and the cavity field is measured by the vacuum Rabi frequency $\Omega_0$. The analogous term "circuit QED" has been introduced for Josephson junctions, because superconducting circuits behave as artificial atoms coupled to the bosonic field of a resonator. In the regime with $\Omega_0$ comparable to the two-level transition frequency, "superradiant" quantum phase transitions for the cavity vacuum have been predicted, e.g. within the Dicke model. Here, we prove that if the time-independent light-matter Hamiltonian is considered, a superradiant quantum critical point is forbidden for electric dipole atomic transitions due to the oscillator strength sum rule. In circuit QED, the capacitive coupling is analogous to the electric dipole one: yet, such no-go property can be circumvented by Cooper pair boxes capacitively coupled to a resonator, due to their peculiar Hilbert space topology and a violation of the corresponding sum rule

Charge Symmetry Breaking in 500 MeV Nucleon-Trinucleon Scattering

Elastic nucleon scattering from the 3He and 3H mirror nuclei is examined as a test of charge symmetry violation. The differential cross-sections are calculated at 500 MeV using a microsopic, momentum-space optical potential including the full coupling of two spin 1/2 particles and an exact treatment of the Coulomb force. The charge-symmetry-breaking effects investigated arise from a violation within the nuclear structure, from the p-nucleus Coulomb force, and from the mass-differences of the charge symmetric states. Measurements likely to reveal reliable information are noted.Comment: 5 page

Radiative capture of protons by deuterons

The differential cross section for radiative capture of protons by deuterons is calculated using different realistic NN interactions. We compare our results with the available experimental data below $E_x = 20 MeV$. Excellent agreement is found when taking into account meson exchange currents, dipole and quadrupole contributions, and the full initial state interaction. There is only a small difference between the magnitudes of the cross sections for the different potentials considered. The angular distributions, however, are practically potential independent.Comment: 4 pages (twocolumn), 4 postscript figures included, submitted for publication, revised versio

Positive pion absorption on 3He using modern trinucleon wave functions

We study pion absorption on 3He employing trinucleon wave functions calculated from modern realistic NN interactions (Paris, CD Bonn). Even though the use of the new wave functions leads to a significant improvement over older calculations with regard to both cross section and polarization data, there are hints that polarization data with quasifree kinematics cannot be described by just two-nucleon absorption mechanisms.Comment: 14 pages, 6 figure

Threshold Electrodisintegration of ^3He

Cross sections were measured for the near-threshold electrodisintegration of ^3He at momentum transfer values of q=2.4, 4.4, and 4.7 fm^{-1}. From these and prior measurements the transverse and longitudinal response functions R_T and R_L were deduced. Comparisons are made against previously published and new non-relativistic A=3 calculations using the best available NN potentials. In general, for q<2 fm^{-1} these calculations accurately predict the threshold electrodisintegration of ^3He. Agreement at increasing q demands consideration of two-body terms, but discrepancies still appear at the highest momentum transfers probed, perhaps due to the neglect of relativistic dynamics, or to the underestimation of high-momentum wave-function components.Comment: 9 pages, 7 figures, 1 table, REVTEX4, submitted to Physical Review

Integrating methods for ecosystem service assessment and valuation: Mixed methods or mixed messages?

A mixed-method approach was used to assess and value the ecosystem services derived from the Dogger Bank, an extensive shallow sandbank in the southern North Sea. Three parallel studies were undertaken that 1) identified and quantified, where possible, how indicators for ecosystem service provision may change according to two future scenarios, 2) assessed members of the public's willingness-to-pay for improvements to a small number of ecosystem services as a consequence of a hypothetical management plan, and 3) facilitated a process of deliberation that allowed members of the public to explore the uses of the Dogger Bank and the conflicts and dilemmas involved in its management. Each of these studies was designed to answer different and specific research questions and therefore contributes different insights about the ecosystem services delivered by the Dogger Bank. This paper explores what can be gained by bringing these findings together post hoc and the extent to which the different methods are complementary. Findings suggest that mixed-method research brings more understanding than can be gained from the individual approaches alone. Nevertheless, the choice of methods used and how these methods are implemented strongly affects the results obtained

Quark-model study of few-baryon systems

We review the application of non-relativistic constituent quark models to study one, two and three non-strange baryon systems. We present results for the baryon spectra, potentials and observables of the NN, N$\Delta$, $\Delta\Delta$ and NN$^*(1440)$ systems, and also for the binding energies of three non-strange baryon systems. We make emphasis on observable effects related to quark antisymmetry and its interplay with quark dynamics.Comment: 82 pages, 36 figures, 18 tables. Accepted for publication in Reports on Progress in Physic