On the efficient numerical solution of lattice systems with low-order couplings

We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model. For the anharmonic oscillator both methods outperform standard Markov Chain Monte Carlo methods and show a significantly improved error scaling. For the quantum mechanical rotor we could, however, not find a successful way employing QMC. On the other hand, the recursive numerical integration method works extremely well for this model and shows an at least exponentially fast error scaling

Sensitivity Analysis in Economic Simulations: A Systematic Approach

Sensitivity analysis studies how the variation in the numerical output of a model can be quantitatively apportioned to different sources of variation in basic input parameters. Thus, it serves to examine the robustness of numerical results with respect to input parameters, which is a prerequisite for deriving economic conclusions from them. In practice, modellers apply different methods, often chosen ad hoc, to do sensitivity analysis. This paper pursues a systematic approach. It formalizes deterministic and stochastic methods used for sensitivity analysis. Moreover, it presents the numerical algorithms to apply the methods, in particular, an improved version of a Gauss-Quadrature algorithm, applicable to one as well as multidimensional sensitivity analysis. The advantages and disadvantages of different methods and algorithms are discussed as well as their applicability. --Sensitivity Analysis,Computational Methods

On the numerical calculation of the roots of special functions satisfying second order ordinary differential equations

We describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solutions of a large class of such equations can be represented via nonoscillatory phase functions, even in the high-frequency regime. Our algorithm achieves near machine precision accuracy and the time required to compute one root of a solution is independent of the frequency of oscillations of that solution. Moreover, despite its great generality, our approach is competitive with specialized, state-of-the-art methods for the construction of Gaussian quadrature rules of large orders when it used in such a capacity. The performance of the scheme is illustrated with several numerical experiments and a Fortran implementation of our algorithm is available at the author's website

Sensitivity analysis in economic simulations : a systematic approach

Sensitivity analysis studies how the variation in the numerical output of a model can be quantitatively apportioned to different sources of variation in basic input parameters. Thus, it serves to examine the robustness of numerical results with respect to input parameters, which is a prerequisite for deriving economic conclusions from them. In practice, modellers apply different methods, often chosen ad hoc, to do sensitivity analysis. This paper pursues a systematic approach. It formalizes deterministic and stochastic methods used for sensitivity analysis. Moreover, it presents the numerical algorithms to apply the methods, in particular, an improved version of a Gauss-Quadrature algorithm, applicable to one as well as multidimensional sensitivity analysis. The advantages and disadvantages of different methods and algorithms are discussed as well as their applicability

Rotochemical heating in millisecond pulsars: modified Urca reactions with uniform Cooper pairing gaps

Context: When a rotating neutron star loses angular momentum, the reduction in the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium that enhance the neutrino emissivity and produce thermal energy. This mechanism is named rotochemical heating and has previously been studied for neutron stars of nonsuperfluid matter, finding that they reach a quasi-steady configuration in which the rate at which the spin-down modifies the equilibrium concentrations is the same at which neutrino reactions restore the equilibrium. Aims: We describe the thermal effects of Cooper pairing with spatially uniform energy gaps of neutrons \Delta_n and protons \Delta_p on the rotochemical heating in millisecond pulsars (MSPs) when only modified Urca reactions are allowed. By this, we may determine the amplitude of the superfluid energy gaps for the neutron and protons needed to produce different thermal evolution of MSPs. Results: We find that the chemical imbalances in the star grow up to the threshold value \Delta_{thr}= min(\Delta_n+ 3\Delta_p, 3\Delta_n+\Delta_p), which is higher than the quasi-steady state achieved in absence of superfluidity. Therefore, the superfluid MSPs will take longer to reach the quasi-steady state than their nonsuperfluid counterparts, and they will have a higher a luminosity in this state, given by L_\gamma ~ (1-4) 10^{32}\Delta_{thr}/MeV \dot{P}_{-20}/P_{ms}^3 erg s^-1. We can explain the UV emission of the PSR J0437-4715 for 0.05 MeV<\Delta_{thr}<0.45 MeV.Comment: (accepted version to be published in A&A