1,281 research outputs found
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
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