The impact of superconductivity and the Hall effect in models of magnetised neutron stars

Equilibrium configurations of the internal magnetic field of a pulsar play a key role in modelling astrophysical phenomena from glitches to gravitational wave emission. In this paper, we present a numerical scheme for solving the Grad–Shafranov equation and calculating equilibrium configurations of pulsars, accounting for superconductivity in the core of the neutron star, and for the Hall effect in the crust of the star. Our numerical code uses a finite difference method in which the source term appearing in the Grad–Shafranov equation, which is used to model the magnetic equilibrium is non-linear. We obtain solutions by linearising the source and applying an under-relaxation scheme at each step of computation to improve the solver’s convergence. We have developed our code in both C++ and Python, and our numerical algorithm can further be adapted to solve any non-linear PDEs appearing in other areas of computational astrophysics. We produce mixed toroidal–poloidal field configurations, and extend the portion of parameter space that can be investigated with respect to previous studies. We find that in even in the more extreme cases, the magnetic energy in the toroidal component does not exceed approximately 5% of the total. We also find that if the core of the star is superconducting, the toroidal component is entirely confined to the crust of the star, which has important implications for pulsar glitch models which rely on the presence of a strong toroidal field region in the core of the star, where superfluid vortices pin to superconducting fluxtubes.

Error estimation of the Besse relaxation scheme for a semilinear heat equation

The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse Relaxation Scheme in time [C. R. Acad. Sci. Paris S{\'e}r. I, vol. 326 (1998)] with a central finite difference method in space. A new, composite stability argument is developed, leading to an optimal, second-order error estimate in the discrete $L_t^{\infty}(H_x^2)-$norm at the time-nodes and in the discrete $L_t^{\infty}(H_x^1)-$norm at the intermediate time-nodes. It is the first time in the literature where the Besse Relaxation Scheme is applied and analysed in the context of parabolic equations.

Effects of operating conditions on cavitation induction of spiral groove liquid-film seal (SG-LFS)

Purpose The purpose of this paper is to study the effects of operating conditions including process coefficient, lubricant viscosity and cavitation pressure on the cavitation of spiral groove liquid-film seal (SG-LFS). Design/methodology/approach A mathematical model of SG-LFS is established based on the JFO boundary and a relative density is introduced. The universal governing equation after a coordinate transformation is discretized by the FVM method and solved by the Gauss-Seidel relaxation scheme. Findings The results indicate that the two-dimensional size of cavitation and cavitation degree are affected significantly by the process coefficient and lubricant viscosity but the effect of cavitation pressure can be ignored. Originality/value The effect mechanisms of operating conditions on the cavitation of SG-LFS are studied by the JFO boundary and cavitation degree characterized by a relative density. The results presented are helpful to perfect and deeply understand the cavitation mechanism of liquid-film seal. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2020-0083/

1-D Dam-Break Modeling: Case Study of Successive Dam-Break

<p>Unexpected disastrous floods or flash floods caused by climate change are becoming more frequent. Therefore, there is a possibility of dam failure due to natural disasters including heavy rainfall, landslide and earthquakes, and an unexpected emergencies may be caused by the defect of dams or appurtenant structures due to the aging of the dam. It is desirable to prevent in advance because emergencies such as dam failure can cause many casualties and property damage.</p><p>Dam failure rapidly propagates enormous flow to the downstream, so the evacuation time is short and causes many casualties compared to other types of floods. In order to minimize casualties from dam failure, it is important to establish emergency action plan, flood hazard map and advance warning system. For the establishment of these three, accurate dam failure modeling is required. Most of the studies on dam failure modeling have been conducted for single dam failure rather than successive failure of two or more dams. This study conducted a successive failure modeling of Janghyun Dam and Dongmak Dam in Korea, which collapsed due to Typhoon Rusa in 2002.</p><p>The DAMBRK (Dam-Break Flood Forecasting Model) has been applied to the successive failure modeling of two dams which are located in parallel. The relaxation scheme was added to DAMBRK to consider the tributary cross-section. In addition, this study proposed a method to estimate the dam failure duration using empirical formulas for the peak discharge of dam failure and failure formation time of ASDSO (Association of State Dam Safety Officials). The failure hydrograph of two dams was estimated using the proposed method and the discharge and water surface elevation were predicted at the main locations of downstream according to the propagation of dam failure discharge. The accuracy and applicability of the modeling were validated by comparing the predicted water surface elevations with field surveyed data and showing good agreements between predictions and measurements.</p><p>Keywords:  Successive Dam-Break, Flooding, DAMBRK</p><p>Acknowlegement</p><p>This work was supported by Korea Environment Industry & Technology Institute(KEITI) though Water Management Research Program, funded by Korea Ministry of Environment(MOE)(79609)</p>