ITER is a challenge of global society

Nowadays, humanity requires more and more and more energy. What is more, present sources of energy can‘t provide modern society with it, besides, they are not rational and ecological enough, so that tends to be the only way to create new, radically new, source of energy and it is fusion reactor. Fusion reactor is a source of energy of new generation. ITER (International Thermonuclear Experimental Reactor) is a first step to create a commercially viable reactor

Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity

A recent paper by Lucas-Serrano et al. indicates that a high-resolution central (HRC) scheme is robust enough to yield accurate hydrodynamical simulations of special relativistic flows in the presence of ultrarelativistic speeds and strong shock waves. In this paper we apply this scheme in full general relativity (involving {\it dynamical} spacetimes), and assess its suitability by performing test simulations for oscillations of rapidly rotating neutron stars and merger of binary neutron stars. It is demonstrated that this HRC scheme can yield results as accurate as those by the so-called high-resolution shock-capturing (HRSC) schemes based upon Riemann solvers. Furthermore, the adopted HRC scheme has increased computational efficiency as it avoids the costly solution of Riemann problems and has practical advantages in the modeling of neutron star spacetimes. Namely, it allows simulations with stiff equations of state by successfully dealing with very low-density unphysical atmospheres. These facts not only suggest that such a HRC scheme may be a desirable tool for hydrodynamical simulations in general relativity, but also open the possibility to perform accurate magnetohydrodynamical simulations in curved dynamic spacetimes.Comment: 4 pages, to be published in Phys. Rev. D (brief report

Accuracy of numerical relativity waveforms from binary neutron star mergers and their comparison with post-Newtonian waveforms

We present numerical relativity simulations of nine-orbit equal-mass binary neutron star covering the quasicircular late inspiral and merger. The extracted gravitational waveforms are analyzed for convergence and accuracy. Second order convergence is observed up to contact, i.e. about 3-4 cycles to merger; error estimates can be made up to this point. The uncertainties on the phase and the amplitude are dominated by truncation errors and can be minimized to 0.13 rad and less then 1%, respectively, by using several simulations and extrapolating in resolution. In the latter case finite-radius extraction uncertainties become a source of error of the same order and have to be taken into account. The waveforms are tested against accuracy standards for data analysis. The uncertainties on the waveforms are such that accuracy standards are generically not met for signal-to-noise ratios relevant for detection, except for some best cases using extrapolation from several runs. A detailed analysis of the errors is thus imperative for the use of numerical relativity waveforms from binary neutron stars in quantitative studies. The waveforms are compared with the post-Newtonian Taylor T4 approximants both for point-particle and including the analytically known tidal corrections. The T4 approximants accumulate significant phase differences of 2 rad at contact and 4 rad at merger, underestimating the influence of finite size effects. Tidal signatures in the waveforms are thus important at least during the last six orbits of the merger process.Comment: Physical Review D (Vol.85, No.10) 201

Population dynamics at high Reynolds number

We study the statistical properties of population dynamics evolving in a realistic two-dimensional compressible turbulent velocity field. We show that the interplay between turbulent dynamics and population growth and saturation leads to quasi-localization and a remarkable reduction in the carrying capacity. The statistical properties of the population density are investigated and quantified via multifractal scaling analysis. We also investigate numerically the singular limit of negligibly small growth rates and delocalization of population ridges triggered by uniform advection.Comment: 5 pages, 5 figure

Stochastic Galerkin method for cloud simulation. Part II: a fully random Navier-Stokes-cloud model

This paper is a continuation of the work presented in [Chertock et al., Math. Cli. Weather Forecast. 5, 1 (2019), 65--106]. We study uncertainty propagation in warm cloud dynamics of weakly compressible fluids. The mathematical model is governed by a multiscale system of PDEs in which the macroscopic fluid dynamics is described by a weakly compressible Navier-Stokes system and the microscopic cloud dynamics is modeled by a convection-diffusion-reaction system. In order to quantify uncertainties present in the system, we derive and implement a generalized polynomial chaos stochastic Galerkin method. Unlike the first part of this work, where we restricted our consideration to the partially stochastic case in which the uncertainties were only present in the cloud physics equations, we now study a fully random Navier-Stokes-cloud model in which we include randomness in the macroscopic fluid dynamics as well. We conduct a series of numerical experiments illustrating the accuracy and efficiency of the developed approach