Model of the Phase Transition Mimicking the Pasta Phase in Cold and Dense Quark-Hadron Matter

A simple mixed phase model mimicking so-called "pasta" phases in the quark-hadron phase transition is developed and applied to static neutron stars for the case of DD2 type hadonic and NJL type quark matter models. The influence of the mixed phase on the mass-radius relation of the compact stars is investigated. Model parameters are chosen such that the results are in agreement with the observational constraints for masses and radii of pulsars.Comment: 6 pages, 4 figure

Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs

This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The only assumption on the coefficient matrix in order for the algorithms to be stable is nonsingularity. These algorithms are implemented using the GiNaC library of C++ and the SymPy library of Python, considering five different data storing classes. Performance analysis of the implementations is done using the high-performance computing (HPC) platforms "HybriLIT" and "Avitohol". The experimental setup and the results from the conducted computations on the individual computer systems are presented and discussed. An analysis of the three algorithms is performed.Comment: 7 pages, 9 tables, 4 figure

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed -- diagonal dominantization and symbolic algorithms.Comment: 4 pages, 1 figure, 1 tabl

Bayesian Analysis for Extracting Properties of the Nuclear Equation of State from Observational Data including Tidal Deformability from GW170817

We develop a Bayesian analysis method for selecting the most probable equation of state under a set of constraints from compact star physics, which now include the tidal deformability from GW170817. We apply this method for the first time to a two-parameter family of hybrid equations of state that is based on realistic models for the hadronic phase (KVORcut02) and the quark matter phase (SFM$\alpha$) which produce a third family of hybrid stars in the mass-radius diagram. One parameter ($\alpha$) characterizes the screening of the string tension in the string-flip model of quark matter while the other ($\Delta_P$) belongs to the mixed phase construction that mimics the thermodynamics of pasta phases and includes the Maxwell construction as a limiting case for $\Delta_P=0$. We present the corresponding results for compact star properties like mass, radius and tidal deformabilities and use empirical data for them in the newly developed Bayesian analysis method to obtain the probabilities for the model parameters within their considered range.Comment: 8 pages, 4 figures, version accepted for publication in univers

An Algorithm for the Simulations of the Magnetized Neutron Star Cooling

The model and algorithm for the cooling of the magnetized neutron stars are presented. The cooling evolution described by system of parabolic partial differential equations with non-linear coefficients is solved using Alternating Direction Implicit method. The difference scheme and the preliminary results of simulations are presented.Comment: 6 pages, 4 figures, accepted to the European Physical Journal Web of Conferences as a contribution of the International Conference Mathematical Modeling and Computational Physics 2015 (High Tatra Mountains, Slovakia, July 13 - July 17, 2015, http://web.tuke.sk/mmcp/mmcp2015/