Separating the scales in a compressible interstellar medium

We apply Gaussian smoothing to obtain mean density, velocity, magnetic and energy density fields in simulations of the interstellar medium based on three-dimensional magnetohydrodynamic equations in a shearing box $1\times1\times2 \, \rm{kpc}$ in size. Unlike alternative averaging procedures, such as horizontal averaging, Gaussian smoothing retains the three-dimensional structure of the mean fields. Although Gaussian smoothing does not obey the Reynolds rules of averaging, physically meaningful central statistical moments are defined as suggested by Germano (1992). We discuss methods to identify an optimal smoothing scale $\ell$ and the effects of this choice on the results. From spectral analysis of the magnetic, density and velocity fields, we find a suitable smoothing length for all three fields, of $\ell \approx 75 \, \rm{pc}$. We discuss the properties of third-order statistical moments in fluctuations of kinetic energy density in compressible flows and suggest their physical interpretation. The mean magnetic field, amplified by a mean-field dynamo, significantly alters the distribution of kinetic energy in space and between scales, reducing the magnitude of kinetic energy at intermediate scales. This intermediate-scale kinetic energy is a useful diagnostic of the importance of SN-driven outflows

Solution of a Class of Optimization Problems Based on Hyperbolic Penalty Dynamic Framework

In this study, a gradient-based dynamic system is constructed in order to solve a certain class of optimization problems. For this purpose, the hyperbolic penalty function is used. Firstly, the constrained optimization problem is replaced with an equivalent unconstrained optimization problem via the hyperbolic penalty function. Thereafter, the nonlinear dynamic model is defined by using the derivative of the unconstrained optimization problem with respect to decision variables. To solve the resulting differential system, a steepest descent search technique is used. Finally, some numerical examples are presented for illustrating the performance of the nonlinear hyperbolic penalty dynamic system

Solution of a Class of Optimization Problems Based on Hyperbolic Penalty Dynamic Framework

In this study, a gradient-based dynamic system is constructed in order to solve a certain class of optimization problems. For this purpose, the hyperbolic penalty function is used. Firstly, the constrained optimization problem is replaced with an equivalent unconstrained optimization problem via the hyperbolic penalty function. Thereafter, the nonlinear dynamic model is defined by using the derivative of the unconstrained optimization problem with respect to decision variables. To solve the resulting differential system, a steepest descent search technique is used. Finally, some numerical examples are presented for illustrating the performance of the nonlinear hyperbolic penalty dynamic system

Conformable Fractional Gradient Based Dynamic System for Constrained Optimization Problem

A conformable fractional gradient based dynamic system with a steepest descent direction is proposed in this paper for a class of nonlinear programming problems. The solutions of the dynamic system, modelled with the conformable fractional derivative are investigated to obtain the minimizing point of the optimization problem. For this purpose, we use a step variational iteration method, adapted to use a conformable integral definition. Numerical simulations and comparisons show that the conformable fractional gradient based dynamic system is both feasible and efficient for a certain class of equality constrained optimization problems. Furthermore, the step variational iteration method, combined with the conformable integral definition, is a reliable tool for solving a system of fractional differential equations

The distribution of mean and fluctuating magnetic fields in the multiphase interstellar medium

We explore the effects of the multiphase structure of the interstellar medium (ISM) on galactic magnetic fields. Basing our analysis on compressible magnetohydrodynamic simulations of supernova-driven turbulence in the ISM, we investigate the properties of both the mean and fluctuating components of the magnetic field. We find that the mean magnetic field preferentially resides in the warm phase and is generally absent from the hot phase. The fluctuating magnetic field does not show such pronounced sensitivity to the multiphase structure.Peer reviewe