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In this paper, magnetohydrodynamics of a Casson fluid flow is inspected with the presence of thermal radiation and chemical reaction. Employing the perturbation procedure, the modeling equations are tenacious; the graphs are acquired to illustrate the results. The Casson fluid velocity increases as the perturbation parameter increases. Grashof values for heat and mass transport enhanced Casson fluid velocity. Increasing Casson, magnetic, heat source, and radiation parameters reduce the flow velocity. Prandtl number, heat source, and radiation parameter all reduced the temperature profiles. Chemical reaction parameters lowered the concentration profiles. The skin friction enhances with Casson parameter impact. However, the skin-friction coefficient, Sherwood and Nusselt numbers reduce with an increment in the perturbation parameter. In certain cases, this study’s answers agreed well with the previous literature. Casson liquid with a magnetic region using mixed convection by an exponential vertical boundary layer is the novelty of the work.

Analyzed in this paper is an investigation of the impacts of the varying source of heat or thermal sink and viscous dissipation on Casson fluid flow from a moving wedge by considering thermal and momentum slips in a mathematical model. Regarding the regulation of concentration fields, we incorporated the Soret and Dufour phenomena. The outcomes are analyzed numerically by using the shooting technique. The governing parametric effects of the flow characteristics are revealed graphically. We also presented the local Sherwood and Nusselt number values for non-Newtonian fluid (Casson fluid) and Newtonian. It is discovered that the thermal and concentration boundary layer is more extensive in Casson fluid while equated with the Newtonian fluid. The thermal and mass transmission in Newtonian fluid is significantly larger than in non-Newtonian fluid. The heat source/sink, Eckert number and Dufour number boost the rate of thermal transport and depreciate the rate of mass transport for both the Newtonian and non-Newtonian fluid cases.

This study highlights the combined effect of heat and mass transfer on MHD Maxwell fluid under time-dependent generalized boundary conditions for velocity, temperature, and concentration. The classical calculus due to the fact that it is assumed as the instant rate of change of the output when the input level changes. Therefore, it is not able to include the previous state of the system called the memory effect. But in the fractional calculus (FC), the rate of change is affected by all points of the considered interval, so it can incorporate the previous history/memory effects of any system. Due to this reason, we applied the modern definition of fractional derivatives (local and nonlocals kernels). Here, the order of fractional derivative will be treated as an index of memory. The exact and semi-analytical solutions are obtained using the integral transform and inversion algorithm. Several important properties of different parameters are analyzed by graphs. Interesting results are revealed by this investigation due to their vast applications in engineering and applied sciences.

The theoretical study focuses on the examination of the convective flow of Oldroyd-B fluid with ramped wall velocity and temperature. The fluid is confined on an extended, unbounded vertical plate saturated within the permeable medium. To depict the fluid flow, the coupled partial differential equations are settled by using the Caputo (C) and Caputo Fabrizio (CF) differential time derivatives. The mathematical analysis of the fractionalized models of fluid flow is performed by Laplace transform (LT). The complexity of temperature and velocity profile is explored by numerical inversion algorithms of Stehfest and Tzou. The fractionalized solutions of the temperature and velocity profile have been traced out under fractional and other different parameters considered. The physical impacts of associated parameters are elucidated with the assistance of the graph using the software MATHCAD 15. We noticed the significant influence of the fractional parameter (memory effects) and other parameters on the dynamics of the fluid flow. Shear stress at the wall and Nusselt number also are considered. It’s brought into notice the fractional-order model (CF) is the best fit in describing the memory effects in comparison to the C model. An analysis of the comparison between the solution of velocity and temperature profile for ramped wall temperature and velocity and constant wall temperature and velocity is also performed.

In earlier works we pointed out that the disk's surface layers are non-turbulent and thus highly conducting (or non-diffusive) because of hydrodynamic and/or magnetorotational (MRI) instabilities are suppressed high in the disk where the magnetic and radiation pressures are larger than the plasma thermal pressure. We have derived equations for the vertical profiles of stationary accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity and the fact that the turbulence vanishes at the surface of the disk. Our recent analysis in Ref. 1 shows that the inward or outward advection of the large-scale magnetic field depends on the ratio of the accretion power going into magnetic disk winds to the viscous power dissipation and the plasma-β which is the ratio of the midplane plasma pressure to the magnetic pressure.

Recent radio emission, polarization, and Faraday rotation maps of the radio jet of the galaxy 3C303 have been obtained in Ref. 2 and show that one component of this jet has a galactic-scale electric current of ~ 3 × 10¹⁸ A flowing along the jet axis. We show that this current can be used to calculate the electromagnetic energy flow in this magnetically dominated jet.

We have investigated the influence of velocity shear on the linear and non-linear development of the CD kink instability. We follow temporal development of the instability within a periodic computational box. We find that helically distorted density structure propagates along the jet with speed and flow structure dependent on the location of the velocity shear relative to the characteristic radius of the helically twisted force-free magnetic field. At small radius the plasma flows through the kink. The kink propagation speed increases as the radius increases and the kink becomes more embedded in the plasma flow. Larger velocity shear radius leads to slower linear growth, makes a later transition to the nonlinear stage, and with larger maximum amplitude than occurs for a static plasma column. However, when the velocity shear radius is much greater than the characteristic radius of the helical magnetic field, linear and non-linear development become more similar to the development of a static plasma column.

Gamma Ray Bursts (GRB) are the extremely energetic transient events, visible from the most distant parts of the Universe. They are most likely powered by accretion on the hyper-Eddington rates that proceeds onto a newly born stellar mass black hole. This central engine gives rise to the most powerful, high Lorentz factor jets that are responsible for energetic gamma ray emission. We investigate the accretion flow evolution in GRB central engine, using the 2D MHD simulations in General Relativity. We compute the structure and evolution of the extremely hot and dense torus accreting onto the fast spinning black hole, which launches the magnetized jets. We calculate the chemical structure of the disk and account for neutrino cooling. Our preliminary runs apply to the short GRB case (remnant torus accreted after NS-NS or NS-BH merger). We estimate the neutrino luminosity of such an event for chosen disk and central BH mass.

We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneity, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in two-dimensional simulations. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that the so-called small-scale dynamo is occurring in the postshock region. We also find that the amplitude of magnetic-field amplification depends on the direction of the mean preshock magnetic field.

We have investigated the relaxation of a hydrostatic hot plasma column containing toroidal magnetic field by the Current-Driven (CD) kink instability as a model of pulsar wind nebulae. In our simulations the CD kink instability was excited by a small initial velocity perturbation and developed turbulent structure inside the hot plasma column. We demonstrated that, as envisioned by Begelman, the hoop stress declines and the initial gas pressure excess near the axis decreases. The magnetization parameter "σ", the ratio of the magnetic energy to the thermal energy for a hot plasma, declined from an initial value of 0.3 to about 0.01 when the CD kink instability saturated. Our simulations demonstrated that axisymmetric models strongly overestimate the elongation of the pulsar wind nebulae. Therefore, the previous requirement for an extremely low pulsar wind magnetization can be abandoned. The observed structure of the pulsar wind nebulae do not contradict the natural assumption that the magnetic energy flux still remains a good fraction of the total energy flux after dissipation of alternating fields.

Stochastic acceleration of charged particles due to their interactions with plasma waves may be responsible for producing superthermal particles in a variety of astrophysical systems. This process can be described as a diffusion process in the energy space with the Fokker-Planck equation. In this paper, a time-dependent numerical code is used to solve the reduced Fokker-Planck equation involving only time and energy variables with general forms of the diffusion coefficients. We also propose a self-similar model for particle acceleration in Sedov explosions and use the TeV SNR RX J1713.7-3946 as an example to demonstrate the model characteristics. Markov Chain Monte Carlo method is utilized to constrain model parameters with observations.

I will review the current status of our theoretical understanding of Pulsar Winds and associated nebulae (PWNe). In recent years, axisymmetric models of pulsar winds with a latitude dependent energy flux have proved very successful at explaining the morphology of PWNe as seen in the X-rays. This success has prompted developments aimed at using multi-wavelength observations of these nebulae as a diagnostics of the hidden physics of the pulsar wind and of the mechanism(s) through which particles are accelerated in these sources.

I will discuss these most recent developments in terms of the information that we infer from detailed comparison of simulated non-thermal emission with current observations.

Pulsar wind nebulae (PWN) provide a unique test-bed for the study of highly relativistic processes right at our astronomical doorstep. In this contribution we will show results from the first 3D RMHD simulations of PWN. Of key interest to our study is the long standing "sigma-problem" that challenges MHD models of Pulsars and their nebulae now for 3 decades. Earlier 2D MHD models were very successful in reproducing the morphology of the inner Crab nebula showing a jet, torus, concentric wisps and a variable knot. However, these models are limited to a purely toroidal field geometry which leads to an exaggerated compression of the termination shock and polar jet — in contrast to the observations. In three dimensions, the toroidal field structure is susceptible to current driven instabilities; hence kink instability and magnetic dissipation govern the dynamics of the nebula flow. This leads to a resolution of the sigma-problem once also the pulsar's obliqueness (striped wind) is taken into account. In addition, we present polarized synchrotron maps constructed from the 3D simulations, showing the wealth of morphological features reproduced in 2D is preserved in the 3D case.

We have investigated the influence of jet rotation and differential motion on the linear and nonlinear development of the current-driven (CD) kink instability of force-free helical magnetic equilibria via three-dimensional relativistic magnetohydrodynamic simulations. In this study, we follow the temporal development within a periodic computational box. Displacement of the initial helical magnetic field leads to the growth of the CD kink instability. In the rotating relativistic jet case, developing helical kink structure propagates along jet as it grows in amplitude. The growth rate of the CD kink instability does not depend on the jet rotation. The coupling of multiple unstable wavelengths is crucial to determining whether the jet is eventually disrupted in the nonlinear stage. The CD kink instability deformed magnetic field may trigger magnetic reconnection in the jet.

We model the propagation of pulsars through the inhomogeneous ISM using nonrelativistic axisymmetric magneto-hydrodynamic (MHD) simulations. We take into account the wind from the star, which carries predominantly azimuthal magnetic field, and investigate the PWN at different levels of magnetization (the ratio of magnetic to matter energy-densities) in the wind. We consider the interaction of PWN with large-scale and small-scale imhomogeneities in the ISM at different values of magnetization. We conclude that the inhomogeneities in the ISM can change the shapes of the bow shocks and magnetotails at different values of the magnetization.

We present the results of MHD simulation of the laboratory experiment for creating plasma jets. In the experiment on a NEODIM laser installation the plasma jet is formed as a result of the action of a powerful laser on the target. We simulated plasma flow, we chose a numerical method, boundary and initial conditions. We investigated the picture of the flow and compared it with the experiment.

Many neutron stars propagate through the interstellar medium with supersonic velocities, and their magnetospheres interact with the interstellar medium (ISM), forming bow shocks and magnetotails. Using numerical MHD simulations, we investigated the propagation of a magnetized neutron stars through a non-uniform ISM, the interaction of the magnetospheres with the ISM and the influence of ISM density on the shape of the magnetosphere tail. We consider the interaction of magnetized neutron stars with small-scale and large-scale inhomogeneities in the ISM. We conclude that the inhomogeneities in the ISM can change the shapes of the bow shocks and magnetotails at different values of the magnetization.

We consider first order perturbations on locally rotationally symmetric (LRS) class II spacetimes. In particular, we investigate the interactions between electromagnetic, gravitational, and plasma related perturbations when allowing for a non-zero magnetic field on the background spacetime. In doing so we focus on mechanisms for generating and magnifying the magnetic fields, as these kinds of mechanisms may have some relevance when trying to explain the origin of the observed large scale cosmic magnetic fields. The equations governing the behavior of the perturbations are gathered from the Ricci identities for certain preferred vector fields, the Bianchi identities, Maxwell’s equations, and from relations describing energy-momentum conservation and particle conservation for the cosmological plasma. After employing a simplified cold magnetohydrodynamic (MHD) description, and harmonically decomposing the spatial dependencies, we arrive at a closed set of ordinary differential equations in time. On analyzing this system, which decouples into an even and an odd subsector, we indeed observe possible mechanisms for generating magnetic field perturbations to first order.

This contribution is a review of some talks presented at the session “MHD processes near compact objects” of the Fourteenth Marcel Grossmann Meeting MG14. We discuss the contemporary developments of MHD processes that occur near black holes and neutron stars. The influence of magneto-plasma processes on the structure of the compact objects and accretion processes is considered.

Using numerical MHD simulations, we investigated the motion of a magnetized neutron star through a non-uniform interstellar medium (ISM), the interaction of the magnetosphere with the ISM and the influence of ISM density on the shape of the magnetosphere tail.

We show that the removal of angular momentum is possible in the presence of large scale magnetic stresses, arisen by fields much stronger than that required for magnetorotational instability, in geometrically thick, advective, sub-Keplerian accretion flows around black holes in steady-state, in the complete absence of alpha-viscosity. The efficiency of such angular momentum transfer via Maxwell stress, with the field well below its equipartition value, could be equivalent to that of alpha-viscosity, arisen via Reynolds stress, with α = 0.01 − 0.08. We find in our simpler vertically averaged advective disk model that stronger the magnetic field and/or larger the vertical-gradient of azimuthal component of magnetic field, stronger the rate of angular momentum transfer is, which in turn may lead to a faster rate of outflowing matter, which has important implications to describe the hard spectral states of black hole sources. When the generic origin of alpha-viscosity is still being explored, mechanism of efficient angular momentum transfer via magnetic stresses alone is very interesting.