arXiv subjects

Z. E. Musielak

Publications and source records attributed to Z. E. Musielak.

49 records · Page 3Linked to original sources

arXiv2014

Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels

We present simulation results of the impulsively generated linear and non-linear Alfvén waves in the weakly curved coronal magnetic flux-tubes (coronal funnels) and discuss their implications for the coronal heating and solar wind acceleration. We solve numerically the time-dependent magnetohydrodynamic (MHD) equations to obtain the temporal signatures of the small (linear) and large-amplitude (non-linear) Alfvén waves in the model atmosphere of expanding open magnetic field configuration (e.g., coronal funnels) by considering a realistic temperature distribution. We compute the maximum transversal velocity of both linear and non-linear Alfvén waves at different heights in the coronal funnel, and study their response in the solar corona during the time of their propagation. We infer that the pulse-driven non-linear Alfvén waves may carry sufficient wave energy fluxes to heat the coronal funnels and also to power the solar wind that originates in these funnels. Our study of linear Alfvén waves show that they can contribute only to the plasma dynamics and heating of the funnel-like magnetic flux-tubes associated with the polar coronal holes.

astro-ph.SR↗

arXiv2013

Generalized Dirac and Klein-Gordon equations for spinor wavefunctions

A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equation for 4-component spinor wavefunctions. New Poincare invariant generalized Dirac and Klein-Gordon equations are also derived. In the non-relativistic limit the generalized Dirac equation gives the generalized Levy-Leblond equation and the generalized Pauli-Schrodinger equation. The main difference between the original and generalized Dirac equations is that the former and latter are obtained with zero and nonzero phase functions, respectively. Otherwise, both equations describe free elementary particles with spin 1/2, which have all other physical properties the same except their masses. The fact that the generalized Dirac equation describes elementary particles with larger masses is used to suggest that non-zero phase functions may account for the existence of three families of elementary particles in the Standard Model. This suggestion significantly differs from those previously made to account for the three families of particle physics.

math-ph↗

arXiv2013

Global and local cutoff frequencies for transverse waves propagating along solar magnetic flux tubes

The propagation of linear transverse waves along a thin isothermal magnetic flux tube is affected by a global cutoff frequency that separates propagating and non-propagating waves. In this paper, wave propagation along a thin but non-isothermal flux tube is considered and a local cutoff frequency is derived. The effects of different temperature profiles on this local cutoff frequency are studied by considering different power-law temperature distributions as well as the semi-empirical VAL C model of the solar atmosphere. The results show that the conditions for wave propagation strongly depend on the temperature gradients. Moreover, the local cutoff frequency calculated for the VAL C model gives constraints on the range of wave frequencies that are propagating in different parts of the solar atmosphere. These theoretically predicted constraints are compared to observational data and are used to discuss the role played by transverse tube waves in the atmospheric heating and dynamics, and in the excitation of solar atmospheric oscillations.

astro-ph.SR↗

arXiv2012

Pulse-driven nonlinear Alfvén waves and their role in the spectral line broadening

We study the impulsively generated non-linear Alfvén waves in the solar atmosphere, and describe their most likely role in the observed non-thermal broadening of some spectral lines in solar coronal holes. We solve numerically the time-dependent magnetohydrodynamic equations to find temporal signatures of large-amplitude Alfvén waves in the model atmosphere of open and expanding magnetic field configuration, with a realistic temperature distribution. We calculate the temporally and spatially averaged, instantaneous transversal velocity of non-linear Alfvén waves at different heights of the model atmosphere, and estimate its contribution to the unresolved non-thermal motions caused by the waves. We find that the pulse-driven nonlinear Alfvén waves with the amplitude $A_{\rm v}$=50 km s$^{-1}$ are the most likely candidates for the non-thermal broadening of Si VIII $λ$1445.75 Å line profiles in the polar coronal hole as reported by Banerjee et al. (1998). We also demonstrate that the Alfvén waves driven by comparatively smaller velocity pulse with its amplitude $A_{\rm v}$=25 km s$^{-1}$ may contribute to the spectral line width of the same line at various heights in coronal hole without any significant broadening. The main conclusion of this paper is that non-linear Alfvén waves excited impulsively in the lower solar atmosphere are responsible for the observed spectral line broadening in polar coronal holes. This is an important result as it allows us to conclude that such large amplitude and pulse-driven Alfvén waves do indeed exist in solar coronal holes. The existence of these waves and their undamped growth may impart the required momentum to accelerate the solar wind.

astro-ph.SR↗

arXiv2012

Fundamental dynamical equations for spinor wave functions. I. Levy-Leblond and Schrodinger equations

A search for fundamental (Galilean invariant) dynamical equations for two and four-component spinor wave functions is conducted in Galilean space-time. A dynamical equation is considered as fundamental if it is invariant under the symmetry operators of the group of the Galilei metric and if its state functions transform like the irreducible representations of the group of the metric. It is shown that there are no Galilean invariant equations for two-component spinor wave functions. A method to derive the Lévy-Leblond equation for a four-component spinor wave function is presented. It is formally proved that the Lévy-Leblond and Schrödinger equations are the only Galilean invariant four-component spinor equations that can be obtained with the Schrödinger phase factor. Physical implications of the obtained results and their relationships to the Pauli-Schrödinger equation are discussed.

math-ph↗

arXiv2012

Various representations of the quantity Newton called inertial mass

Newton introduced the concept of mass in his {\it Principia} and gave an intuitive explanation for what it meant. Centuries have passed and physicists as well as philosophers still argue over its meaning. Three types of mass are generally identified: inertial mass, active gravitational mass and passive gravitational mass. In addition to the question of what role mass plays in dynamical equations and why, the origin of the particular amount of matter associated with an elementary particle as a consequence of fundamental fields has long been a topic of research and discussion. In this paper, various representations of inertial mass are discussed within the framework of fundamental (either Galilean or Poincaré invariant) dynamical equations of waves and point particles. It is shown that the derived equations have mass-like and mass parameters for waves and point particles, respectively, and that the physical meaning of these parameters sheds a new light on the fundamental problem of the nature of inertial mass.

physics.gen-ph↗

arXiv2011

The Instability Transition for the Restricted 3-Body Problem. III. The Lyapunov Exponent Criterion

We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spectra. The obtained results are compared to results presented in the two previous papers of this series. It is shown that the maximum Lyapunov exponent can be used as an indicator for chaotic behaviour of planetary orbits, which is consistent with previous applications of this method, particularly studies for the Solar System. The chaotic behaviour corresponds to either orbital stability or instability, and it depends solely on the mass ratio of the binary components and the initial distance ratio of the planet relative to the stellar separation distance. Our theoretical results allow us to link the study of planetary orbital stability to chaos theory noting that there is a large array of literature on the properties and significance of Lyapunov exponents. Although our results are given for the special case of the CR3BP, we expect that it may be possible to augment the proposed Lyapunov exponent criterion to studies of planets in generalized stellar binary systems, which is strongly motivated by existing observational results as well as results expected from ongoing and future planet search missions.

astro-ph.SR↗

arXiv2011

Case Studies of Habitable Trojan Planets in the System of HD 23079

We investigate the possibility of habitable Trojan planets in the HD 23079 star-planet system. This system consists of a solar-type star and a Jupiter-type planet, which orbits the star near the outer edge of the stellar habitable zone in an orbit of low eccentricity. We find that in agreement with previous studies Earth-mass habitable Trojan planets are possible in this system, although the success of staying within the zone of habitability is significantly affected by the orbital parameters of the giant planet and by the initial condition of the theoretical Earth-mass planet. In one of our simulations, the Earth-mass planet is captured by the giant planet and thus becomes a habitable moon.

astro-ph.SR↗

arXiv2008

Orbital Stability of Planets in Binary Systems: A New Look at Old Results

About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical research, including the derivation of mathematically stringent criteria for the orbital stability of planets in stellar binary systems, valid for the "coplanar circular restricted three-body problem". In the following, we use these criteria to explore the validity of results from previous theoretical studies.

astro-ph↗

arXiv2007

Orbital Stability of Earth-Type Planets in Binary Systems

About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. Here we study the onset of instability for an Earth-type planet that is part of a binary system. Our investigation makes use of previous analytical work allowing to describe the permissible region of planetary motion. This allows us to establish a criterion for the orbital stability of planets that may be useful in the context of future observational and theoretical studies.

astro-ph↗

arXiv2007

Cutoff-Free Propagation of Torsional Alfvén Waves Along Thin Magnetic Flux Tubes

Propagation of torsional Alfvén waves along magnetic flux tubes has been extensively studied for many years but no conclusive results regarding the existence of a cutoff frequency for these waves have been obtained. The main purpose of this paper is to derive new wave equations that describe the propagation of linear torsional Alfvén waves along thin and isothermal magnetic flux tubes, and use these wave equations to demonstrate that the torsional wave propagation is not affected by any cutoff frequency. It is also shown that this cutoff-free propagation is independent of different choices of the coordinate systems and wave variables adopted in the previous studies. A brief discussion of implications of this cutoff-free propagation of torsional tube waves on theories of wave heating of the solar and stellar atmospheres is also given.

astro-ph↗

arXiv1994

Limits to Extensions of Burgers Equation

The vector Burgers equation is extended to include pressure gradients and gravity. It is shown that within the framework of the Cole-Hopf transformation there are no physical solutions to this problem. This result is important because it clearly demonstrates that any extension of Burgers equation to more interesting physical situations is strongly limited.

solv-int↗

arXiv1994

Analytic Solutions of the Vector Burgers' Equation

The well-known analytical solution of Burgers' equation is extended to curvilinear coordinate systems in three-dimensions by a method which is much simpler and more suitable to practical applications than that previously used. The results obtained are applied to incompressible flow with cylindrical symmetry, and also to the decay of an initially linearly increasing wind.

solv-int↗