Formulation of fundamental theories of physics, the origin and nature of Dark Matter and Dark Energy, methods to derive Lagrangians, wave propagation in stellar atmospheres, stability of planetary orbits in extra-solar systems, and high-dimensional chaos.
The main focus of my current research is on finding new physics that would explain the origin and nature of Dark Matter and Dark Energy. I seek new invariant dynamical equations that can be derived from the requirement that they describe state functions, which transform like irreducible representations of a group of all transformations that leave the metric invariant. This approach follows Wigner and others in their assessment that an elementary particle must transform as one of the irreducible representations of the metric's group in a Hilbert space. The developed method and the first obtained results are described in two recent papers (MF1 and MF2).
Now, I investigate analytic state functions being either scalars or vectors, or spinors, or tensors of rank two or higher, and consider Galilean, Minkowski and other metrics; note that different metrics lead to different fundamental physical theories and different sets of elementary particles. The obtained invariant dynamical equations include both already known dynamical equations, like Schrödinger, Klein-Gordon, Dirac, Proca and other equations, as well as new equations that are being used to formulate new physical theories of particles. An anticipated result is that one of these new theories of particles will correctly describe the nature and behavior of Dark Matter, and that predictions of this theory can be verified experimentally.
I am a Guest Editor of the Special Issue on 'Dark Sides of Our Universe', which is devoted to our current understanding of Dark Matter and Dark Energy, and it will be published by 'Advances in Astronomy' in August 2009
The fact that most equations of modern physics can be derived from a Lagrangian formalism is well-known. However, it is not always obvious that Lagrangians for these equations were obtained in an ad hoc fashion and that they were not part of an a priori process that originally led to the equations. I have worked on methods to formally derive standard and non-standard Lagrangians for dynamical equations that describe a broad range of problems in different areas of classical and quantum physics. My recent results demonstrate that Bessel, Legendre, Laguerre, Hermite, Chebyshev, Jacobi, hypergeometric and confluent hypergeometric equations, the Lane-Emden equation, and other equations admit Lagrangian formulation (MRS, M1 and M2).
Theoretical Astrophysics
My contributions are on the generation, propagation and dissipation of non-radiative energy in atmospheres of late-type stars, and on construction of theoretical chromosphere models and winds. I have also worked on some white dwarfs problems including a search for coronal X-ray emissions from magnetic and non-magnetic cool white dwarfs using ROSAT and Chandra. I have developed a novel analytical technique based on the Klein-Gordon equation and used it to determine cutoff frequencies for acoustic waves propagating in inhomogeneous media (MMM). The method has also been used in my recent studies of the wave propagation in solar magnetic flux tubes and the obtained results are published in several papers (e.g., MRH and RMH), and presented in posters (e.g., Poster) and in talks (e.g., Talk1 andTalk2).
I have also been involved in theoretical prediction of the enhanced stellar activity in selected planetary systems resulting from the proximity of giant planets to their host stars. This theoretical prediction was confirmed by observations and this triggered a number of citations of both the observational and theoretical results.
Citations in scientific magazines (e.g., Science, Astrobiology Magazine, Sky & Telescope), the popular press (USA Today, New York Times), and on national TV (CNN) and local radio stations.
My current work involves studies of the zones of stability of planetary orbits in the newly discovered planetary systems including double and triple stellar systems. I also investigate orbital stability of Earth-like planets in stellar habitable zones. In two recent papers (CEM and ECM), the stringent criteria for orbital stability of planets in stellar binary systems are determined and the instability transition in the restricted 3-body problem is established.
Chaos and Nonlinear Physics
My research activities in this field include generalization of Julia and Mandelbrot sets, studies of routes to chaos in coupled Duffing oscillators, and application of fractal statistics to solar magnetic field measurements. Pictures of generalized Julia sets shown below were selected to illustrate the cover of FRACTALS and the 2007 APS Calendar.
I have also worked on extending the 3D Lorenz model to higher dimensions by adding energy conserving higher-order modes in double Fourier expansions of stream functions and temperature variations. The obtained results show that the lowest-order Lorenz model is an 8D system and that the onset of chaos and routes to chaos are different in this system than in the original Lorenz model (RM1, RM2 and RM3).
In 2007, I was invited to present a 3-hour tutorial on 'High-Dimensional Chaos' at the IASTED International Conference on Modern Nonlinear Theory: Bifurcations and Chaos in Montreal, Canada (Tutorial1, Tutorial2 and Tutorial3). A review paper that is an extended version of this tutorial will appear in 'Bifurcation and Chaos' in 2009 (MM).
“High-Dimensional Chaos in Dissipative and Driven Dynamical Systems”, Musielak, Z.E., and Musielak, D.E., Bifurcation and Chaos, in press (2009)
2009
“General Dynamical Equations for Free Particles and their Galilean Invariance”, Musielak, Z.E., and Fry, J.L., Int. J. Theor. Physics, in press (2009)
2009
“Physical Theories in Galilean Space-Time and the Origin of Schrödinger-like Equations”, Musielak, Z.E., and Fry, J.L., Annals of Physics, in press (2009)
2008
“The Instability Transition for the Restricted 3-Body Problem. I. Theoretical Approach”, Eberle, J., Cuntz, M., and Musielak, Z.E., Astron. Astrophys,, 489, 1329-1335 (2008)
2008
“Method to Derive Lagrangian and Hamiltonian for a Nonlinear Dynamical System with Variable Coefficients", Musielak, Z. E., Roy, D., and Swift, L.D., Chaos, Solitons & Fractals, 38, 894-902 (2008)
Outstanding Research Award, UTA, 2002
Humboldt Prize, Germany, 1997
DFG Research Award, Germany, 1995
Research and Creative Achievement Award, UAH, 1992
Smithsonian Research Award, SAO, 1987
NAS/NRC Award, NASA/MSFC, 1986
Teaching Awards
Campus Kahuna Award, UTA, 2003
Best Instructor Award, UAH, 1997
Outstanding Assistant Professor, UAH, 1993
Teaching
I teach undergraduate and graduate courses in physics, astronomy and mathematics, from undergraduate Astronomy to graduate Quantum Field Theory and General Relativity. I greatly enjoy teaching classes at different levels and the interaction with students. My philosophy of teaching is straightforward: provide an atmosphere to get my students interested in a subject and stimulate their thinking by asking challenging questions or leading an interactive discussion. I am very enthusiastic about the subject of my teaching and this, I believe, creates excitement and motivation in the classroom.
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Faculty Profile
Arlington, TX 76019 
Mail Box: 19059, Chemistry and Physics Building, Room No.: 328 
817-272-2513 
