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Physics Faculty

Professor Musielak

Zdzislaw MusielakDr. Zdzislaw Musielak
Professor of Physics
PhD, University of Gdansk, Poland  
Faculty Research Page
Chaos & Nonlinear Physics
Location: Room 328 CPB 
Phone: 817-272-2513

Research Interests

Formulation of fundamental theories of physics, the origin and nature of Dark Matter and Dark Energy, methods to derive standard and non-standard Lagrangians, wave propagation in stellar atmospheres, stability of planetary orbits in extra-solar systems, and high-dimensional chaos.

Research | Selected Recent Publications | Teaching


Theoretical Physics

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.

Matter graph

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 (MRSM1 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., Talk 1 and Talk 2).

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.

Star 2

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.

Fractals cover
fractal image

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 (RM1RM2 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 (Tutorial 1Tutorial 2 and Tutorial 3). A review paper that is an extended version of this tutorial will appear in ‘Bifurcation and Chaos’ in 2009 (MM).


Research Grants



Research Awards

Research Excellence Award, Provost's Office, UTA (2007)
Alexander von Humboldt Research Award, Germany (2005)
Research Excellence Award, Dean's Office, UTA (2004)
Outstanding Research Award, College of Science, UTA (2003)
Alexander von Humboldt Prize, Germany (1997)
DFG Award, University of Heidelberg, Germany (1996)
Research and Creative Achievement Award, UAH (1993)
Research Award, Smithsonian Astrophysical Observatory (1987)
NAS/NRC Award, National Academy of Sciences (1986)

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“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)

“General Dynamical Equations for Free Particles and their Galilean Invariance”, Musielak, Z.E., and Fry, J.L., Int. J. Theor. Physics, in press (2009)

“High-Dimensional Chaos in Dissipative and Driven Dynamical Systems”, Musielak, Z.E., and Musielak, D.E., Bifurcation and Chaos, in press (2009)

“Standard and Non-Standard Lagrangians for Dissipative Dynamical Systems with Variable Coefficients”, Musielak, Z.E., J. Phys. A: Math. Theor., 41, 055205 (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)

“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)

“Stringent Criteria for Stable and Unstable Planetary Orbits in Stellar Binary Systems”, Cuntz, M., Eberle, J., and Musielak, Z.E., Astrophys. J. Letters, 669, L105-L108 (2007)

“Generalized Lorenz Models and Their Routes to Chaos. I. Energy-Conserving Vertical Mode Truncations”, Roy, D., and Musielak, Z.E., Chaos, Solitons & Fractals, 32, 1038-1052 (2007)

“Generalized Lorenz Models and Their Routes to Chaos. II. Energy-Conserving Horizontal Mode Truncations”, Roy, D., and Musielak, Z.E., Chaos, Solitons & Fractals, 31, 747-756 (2007)

“Generalized Lorenz Models and Their Routes to Chaos. III. Energy-Conserving Horizontal and Vertical Mode Truncations”, Roy, D., and Musielak, Z.E., Chaos, Solitons & Fractals, 33, 1064-1070 (2007)

“Acoustic Heating of the Solar Chromosphere: Present Indeed and Locally Dominant”, Cuntz, M., Rammacher, W., and Musielak, Z.E., Astrophys. J. Letters, 657, L57-60 (2007)

“Cutoff-Free Propagation of Torsional Alfven Waves Along Thin Magnetic Flux Tubes”, Musielak, Z.E., Routh, S., and Hammer, R., Astrophys. J., 659, 650-654 (2007)

“Conditions for Propagation of Torsional Waves in Solar Magnetic Flux Tubes”, Routh, S., Musielak, Z.E., and Hammer, R., Solar Physics, 246, 133-143 (2007)

“Method to Determine Cutoff Frequencies for Acoustic Waves Propagating in Nonisothermal Media”, Musielak, Z.E., Musielak, D.E., and Mobashi, H., Physical Review E, 73, 036612 (2006)

“Quantum Action Principle and Base Operators for Bosons and Fermions”, Swift, L.D., Musielak, Z.E., and Fry, J.L., Physics Letters B, 626, 256-261 (2005)

”Fast and Accurate Method for Calculating Chromospheric Radiative Losses in Ca II and Mg II Lines", Rammacher, W., Fawzy, D., Ulmschneider, P., and Musielak, Z. E., Astrophys. J. , 631, 1113-1119 (2005)

”On the Validity of Stellar Theoretical Chromosphere Models", Ulmschneider, P., Rammacher, W., Musielak, Z. E., and Kalkofen, W., Astrophys. J. Letters , 631, (2005)

”Atmospheric Oscillations in White Dwarfs: A New Indicator of Chromospheric Activity", Musielak, Z. E., Winget, D.E., and Montgomery, M., Astrophys. J. , 630, 506-510 (2005)

”Stability of Planetary Orbits in Binary Systems", Musielak, Z. E., Cuntz, M., Marshall, E. A., and Stuit, T. D., Astron. Astrophys. , 434, 355-364 (2005)

”The Onset of Chaos in Nonlinear Dynamical Systems Determined with a New Fractal Technique", Musielak, D. E., Musielak, Z. E., and Kennamer, K, S. Fractals, 13, 1-13 (2005)

”Chaos and Routes to Chaos in Coupled Duffing Oscillators with Multiple Degrees of Freedom", Musielak, D. E., Musielak, Z. E. and Benner, J. S., Chaos, Solitons & Fractals, 24, 907-922 (2005)

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I have been teaching undergraduate and graduate courses in physics, astronomy and mathematics for more than twenty years. Classes that I taught covered the entire spectrum of courses offered by most Physics Departments and they ranged from Astronomy for undergraduate students with non-science majors to the highest level graduate courses in General Theory of Relativity and Quantum Field Theory. I greatly enjoy teaching classes at different levels and the resulting interaction with different groups of students.

My philosophy of teaching is very straightforward: provide an atmosphere to get students interested in a subject and stimulate their thinking by asking challenging questions or leading an interactive discussion. I strongly encourage my students to formulate their own questions on the discussed topic and ask them during the class. Even the simplest question asked by a student, I always treat as the most important one and take time to answer it in detail. I make myself very approachable to anyone in the class and invite students to drop by my office if they have additional questions or want to discuss the material covered in class. I am very enthusiastic about the subject of my teaching and this, I believe, creates excitement and motivation in the classroom.


Teaching Awards

Campus Kahuna Award, UTA, 2003
Best Instructor Award, UAH, 1997
Outstanding Assistant Professor, UAH, 1993


Recent Talks and Presentations

  Tutorial 1  Tutorial 2   Tutorial 3 
  Talk 1 Talk 2  


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