Chris McMullen, Ph.D.

Instructor of Physics

Louisiana School for Math, Science, and the Arts

Student Research

Distinction Projects:

• Neutrino oscillations: Renaldo Webb used experimental data to construct a mass matrix to theoretically describe three-way neutrino oscillations. He did this by solving the eigenvalue problem in reverse: That is, experimental data provided limited information about the eigenvalues and eigenvectors of the mass matrix, so it was necessary to work “backwards” to determine the mass matrix (“forward” corresponding to starting with the mass matrix and determining the eigenvalues and eigenvectors through diagonalization). Challenges included the fact that not all of the eigenvalues or components of the eigenvectors had been measured, there were large uncertainties in the measurements, and it was well-known that one of the measurements was not in agreement with the others. Renaldo went on to major in physics at MIT.

• Carbon nanotubes: Omar Mysore’s Distinction project evolved from research that he did at MIT’s RSI program in the summer prior to his senior year. Omar also went on to major in physics at MIT.

• Three-body problem: Alexander Duchene developed a numerical solution to the three-body problem. He is currently analyzing applications of his program as well as the rate of convergence and errors.

• Quantum mechanics experiments: Megan Ratcliff is studying experiments in quantum mechanics with results that have semi-philosophical interpretations. After mastering past experiments, she will apply the fundamental concepts that she has learned to resolve modern paradoxes.

Physics Lab Projects:

• Two-dimensional harmonic oscillator: A student wrote a program to determine position, velocity, acceleration, force, momentum, potential energy, kinetic energy, and total energy as functions of time for the two-dimensional harmonic oscillator. His program also graphed the Lissajous curves.

• Variation of gravitational acceleration with altitude: A student modified her previous projectile motion project, involving a moving source, to account for the variation of gravitational acceleration with altitude through a numerical solution to the second-order differential equation that results from Newton’s second law.

• Simulation of complex waveforms: A student wrote a program to plot the superposition of traveling waves as a function of position and time. For a fixed time, this demonstrated the basic principle of superposition. Another special case considered was beats. The program also simulated more complex waveforms.

• Projectile motion with air resistance: A student applied Euler’s method to account for the effects of air resistance in projectile motion. His program was able to compute the launch angle that maximizes horizontal range when air resistance is not neglected.

• Projectile motion with a moving source: A student solved the problem of what launch angle maximizes the horizontal range when a projectile is launched from a moving source in the absence of air resistance.

• Average wind power: A student wrote a program to determine in what direction a windmill should be oriented in order to harness the most power from the wind. She collected data for average daily wind speed and direction over the course of a month. First, she added these wind velocities vectorially. Later, she used the formula for the average power produced by the windmill and numerically determined which direction maximized the power produced in one month, which differed slightly from the direction of the resultant velocity.

• Numerical solution to statics problems: A student wrote a program to determine the tension in a tie rope and stress on a hingepin for various statics problems.

• Calculation of seasonal tidal effects: A student wrote a program to determine the magnitude and direction of the difference in the net force that the moon exerts on 1 kg of water on the near and far sides of the earth as well as the for the sun, then added these vectorially to determine the net tidal effect. She graphed this net difference in force as a function of time to illustrate spring and neap tides.

• Balancing torques: A student wrote a program to determine what unknown force would balance a set of torques at a particular position or where a force should be applied to balance a set of torques.

Research Opportunities: Students interested in working on a research project in physics are encouraged to see Dr. McMullen, who will be happy to discuss possible projects and what they would entail. More mathematically involved projects in mathematical physics and computer programming projects in computational physics are also available for students who wish to make good use of their math or programming skills.

• Distinction and Junior Thesis: The Distinction and Junior Thesis programs offer qualifying students (based on overall and subject GPA, for one) a great platform, with a timeline to help stay on track, by which to undertake and complete an advanced research project. The formal Distinction paper and review by a committee of faculty members is good experience for a collegiate thesis, and the presentation among peers provides some recognition for the accomplishment.

• Future Scientist Program (FSP): Students who are eligible for FSP (based on overall and science GPA and other criteria) should consider joining FSP during their sophomore or junior year. The quarter-credit SC300 course, which FSP students take, will help students develop their research skills. FSP students are encouraged to work on research projects and to participate in regional and national science competitions.

• Science Competitions: Students may present their research projects at the annual LSMSA science fair, held after the Thanksgiving break, as well as regional and national competitions, including

• Developing a Project: Students interested in working on a research project in physics – whether it is for physics lab, FSP, Distinction, or just for fun – should see Dr. McMullen. The first step is to determine areas of interest in physics and beyond, such as math and programming. Dr. McMullen has numerous ideas of research projects in physics, mathematical physics, and computational physics, and will be happy to help students find a suitable project.

Personal Research

Expertise:

• General area of expertise: high-energy collider phenomenology. This includes elementary particles and their fundamental interactions, governed by quantum field theory. It involves developing new theoretical models and comparing with existing high-energy collider data as well as making predictions for future high-energy collider experiments. Connecting the theory to experiment in this field generally requires application of various methods from numerical analysis.

• Principal area of active research: superstring-inspired large extra dimensions. New developments in superstring theory in the 1990’s motivated the case for large extra dimensions – much larger than originally predicted by string theory – as a novel solution to a fundamental hierarchy problem that would otherwise be present in supersymmetry. Current and upcoming experiments have the potential to discover extra dimensions in our universe. This means that superstring theory and the extra dimensions that it predicts are now more than mere mathematical and philosophical wonders.

• Other areas of interest: cross products and Maxwell’s equations in higher dimensions; writing computer programs to aid in visualization in higher-dimensional geometry; developing novel, pedagogically useful derivations in quantum mechanics, special relativity, classical mechanics, electromagnetism, and mathematical physics; preparing numerical solutions to standard problems in quantum mechanics, classical mechanics, electromagnetism, and mathematical physics.

Alumni Projects:

• Cross products and Maxwell’s equations in extra dimensions: Anthony McDavid and I collaborated on a paper on generalizing cross products and Maxwell’s equations to extra dimensions in the summer of 2006. The problem is that it is well-known that the cross product is only physically meaningful in 3D, yet there is active research in superstring-inspired universal extra dimensions, in which the particles of our universe propagate into one or more extra compact dimensions. We developed a tensor construction of the usual cross product formulas and Maxwell’s equations that does generalize to higher dimensions, expressing our results in a form that closely resembles the usual vector calculus formalism. Pedagogically, this form is more accessible than the differential geometry alternative. Anthony was a double major in physics and math at LSU at the time of this research.

• Hydrogen atom derivation and neutrino oscillations: As a short-term project, Renaldo Webb and I are working on a pedagogically useful solution to the hydrogen atom problem from quantum mechanics. In the long term, we have discussed how we might extend and apply his Distinction research to a problem involving 5x5 matrices.

Research Papers:

· “A Mechanism for Kaluza-Klein number violation in universal extra dimensions,” C.D. McMullen and S. Nandi, J. Phys. G: Nucl. Part. Phys. 35, 095002, 2008.

· “Collider implications of a non-universal Higgs,” C.D. McMullen and S. Nandi, Phys. Rev. D75, 095001, 2007.

· “Collider implications of multiple non-universal extra dimensions,” R. Ghavri, C.D. McMullen, and S. Nandi, Phys. Rev. D74, 015012, 2006.

· “Collider implications of models with extra dimensions,” C. Macesanu, C.D. McMullen, and S. Nandi, Amsterdam, 2002, ICHEP, 764, 2002.

· “New signal for universal extra dimensions,” C. Macesanu, C.D. McMullen, and S. Nandi, Phys. Lett. B546, 253, 2002.

· “Collider implications of universal extra dimensions,” C. Macesanu, C.D. McMullen, and S. Nandi, Phys. Rev. D66, 015009, 2002.

· “Collider implications of Kaluza-Klein excitations of the gluons,” D.A. Dicus, C.D. McMullen, and S. Nandi, Phys. Rev. D65, 076007, 2002.

Books:

· The Visual Guide to Extra Dimensions, Volume 1: Visualizing the Fourth Dimension, Higher-Dimensional Polytopes, and Curved Hypersurfaces, Chris McMullen, Custom Books, 2008, ISBN: 1438298927.

· A Research-Oriented Laboratory Manual for First-Year Physics: A Manual that Incorporates a Semester-Long Research Project into the First-Year Physics Curriculum, Chris McMullen, Custom Books, 2008, ISBN: 1440404143.

· The Observational Astronomy Skywatcher Notebook: Record 50 Detailed Observations of the Night Sky, Chris McMullen, Custom Books, 2008, ISBN: 1438287062.

· Laboratory Notebook for Physics Experiments: Record and Analyze Data for 15 Physics Experiments, Chris McMullen, Custom Books, 2008, ISBN: 1438284438.

Presentations:

• Oklahoma State University: Seminar on the collider phenomenology of a non-universal Higgs boson (August, 2008).

• Oklahoma State University (and the University of Oklahoma via satellite talkback t.v.): Seminar on the collider phenomenology of multiple universal extra dimensions.

• LSMSA: Colloquium on fundamental concepts in particle physics and high-energy colliders,

• Pennsylvania State University: Invited talk on the collider phenomenology of large extra dimensions (spring 2003).