Research interests

All these topics fall into two quite different areas: space plasma physics and cardiac bioelectricity. I use a combination of computer simulation and theory to study them.

Cardiac Bioelectricity

Abstracts of my recent cardiac electrophysiology papers.

Cardiac rhythm Java applet.

  1. Dynamical systems models of abnormal cardiac rhythms. The details of why the heart sometimes develops irregular rhythms are probably related to the rules governing how a patch of cardiac tissue responds given the time of arrival of stimulating action potential and the history of the tissue. One method of studying these rules is by applying rapid stimulation to a small tissue sample and record the response of the membrane potential as a function of time. We have been involved in developing dynamical systems models which reproduce the observed experimental data. In a paper recently appearing in Journal of Theoretical Biology, we show that a dynamical system involving just two variables can explain several features of the complicated behavior observed in pacing experiments involving small cardiac tissue preps. Three animations and a Java applet, available on this site, illustrate one of the models and some of the results presented in the paper.
  2. Spiral and Scroll Waves in Excitable Media. One of the most interestng controversies associate with cardiac arrhythmia is whether so-called spiral or scroll waves are responsible for many of the abnormal rhythms observed clinically. Several computer models have verified that distributed systems with local excitable dynamics can support spiral and scroll waves. One such model appears in my Physica D paper (1994). Another model, using an eigenvalue approach was presented at the 1999 BMES/EMBS Conference. These computer experiments have raised the question of whether such waves can exist in diseased or even healthy hearts. If these waves are possible in the healthy heart, then all that may be required to kill you is the wrong electrical pattern, a scary possibility! I am currently involved in improving these dynamical systems models to include more of the essential properties of cardiac cells as they pertain to the propagation of these waves. Ultimately, I hope to be able to determine which cardiac cell parameters are crucial for spiral and scroll wave development, and whether indeed these waves can persist in normal and diseased hearts.

Space Plasma Physics

What is a plasma?

See a plasma particle simulation (Java applet)

  1. Dusty plasmas. Latest paper (July, 1996). Dusty plasmas appear in several space and astrophysical settings, and also occur in process plasmas. It turns out that the charged dust grains in these plasmas are similar from a statistical mechanics viewpoint to the atoms or molecules that make up crystals, liquids or gases. This means that these dust grains can be behave like a liquid or even a solid crystal all the while they are floating in a background plasma. I am currently investigating these basic phenomena with A. Bhattacharjee (U. Iowa) using one-dimensional particle simulation techniques. We hope to be able to explain the some of the experimental results of J. Goree's group, and those of R. Merlino and N. D'Angelo.
  2. Electron acceleration above the Aurora Borealis (Under development) . The Aurora Borealis (sometimes called the Northern Lights) is caused by high-speed electrons racing the down the Earth's magnetic field crashing into the upper layers of the atmosphere. A number of plasma phenomena are often observed in or near the path of these electrons. Among these are: Alfven waves, waves which propagate as wiggles on the magnetic field lines, and double layers, small but deep density variations which are accompanied by strong electric fields. Both double layers and Alfven waves can accelerate electrons, and conversely, accelerated electrons can give rise to Alfven waves and double layers. The question is then naturally: what causes what? We have been attempting to answer this with one- and two-dimensional particle-in-cell simulations, which treat all these phenomena self-consistently. Abstracts of papers describing our novel particle simulation method which includes both the Alfven wave and parallel kinetic particle dynamics in a self-consistent manner, and the results from our simulations, are available on this web site.
  3. Farley-Buneman instability in the Earth's ionosphere. One hundred kilometers above the Earth's equator, a huge electrical current flows in an ionospheric structure called the equatorial electrojet. The current is often so intense that it creates density irregularities through a collisional two-stream process often called the Farley-Buneman instability. We have used a hybrid simulation model (particle ions and fluid electrons) to model the nonlinear behavior of this instability. See some movies of the instability, generated by our simulation code. Also available: abstracts, full text and figures from from our three Farley-Buneman simulation papers 1, 2 and 3, a preliminary report, in postscript (1.66 Meg), on a reduced mode description of the saturation of the instability, and slides and animations from a talk given locally in our department, describing the Farley-Buneman instability, our simulations, and our reduced-mode theory.
  4. Development of new particle-in-cell simulation algorithms. The inclusion of long-wavelength, slow-timescale phenomena such as Alfven waves and small, fleeting structures such as double layers in the same simulation code is often a difficult or impossible task. We have been able to accomplish this while still maintaining much of the important physics. We are now investigating the possibility of modeling double layers with an implicit method, which, if successful, will make possible faster simulations of larger, longer-timescale problems.
  5. Lower-Hybrid Cavitons in the Auroral Zone. This topic is currently on the back burner. See, however, the recent work on this subject by Rich Andrulis.
  6. Magnetohydrodynamic (MHD) dynamos: how does the Sun generate its magnetic field? If a turbulent resistivity and magnetic field scalelength are estimated for the Sun based on its observed convective activity, the Sun's magnetic field should decay away in a decade or so. It doesn't though, so what keeps it going? A likely possibility is that this convective activity strengthens the magnetic field by stretching it. Our investigation has shown that this mechanism probably does work for a particular type of flow.

Back to home page