Edward T. Gawlinski
(Computational) My research activity is concentrated in two broad areas of applied physics. The first, quantum transport in sub-micron semiconducting devices, is a very interesting area of research due to the many novel devices whose operation explicitly depends on the quantum mechanical properties of the electrons which flow through them. An example of such a device is the Esaki diode, which for a broad range of applied voltage actually displays a negative resistance. The second area of research that I am actively engaged in is the study of accelerated superconducting devices and circuits. My students and I are currently studying the feasibility of building a "no moving parts" gyroscope based on the property that a rotating superconductor produces a magnetic field proportional in strength to the rate of rotation.
In each of the areas outlined above, my students and I use computer simulations to gain a detailed understanding of the behavior of the system in question. This is necessary because the complexity of these systems and the non-linearity of the basic equations describing them make it impossible to obtain analytic, closed-form results. In this field of computational physics we use supercomputers and high performance workstations to simulate our systems either by molecular dynamics, Monte Carlo, or by iterative solutions of non-linear differential equations. Sate-of-the-art computer graphics is required to visualize our results. Therefore students working in this area must develop exceptional computer skills involving programming, operating systems and scientific visualization, all essential requirements of the modern technical job market.
The following are more technical descriptions of the research areas outlined above:
In the area of quantum transport, we have been applying the density-functional techniques of Kohn and Sham to the problem of understanding the effects of space-charge build-up, inelastic carrier scattering and bound carrier-hole excitonic states upon the transport of carriers and holes through semiconducting devices of spatial dimension less than 100 Angstroms. A typical device considered has been the Esaki (or quantum-well) tunnel diode. At such small length scales the electron transport is dominated by quantum effects. The density-functional technique allows for the self-consistent solution of the carrier wave-function with the electrostatic potential developed by the many-electron, many-hole charge distribution, as well as effective potentials used to model spin effects. Using these techniques we have been able to predict device performance characteristics under a wide variety of temperature, geometric and material constituent conditions.
In the area of superconducting devices, we have been using a high-performance numerical technique, the finite-element method (FEM), to solve the Ginszburg-Landau (GL) equations for superconductors. These equations, along with their boundary condition, describe the spatial distribution of the magnetic vector potential and the wave function of the Cooper-pair condensate within a superconducting sample. The GL equations are a system of five coupled non-linear partial differential equations in the three components of the vector potential and the real and imaginary parts of the Cooper-pair condensate wave-function. As such, state-of-the-art numerical methods are required for their solution. Such solutions are obtained by iterating appropriately linearized versions of the GL equations, using the FEM to obtain a single iterate solution. This program is now being applied to the problem of determining the current-density and magnetic field distributions of superconducting patterns being used in particle detectors (see research description of Professor C. J. Martoff).
Along these same lines, my students and I have made progress in the derivation of the GL equations for accelerated superconductors. Using the same numerical methods described above, we have been testing the feasibility of constructing a "no moving parts gyroscope" based on the angular velocity-dependent London moment produced by a rotating superconductor. At present, we are using our numerical solutions of the modified GL equations to determine the best magnetic shielding strategy for this device.
Mathematical models of tumour invasion mediated by transformation-induced alteration of microenvironmental pH, Gatenby, R. A. and E. T. Gawlinski, Novartis Found Symp 240: 85-96; discussion 96-9 (2001).
A cellular automaton model of early tumor growth and invasion. Patel, A. A., E. T. Gawlinski, et al., J Theor Biol 213(3): 315-31 (2001).
The possible role of postoperative azotemia in enhanced survival of patients with metastatic renal cancer after cytoreductive nephrectomy, Gatenby, R. A., E. T. Gawlinski, et al., Cancer Res 62(18): 5218-22 (2002).
Analysis of tumor as an inverse problem provides a novel theoretical framework for understanding tumor biology and therapy, Gatenby, R. A., Maini, P. K. and Gawlinski, E. T., Appl Math Lett 15(3): 339-345 (2002).
The glycolytic phenotype in carcinogenesis and tumor invasion: insights through mathematical models, Gatenby, R. A. and E. T. Gawlinski, Cancer Res 63(14): 3847-54 (2003).