Applied Physics and Applied Mathematics
The Department of Applied Physics and Applied Mathematics includes undergraduate and graduate studies in the fields of applied physics, applied mathematics, and materials science and engineering. The graduate program in applied physics includes plasma physics and controlled fusion; solid-state physics; optical and laser physics; medical physics; atmospheric, oceanic, and earth physics; and applied mathematics. The graduate programs in materials science and engineering are described here.
Current Research Activities in Applied Physics and Applied Mathematics
Plasma physics and fusion energy. In experimental plasma physics, research is being conducted on (1) equilibrium, stability, and transport in fusion plasmas: high-beta tokamaks, spherical tokamaks, and levitated dipoles; (2) magnetospheric physics: trapped particle instabilities and stochastic particle motion; (3) confinement of toroidal nonneutral plasmas; (4) plasma source operation and heating techniques; and (5) the development of new plasma measurement techniques. The results from our fusion science experiments are used as a basis for collaboration with large national and international experiments. For example, our recent demonstration of active feedback control of high temperature plasma instability is guiding research on NSTX at the Princeton Plasma Physics Laboratory, on the DII-D tokamak at General Atomics, and for the design of the next generation burning plasma experiment, ITER. In theoretical plasma physics, research is conducted in the fluid theory of plasma equilibrium and stability, active control of MHD instabilities, the kinetic theory of transport, and the development of techniques based on the theory of general coordinates and dynamical systems. The work is applied to magnetic fusion, nonneutral and space plasmas.
Optical and laser physics. Active areas of research include inelastic light scattering in nanomaterials, optical diagnostics of film processing, new laser systems, nonlinear optics, ultrafast optoelectronics, photonic switching, optical physics of surfaces, laserinduced crystallization, and photon integrated circuits.
Solid-state physics. Research in solid-state physics covers nanoscience and nanoparticles, electronic transport and inelastic light scattering in low-dimensional correlated electron systems, fractional quantum Hall effect, heterostructure physics and applications, molecular beam epitaxy, grain boundaries and interfaces, nucleation in thin films, molecular electronics, nanostructure analysis, and electronic structure calculations. Research opportunities also exist within the NSF Nanoscale Science and Engineering Center, which focuses on electron transport in molecular nanostructures; and the DOE Energy Frontier Research Center, which focuses on conversion of sunlight into electricity in nanometer-sized thin films.
Applied mathematics. Current research encompasses analytical and numerical analysis of deterministic and stochastic partial differential equations, large-scale scientific computation, fluid dynamics, dynamical systems and chaos, as well as applications to various fields of physics and biology. The applications to physics include condensed-matter physics, plasma physics, nonlinear optics, medical imaging, and the earth sciences, notably atmospheric, oceanic, and climate science, and solid earth geophysics (see below). The applications to biology include cellular biophysics, machine learning, and functional genomics, including collaborations with Columbia’s Center for Computational Biology and Bioinformatics (C2B2), the Center for Computational Learning Systems (CCLS), the NIH-funded Center for Multiscale Analysis of Genetic and Cellular Networks (MAGNet), and the NIH-funded Nanomedicine Center for Mechanobiology. Extensive collaborations exist with national climate research centers (the Geophysical Fluid Dynamics Laboratory and the National Center for Atmospheric Research) and with national laboratories of the U.S. Department of Energy, custodians of the nation’s most powerful supercomputers.
Atmospheric, oceanic, and earth physics. Current research focuses on the dynamics of the atmosphere and the ocean, climate modeling, cloud physics, radiation transfer, remote sensing, geophysical/geological fluid dynamics, geochemistry. The department engages in ongoing research and instruction with the NASA Goddard Institute for Space Studies and the Lamont-Doherty Earth Observatory. Six faculty members share appointments with the Department of Earth and Environmental Sciences.
In addition to the faculty and graduate students, many others participate in these projects, including full-time research faculty, faculty and students from other departments, and visiting scientists.
Laboratory Facilities in Applied Physics and Applied Mathematics
The Plasma Physics Laboratory, founded in 1961, is one of the leading university laboratories for the study of plasma physics in the United States. There are four experimental facilities. The Columbia High-Beta Tokamak (HBT-EP) supports the national program to develop controlled fusion energy. It utilizes high voltage, pulsed power systems, and laser and magnetic diagnostics to study the properties of high-beta plasmas and the use of feedback stabilization to increase the achievable beta. A collaborative program with the Princeton Plasma Physics Laboratory and the DII-D tokamak group at General Atomics is studying the properties of high-beta plasmas in order to maximize fusion power production in these large, neutral beam-heated tokamaks and spherical tori. The plasma physics group and MIT have jointly constructed the Levitated Dipole Experiment (LDX), a large plasma confinement experiment incorporating a levitated superconducting ring. The Columbia Nonneutral Torus (CNT) is an experiment devoted to the first study of non-neutral plasmas confined on magnetic surfaces. The Columbia Linear Machine (CLM) is a continuously operating, linear mirror device for the study of collisionless plasma instabilities, plasma, transport, and feedback stabilization. Columbia’s Collisionless Terrella Experiment investigates plasma transport in magneto-spheric geometry and the generation of strong plasma flow from nonlinear electrostatic potentials.
Experimental research in solid-state physics and laser physics is conducted within the department and also in association with the Columbia Center for Integrated Science and Engineering and the School of Mines. Facilities include laser processing and spectroscopic apparatus, ultrahigh vacuum chambers for surface analysis, picosecond and femtosecond lasers, a molecular beam epitaxy machine, and a clean room that includes photo-lithography and thin film fabrication systems. Within this field, the Laser Diagnostics and Solid-State Physics Laboratory conducts studies in laser spectroscopy of nanomaterials and semiconductor thin films, and laser diagnostics of thin film processing. The Laser Lab focuses on the study of materials under high pressure, laser surface chemical processing, and new semiconductor structures. Research is also conducted in the shared characterization laboratories and clean room operated by the NSF Nanoscale Science and Engineering Center.
The department maintains an extensive network of workstations and desktop computers. The research of the Plasma Lab is supported by a dedicated data acquisition/data analysis system, and the applied math group has access to a Beowulf cluster. Through the Internet, researchers in the department are currently using supercomputing facilities at the National Center for Atmospheric Research; the San Diego Supercomputing Center; the National Energy Research Supercomputer Center in Berkeley, California; the National Leadership Class Facility at Oak Ridge, Tennessee; the IBM SUR cluster at Brookhaven National Laboratory in Upton, New York; and others.