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 and medical physics. The graduate program in applied mathematics includes research in applied analysis, data science, and atmospheric, oceanic, and earth physics. 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, methods of active feedback control of plasma instability developed at Columbia University are guiding research on NSTX at the Princeton Plasma Physics Laboratory, on the DIII-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 theory of plasma equilibrium and stability, active control
of MHD instabilities, the kinetic theory of turbulence and 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 lowdimensional 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 Materials Research Science and Engineering Center, which focuses on low-dimensional materials.
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, inverse problems, algorithms for data and learning, as well as applications to various fields of physical and biological sciences. The applications to physical science include quantum and condensed-matter physics, materials science, electromagnetics, optics, photonics, plasma physics, medical imaging, and the earth sciences, notably atmospheric, oceanic, and climate science, and solid earth geophysics (see below). Other applications include machine learning and biophysical modeling, including collaborations with Columbia’s Data Science Institute (DSI), the Department of Systems Biology, and the Department of Statistics. 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. Seven 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 DIII-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 stellarator known as Columbia Nonneutral Torus (CNT) conducts research on the magnetohydrodynamic stability, microwave heating, and microwave diagnostics of neutral stellarator plasmas. Two smaller devices investigate respectively an innovative tokamak-stellarator hybrid plasma confinement concept and the use of toroidal electron-heated plasmas as sources of ions for accelerators. 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 magnetospheric 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 Nano Initiative. 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 CNI.
The department maintains an extensive network of computing clusters 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. Materials Science and Applied Physics built an intel-based 600 core computing cluster that is dedicated to performing first-principles computations of materials. Researchers in the department are additionally 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;
various allocations via XSEDE; and others. The Amazon Elastic Compute Cloud (EC2) is also utilized to supplement computing resources in times of high demand.