Applied Physics and Applied Mathematics

Program Category: PhD Programs

Chair: Irving P. Herman

Website: apam.columbia.edu

Email Address: seasinfo.apam [at] columbia.edu

Degree Programs: Full-Time: MPhil, PhD

Please note: the degree for this program is conferred by GSAS, but program specifics, such as admissions, degree requirements, and financial aid, are administered by The Fu Foundation School of Engineering and Applied Science. Please visit its website for more information about graduate admissions.

Program in Applied Physics and Applied Mathematics

The following fields of specialty are provided in the department:

Plasma Physics: In experimental plasma physics, research is being conducted on:

  • equilibrium, stability, and transport in fusion plasmas: high-beta tokamaks, spherical tokamaks, and levitated dipoles;
  • magnetospheric physics: trapped particle instabilities and stochastic particle motion;
  • confinement of toroidal nonneutral plasmas;
  • plasma source operation and heating techniques; and
  • 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, the DIII-D tokamak group of 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, the free-electron laser, accelerators, optical diagnostics of film processing, new laser systems, nonlinear optics, ultrafast optoelectronics, photonic switching, optical physics of surfaces, laser-induced crystallization, photon integrated circuits, energy transfer in molecules, and laser chemistry.

Solid-State Physics: Research in solid-state physics covers nanoscience and nanoparticles, the optical spectroscopy of semiconductor structures that are subjected to high pressure, electric 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, and surface physics.

Facilities include a microelectronics laboratory, a direct-laser writing facility, high-pressure diamond anvil cells, a molecular beam epitaxy machine, ultrahigh vacuum systems, lasers, and equipment for the study of optical properties. Facilities and research opportunities also exist within the interdisciplinary NSF Materials Research Science and Engineering Center, which focuses on complex films composed of nanocrystals, and the NSF Nanoscale Science and Engineering Center, which focuses on electron transport in molecular nanostructures.

Applied Mathematics: Current research encompasses analytical and numerical analysis of 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 physics (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 of Mechanical Biology. 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, and geochemistry.

The department engages in ongoing research and instruction with the NASA Goddard Institute for Space Studies and the Lamont-Doherty Earth Observatory. Five faculty members share appointments with the Department of Earth and Environmental Sciences.

Program in Materials Science and Engineering (MSE)

Current research includes the study of:

  • interfaces, stresses, and grain boundaries in thin films 
  • lattice defects and electrical properties of semiconductors
  • laser processing and ultra-rapid solidification of thin films
  • nucleation in condensed systems
  • optical and electric properties of wideband semiconductors
  • synthesis of nanocrystals, carbon nanotubes, and nanotechnology-related materials
  • deposition and characterization of magnetic thin films
  • diffraction physics
  • mechanical response analysis in single and polycrystals over multiple length scales

In addition, there is research in surface and colloid chemistry involving both inorganic and organic materials such as surfactants, polymers, and latexes, with emphasis on materials/environment of interactions.

The MSE program, under the aegis of the Department of Applied Physics and Applied Mathematics and the Henry Krumb School of Mines, is closely linked to other engineering departments, to the Departments of Physics, Chemistry, and Biological Sciences, and to the NSF Materials Research Science and Engineering Center.

Degree Programs: Full Time