Department of Aerospace and Mechanical Engineering
University of Southern California
University Park
Los Angeles, CA 90089-1191

RRB 221
Tel: (213) 740-7782
FAX: (213) 740-7774

email:

newton@usc.edu

B.S. Cum Laude (Applied Math/Physics), Harvard University, 1981

M.S. Applied Mathematics, Brown University, 1982

Ph.D. Applied Mathematics, Brown University, 1986

Fluid Dynamics

Geophysical Fluid Dynamics

Hamiltonian Systems/Dynamical Systems

Vortex Dynamics

Nonlinear Waves

Weak Turbulence Theory

Current Research Projects:

Vortex dynamics, mixing, and transport on spheres

Geometric phases and turbulent mixing

Nonlinear shock-dispersive wave interactions

Asymptotics and scaling for nonlinear eigenvalue problems

Control of 2D turbulence

Vortex statistical mechanics

• USC Center for Applied Mathematical Sciences (CAMS)
• USC Nonlinear Dynamics
• USC Center for Modeling and Simulation
• http://www.siam.org/siags/siagds.htm
• http://online.itp.ucsb.edu/online/hydrot00/newton

• http://www.siam.org/meetings/SIAM50/
• http://www.fields.utoronto.ca/programs/scientific/02-03/marsden_workshop
• http://www.icos.ethz.ch/vortex_workshop/vortex_workshop.htm
• http://www.siam.org/meetings/ds03/index.htm

Selected Recent Publications:

The N-Vortex Problem: Analytical Techniques, P.K. Newton, Vol. 145, Appl. Math. Sci. Series, Springer-Verlag, 2001;

URL: http://www.springer-ny.com/detail.tpl?cart=993587465187652& ISBN=0387952268

Geometry, Mechanics, and Dynamics, eds. P.K. Newton, P. Holmes, A. Weinstein, Springer-Verlag, Special Volume, Aug. 2002.

• `Amplitude equation models for the interaction of shocks with nonlinear dispersive wave envelopes', Chapter 2, pp 35-75, in Selected Topics in Nonlinear Wave Mechanics , eds. C.I. Christov, A. Guran, Birkhauser, 2002.
• `Streamline topologies for integrable vortex motion on a sphere' (with R. Kidambi), Physica D, 140, 95-125, 2000.
• `Vortex motion on a sphere with solid boundaries' (with R. Kidambi),Phys. Fluids 12(3), 581-588, March 2000.
• `Geometric phases for co-rotating elliptical vortex patches' (with B. Shashikanth), J. Math. Phys. 41(12), 8148-8162, 2000.
• `Collapse of three vortices on a sphere' (with R. Kidambi), Il Nuovo Cimento, Vol. 22C, no. 6, 779-791, 1999.
• `Motion of three point vortices on a sphere' (with R. Kidambi), Physica D, 116, 143-175, 1998.
• `Vortex motion and the geometric phase: Part I. Basic configurations and asymptotics', (with B. Shashikanth), J. Nonlinear Sci. Vol. 8, 183-214, 1998.
• `Vortex motion and the geometric phase: Part II. Slowly varying spiral structures', (with B. Shashikanth), to appear, J. Nonlinear Sci., 1998.
• `On the interaction of shocks with dispersive waves: Part II. Incompressible-integrable limit', (with R. Axel), Studies in Appl. Math., 100, 311-363, 1998.
• `On the interaction of shocks with dispersive waves: Part I. Weak coupling limit', (with R. Axel), Studies in Appl. Math., 96, 201-246, 1996.
• `Vortex problems, rotating spiral structures and the Hannay-Berry phase', (with B. Shashikanth), Inst. Henri Poincare, 1996.
• `Scaling laws near nonlinear Schrodinger defect sites', (with M. O'Connor), Physical Review E, Vol. 53, No. 4, April 1996.
• `Unsteady models for the nonlinear evolution of the mixing layer', (with E. Meiburg, N. Raju, G. Reutsch), Physical Review E, Vol. 52, 1639-1657, 1995.
• `Dynamics of heavy particles in a Burgers vortex', (with B. Marcu, E. Meiburg), Physics of Fluids, Feb., 1995.
• `Hannay-Berry phase and the restricted three vortex problem', Physica D, 79, 416-423, 1994.
• `The geometry of nonlinear Schrodinger standing waves: pure power nonlinearities', (with S. Watanabe), Physica D, 67, 19-44, 1993.
• `Rapidly forced initial value problems', SIAM Journal of Applied Math, Vol. 53, No. 5, pp 1331-1351, Oct. 1993.
• `Dynamics of perturbed amplitude equations', in Research Trends in Physics: Chaotic Dynamics and Transport in Fluids and Plasmas, Eds:I. Prigogine et al., AIP, 1992.
• `Particle dynamics in a viscously decaying cat's eye: The effect of finite Schmidt numbers', (with E. Meiburg), Physics of Fluids A, Vol. 3, May 1991.
• `Wave interactions in the singular Zakharov system', J. Math. Phys. 32(2), 41, 1991.
• `Particle dynamics and mixing in a viscously decaying shear layer', (with E. Meiburg), J. Fluid Mech. Vol. 227, June 1991.
• `Escape from KAM regions and the breakdown of uniform rotation', Phys. Rev. A., Vol. 40, No. 6, Sept. 15, 1989.
• `Branching near nonlinear plane waves in dispersive systems', SIAM Journal of Appl. Math., Vol. 49, No. 4, Aug. 1989.
• `The perturbed cubic Schrodinger equation: selection mechanism, resonant li mits and spatial chaos', J. Math. Phys. 29(10), October 1988.