Mark Hoefer's Publications Page

Mark Hoefer

Mark Hoefer's Research Interests and Publications

Research in physical applied mathematics, motivated by real world problems is central to my investigations. My research is generally in the field of nonlinear waves with a focus on two areas: 1) fluid dynamics of dispersive media with accompanying wave excitations including dispersive shock waves and solitary waves; 2) dynamics of ferromagnetic media, spin torque, and localized excitations in nanomagnetism. Methods employed include mathematical modeling, analysis, asymptotics, Whitham modulation theory, and numerical analysis. Whenever possible, comparisons with experiment are carried out.

Current research involves the construction and stability of dispersive shock waves in single and multiple dimensions with applications to boundary value problems in supersonic Bose-Einstein condensates, nonlinear photonics, viscously deformable media (i.e. magma migration), and shallow water waves. This research is supported by the National Science Foundation through an applied math individual investigator grant DMS 1008973.

In the field of magnetodynamics, I am currently studying the excitation of localized wave structures via the spin torque effect and their coherent propagation. Numerical methods to compute time-periodic, dynamic, localized structures are being pursued.

Students

Seeking undergraduate and current/prospective graduate students interested in studying nonlinear waves and applications. Funding may be available. Please contact me if you are interested.

Manuscripts in Review

Shock waves in dispersive Eulerian fluids, M. A. Hoefer.

Journal Publications

Spin torque-generated magnetic droplet solitons, S. M. Mohseni, S. R. Sani, J. Persson, T. N. Anh Nguyen, S. Chung, Ye. Pogoryelov, P. K. Muduli, E. Iacocca, A. Eklund, R. K. Dumas, S. Bonetti, A. Deac, M. A. Hoefer, and J. Åkerman, Science, 339, 1295 (2013). (pdf and news release).
Dispersive shock waves in viscously deformable media, N. K. Lowman, M. A. Hoefer, Journal of Fluid Mechanics, 718, 524-557 (2013). (pdf © Cambridge University Press)
Propagation and control of nanoscale magnetic-droplet solitons, M. A. Hoefer, M. Sommacal, T. J. Silva, Physical Review B, 85, 214433 (2012). (pdf).
Beating dark-dark solitons in Bose-Einstein condensates, D. Yan, J. J. Chang, C. Hamner, M. Hoefer, P. G. Kevrekidis, P. Engels, V. Achilleos, D. J. Frantzeskakis, and J. Cuevas, Journal of Physics B, 45, 115301 (2012).
Propagating two-dimensional magnetic droplets, M. A. Hoefer and M. Sommacal, Physica D, 241, 890-901 (2012). preprint: arXiv:1111.2310 [nlin.PS].
Dark solitons, dispersive shock waves, and transverse instabilities, M. A. Hoefer and B. Ilan, SIAM Multiscale Modeling and Simulation, 10, 306-341 (2012). (pdf).
Dark-dark solitons and modulational instability in miscible, two-component Bose-Einstein condensates, M. A. Hoefer, C. Hamner, J.J. Chang, and P. Engels, Physical Review A, 84, 041605(R) (2011). (pdf)
Generation of dark-bright soliton trains in superfluid-superfluid counterflow, C. Hamner, J.J. Chang, P. Engels, and M. A. Hoefer, Physical Review Letters, 106, 065302 (2011). (pdf)
Defect modes and homogenization of periodic Schrödinger operators, M. A. Hoefer and M. I. Weinstein, SIAM Journal on Mathematical Analysis, 43, 971-996 (2011). (pdf)
Semiclassical dynamics of quasi-one-dimensional attractive Bose-Einstein condensates, A. Tovbis and M. A. Hoefer, Physics Letters A, 375, 726-732 (2010). (arXiv:1006.1438 [cond-mat.quant-gas])
Theory for a dissipative droplet soliton excited by a spin torque nanocontact, M. A. Hoefer, T. J. Silva and Mark W. Keller, Physical Review B, 82, 054432 (2010). (pdf)
Theory of Two-Dimensional Oblique Dispersive Shock Waves in Supersonic Flow of a Superfluid, M. A. Hoefer and B. Ilan, Physical Review A, 80, 061601(R) (2009). (pdf) (supporting simulations for Figures 3a, 3b, 3c, 3d, and zoom in of Figure 3a)
Dispersive Shock Waves, M. A. Hoefer and M. J. Ablowitz, Scholarpedia, 4, 5562 (2009). (curator)
Soliton Generation and Multiple Phases in Dispersive Shock and Rarefaction Wave Interaction, M. J. Ablowitz, D. E. Baldwin, and M. A. Hoefer, Physical Review E, 80, 016603 (2009). (pdf)
Matter-Wave Interference in Bose-Einstein Condensates: a Dispersive Hydrodynamic Approach, M. A. Hoefer, P. Engels, and J. J. Chang, Physica D, 238, 1311-1320 (2009). (preprint) (invited article for a special issue on Nonlinear Phenomena in Degenerate Quantum Gases)
Formation of Dispersive Shock Waves by Merging and Splitting Bose-Einstein Condensates, J. J. Chang, P. Engels, and M. A. Hoefer, Physical Review Letters, 101, 170404 (2008). (pdf) (supporting numerical simulation results)
Model for a Collimated Spin-Wave Beam Generated by a Single-Layer Spin Torque Nanocontact, M. A. Hoefer, T. J. Silva, and M. D. Stiles, Physical Review B, 77, 144401 (2008). (pdf)
Piston Dispersive Shock Wave Problem, M. A. Hoefer, M. J. Ablowitz, and P. Engels, Physical Review Letters, 100, 084504 (2008). (pdf)
Interactions of Dispersive Shock Waves, M. A. Hoefer and M. J. Ablowitz, Physica D, 236, 44-64 (2007). (preprint) (doi:10.1016/j.physd.2007.07.017)
Observation of Faraday Waves in a Bose-Einstein Condensate, P. Engels, C. Atherton, and M. A. Hoefer, Physical Review Letters, 98, 095301 (2007). (pdf) (editor's suggestion)
Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics, M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Physical Review A, 74, 023623 (2006). (pdf)
Ph.D. Thesis: Dispersive Shock Waves in Bose-Einstein Condensates and Nonlinear Nano-oscillators in Ferromagnetic Thin Films, M. A. Hoefer, Department of Applied Mathematics, University of Colorado, Boulder (5/2006). (pdf) (received Research and Creative Work Award)
Theory of Magnetodynamics Induced by Spin Torque in Perpendicularly Magnetized Thin Films, M. A. Hoefer, M. J. Ablowitz, B. Ilan, M. R. Pufall, and T. J. Silva, Physical Review Letters 95, 267206 (2005). (pdf)

Unpublished

Spin Momentum Transfer and Oersted Field Induce a Vortex Nano-Oscillator in Thin Ferromagnetic Film Devices, M. A. Hoefer and T. J. Silva, cond-mat/0609030 (2007). (pdf)