Research Interests
Research in physical applied mathematics, motivated by real world
problems is central to my investigations. Methods employed involve
modeling physical systems in terms of partial and ordinary
differential equations and then analyzing these equations with
asymptotic, analytic, and numerical methods. Whenever possible,
comparisons with experiment are carried out. Current mathematical
results have direct application to Bose-Einstein condensation,
nonlinear optics, and nano-scale magnetics.
Journal Publications
-
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)
(also appeared in
Virtual
Journal of Atomic Quantum Fluids, 1:6 (Dec 2009))
-
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) (also appeared
in
Virtual
Journal of Nanoscale Science and
Technology, 17:15 (Apr 2008))
- 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)
- 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)
(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
Other Interests
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