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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 multiple dimensions with applications to boundary value
problems in supersonic Bose-Einstein condensate and nonlinear optical
flows.
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.
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
- Propagation and control of nano-scale, magnetic droplet
solitons, M. A. Hoefer and M. Sommacal,
preprint: arXiv:1202.3421
[nlin.PS].
Journal Publications
- Beating dark-dark solitons in Bose-Einstein condensates,
D. Yan, J. J. Chang, C. Hamner, M. A. Hoefer, P. G. Kevrekidis,
P. Engels, V. Achilleos, D. J. Frantzeskakis, and
J. Cuevas, Journal of Physics B, to appear.
-
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) (also appears
in
Virtual
Journal of Nanoscale Science and
Technology, 22:11 (Sept 2010))
-
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 appears 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 appears
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)
(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
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