Mark Hoefer

About

Mark Hoefer is a Professor and Department Chair in Applied Mathematics at the University of Colorado Boulder. His research is centered on physical applied mathematics motivated by real-world problems, with a focus on nonlinear waves. His work primarily involves the fluid dynamics of dispersive media, including dispersive shock waves (DSWs) and solitary waves, as well as the dynamics of ferromagnetic media in nanomagnetism. Hoefer employs a variety of methods such as mathematical modeling, analysis, asymptotics, Whitham modulation theory, numerical analysis, and in-house experiments within the Dispersive Hydrodynamics Lab. His research on DSWs explores their role as a universal mechanism to resolve hydrodynamic singularities in dispersive media, with physical manifestations including undular bores, nonlinear diffraction patterns, and matter waves. Additionally, Hoefer investigates nonlinear, dispersive phenomena in ferromagnetic media, particularly the excitation of magnetization dynamics at the nanometer scale using spin polarized currents, leading to the observation of strongly nonlinear magnetic solitons or 'droplets' in nanomagnetic systems.

Research topics

• Physics
• Mechanics
• Quantum mechanics
• Optics
• Mathematics
• Classical mechanics
• Mathematical analysis
• Mathematical physics

Selected publications

• Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

  Studies in Applied Mathematics · 2023-07-09 · 30 citations

  article

  Abstract The mathematical description of localized solitons in the presence of large‐scale waves is a fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear optics, and condensed matter physics. Here, the evolution of a soliton as it interacts with a rarefaction wave or a dispersive shock wave, examples of slowly varying and rapidly oscillating dispersive mean fields, for the Korteweg–de Vries equation is studied. Step boundary conditions give rise to either a r…

  PublisherDOI

• Dispersive Riemann problems for the Benjamin-Bona-Mahony equation

  Studies in Applied Mathematics · 2021 · 17 citations

  Long time dynamics of the smoothed step initial value problem or dispersive Riemann problem for the Benjamin‐Bona‐Mahony (BBM) equation u t + u u x = u xxt are studied using asymptotic methods and numerical simulations. The catalog of solutions of the dispersive Riemann problem for the BBM equation is much richer than for the related, integrable, Korteweg‐de Vries equation u t + u u x + u xxx = 0 . The transition width of the initial smoothed step is found to significantly impact the dynamics. N…

  DOI

• Hydrodynamics of a discrete conservation law

  Studies in Applied Mathematics · 2024-10-23 · 8 citations

  articleOpen accessSenior author

  Abstract The Riemann problem for the discrete conservation law is classified using Whitham modulation theory, a quasi‐continuum approximation, and numerical simulations. A surprisingly elaborate set of solutions to this simple discrete regularization of the inviscid Burgers' equation is obtained. In addition to discrete analogs of well‐known dispersive hydrodynamic solutions—rarefaction waves (RWs) and dispersive shock waves (DSWs)—additional unsteady solution families and finite‐time blowup are…

  PublisherOA PDFDOI

• Observation of Traveling Breathers and Their Scattering in a Two-Fluid System

  Physical Review Letters · 2023 · 8 citations

  Senior authorCorresponding

  The observation of traveling breathers (TBs) with large-amplitude oscillatory tails realizes an almost 50-year-old theoretical prediction [E. A. Kuznetsov and A. V. Mikhailov, Stability of stationary waves in nonlinear weakly dispersive media, Zh. Eksp. Teor. Fiz. 67, 1717 (1974) ZETFA70044-4510[E. A. Kuznetsov and A. V. MikhailovSov. Phys. JETP 40, 855 (1975)] SPHJAR0038-5646] and generalizes the notion of a breather. Two strongly nonlinear TB families are created in a core-annular flow by inte…

  PublisherDOI

• Computation of high-frequency magnetoelastic waves in layered materials

  Physical review. B./Physical review. B · 2023-03-27 · 7 citations

  articleOpen accessSenior author

  The direct calculation of magnetoelastic wave dispersion in layered media is presented using an efficient, accurate computational technique. The governing, coupled equations for elasticity and magnetism, the Navier and Landau-Lifshitz equations, respectively, are linearized to form a quadratic eigenvalue problem that determines a complex web of wave-number--frequency dispersion branches and their corresponding mode profiles. Numerical discretization of the eigenvalue problem via a spectral collo…

  PublisherOA PDFDOI

Recent grants

• Conference: Emergent Phenomena in Nonlinear Dispersive Waves

  NSF · $15k · 2024–2025

• Dispersive Hydrodynamics and Applications

  NSF · $434k · 2018–2023

• Supersonic Dispersive Fluid Dynamics

  NSF · $131k · 2010–2014

Frequent coauthors

• Ezio Iacocca

  University of Colorado Colorado Springs

  31 shared

• G. A. Él

  Northumbria University

  22 shared

• Michelle Maiden

  University of Colorado Boulder

  18 shared

• Peter Engels

  Washington State University

  18 shared

• Patrick Sprenger

  University of California, Merced

  18 shared

• T. J. Silva

  NAVSYS (United States)

  14 shared

• Gino Biondini

  10 shared

• Nicholas K. Lowman

  10 shared

Education

• PhD in Applied Mathematics, Applied Mathematics

  University of Colorado Boulder

  2006

• MS in Applied Mathematics, Division of Engineering and Applied Sciences

  Harvard University

  2000

• BS in Mathematics of Computation, Mathematics

  University of California Los Angeles

  1997

Similar researchers at University of Colorado Boulder

• Mark J. Ablowitzh-86
• James Curryh-64
• Gregory Beylkinh-47