August 2020 Prize Spotlight

Mark Hoefer of the University of Colorado, Boulder is the 2020 recipient of the T. Brooke Benjamin Prize. The award recognizes him for his significant contributions to the understanding of dispersive shock waves in hydrodynamics and other physical systems. Hoefer would have received his award at the cancelled SIAM Conference on Nonlinear Waves and Coherent Structures (NWCS20). He presented his talk, “A New Kind of Wave-Mean Flow Interaction,” virtually on July 27, 2020.

The SIAM Activity Group on Nonlinear Waves and Coherent Structures (SIAG/NWCS) awards the T. Brooke Benjamin Prize every two years to one mid-career established researcher who has been in the profession at least 10 years and no more than 20 years preceding the award year. The prize is awarded for recent outstanding work on a topic in nonlinear waves, evidenced by a body of work with at least one significant publication in English in a peer-reviewed journal or conference proceedings within the four calendar years preceding the award year.

Mark Hoefer is currently an Associate Professor of Applied Mathematics at the University of Colorado, Boulder, where he has been a faculty member since 2014. He received his PhD in Applied Mathematics at the University of Colorado, Boulder in 2006 under the guidance of Mark J. Ablowitz. He then held two postdoc positions, at NIST in Boulder with Thomas J. Silva and at Columbia University with Michael Weinstein. Prior to moving to Colorado, he was an Assistant Professor of Mathematics at North Carolina State University. Research in physical applied mathematics, motivated by real world problems is central to Hoefer’s investigations. His 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 (DSWs) and solitary waves; and 2) dynamics of ferromagnetic media, spin torque, and localized excitations in nanomagnetism. 


Q: Why are you excited to receive the T. Brooke Benjamin Prize?

A: T. Brooke Benjamin's contributions to nonlinear waves, fluid dynamics, and applied mathematics are renowned. To be associated with his legacy and recognized by my nonlinear waves colleagues is very special to me. I am so grateful to all my mentors and collaborators for having inspired and taught me so much.

Q: Could you tell us a bit about the research that won you the prize?

A: Dispersive hydrodynamics generally describe the multiscale solutions of nonlinear partial differential equations—conservation laws—modified by small dispersion terms. Extended dispersive shock waves and localized solitary waves are well-known solutions that are ubiquitous in physical applications. In our research, we developed an asymptotic description of solutions representing the propagation and interaction of dispersive shock waves and solitary waves that we confirmed with fluid experiments. Key to the analysis are certain approximately conserved quantities that predict the effective transmission or trapping of a solitary wave by a dispersive shock wave.

It is fitting that T. Brooke Benjamin's first paper was on undular bores—a dispersive shock wave in shallow water flow—and he was a prolific experimentalist, successfully marrying applied mathematics with experimental observations of fluid dynamics. Benjamin made extensive use of conserved quantities in his mathematical work.

Q: What does your work mean to the public?

A: Our research considers fundamental questions involving nonlinear wave dynamics that encompass a variety of application areas from the familiar, such as surface and internal ocean waves, to the more exotic, like condensed matter and nonlinear optics. The fact that these complex wave interactions can be observed provides a compelling backdrop for learning by researchers, students, and armchair scientists alike.

Q: What does being a SIAM member mean to you?

A: My career has benefited from and been driven by my interactions at numerous SIAM meetings. The SIAM Activity Group on Nonlinear Waves and Coherent Structures and the community it supports feels like home to me. The SIAM community has so many talented mathematicians who deeply value the application of mathematics. I am honored to know them, be inspired by them, and have them as friends.

Vladimir Zakharov’s name is inseparably linked with the origin and development of modern nonlinear physics and mathematics. His achievements in this area long ago became classical and acknowledged by the world scientific community, a reflection of which is the high rating of his scientific papers (his citation index amounts to more than 42,000). His main contribution to science is related to the development of these three most important avenues: the theory of wave collapses, the soliton theory, and the theory of wave turbulence.