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Mahmoud I. Hussein
Alvah and Harriet Hovlid Professor, Ann & H.J. Smead Department of Aerospace Engineering Sciences, Â鶹ÊÓƵ
Friday, April 5 | 10:40 a.m. | AERO 120

Abstract: Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. While the theory of linear waves is fairly established, nonlinear wave motion remains a complex, often mysterious, object—particularly when the nonlinearity is strong.

For example, an unbalanced nonlinear wave distorts acutely as it travels and appears to ultimately fully lose its original shape, and in many instances the final outcome is onset of a form of instability. Inherent to this distortion is an intricate mechanism of harmonic generation manifesting in intensive time-varying exchange of energy between the harmonics that matches the wave’s ongoing nonlinear evolution in space and time.

In this work, a general theory is presented for the dispersion of these generated harmonics as they emerge and develop in a traveling nonlinear wave. The harmonics dispersion relation−derived by the theory−provides direct and exact analytical prediction of the collective harmonics spectrum in the frequency-wavenumber domain, and does so without prior knowledge of the spatial-temporal solution.

Despite its time-independence, the new relation is shown to be applicable at any temporal state of evolution of the nonlinear wave as long as the wave is balanced or has not yet reached its breaking point. The theory is applied to nonlinear elastic waves in a homogeneous rod and an extension is demonstrated to rods with a periodic array of property modulation (phononic crystal) or intrinsic resonators (elastic metamaterial). Finally, the theory is shown to provide a rigorous foundation for the analytical synthesis of solitons.

Bio: Mahmoud I. Hussein is the Alvah and Harriet Hovlid Professor at the Smead Department of Aerospace Engineering Sciences at the Â鶹ÊÓƵ. He holds a courtesy faculty appointment in the Department of Physics and has formally served as the Engineering Faculty Director of the Pre-Engineering Program and the Program of Exploratory Studies. He received a BS degree from the American University in Cairo (1994) and MS degrees from Imperial College London (1995) and the University of Michigan‒Ann Arbor (1999, 2002). In 2004, he received a PhD degree from the University of Michigan‒Ann Arbor, after which he spent two years at the University of Cambridge as a postdoctoral research associate.

Dr. Hussein’s research focuses on the dynamics of materials and structures, especially phononic crystals and metamaterials, at both the continuum and atomistic scales. He received a DARPA Young Faculty Award in 2011, an NSF CAREER award in 2013, and in 2017 was honored with a Provost’s Faculty Achievement Award for Tenured Faculty at CU Boulder. He was awarded as PI two multi-million dollar grants, both on concepts he discovered—nanophononic metamaterials (NPMs, Phys. Rev. Lett., 2014; ARPA-E 2019-2023) and phononic subsurfaces (PSubs, Proc. R. Soc. A, 2015; ONR MURI 2024-2029).

He has co-edited a book titled Dynamics of Lattice Materials published by Wiley. He is a Fellow of ASME and has served as an associate editor for the ASME Journal of Vibration and Acoustics. In addition, he is the founding vice president of the International Phononics Society and has co-established the biennial Phononics 20xx conference series which has helped create a new multidisciplinary research community and is widely viewed as the world’s premier event in the emerging field of phononics.