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]]>The study of structural periodicity in engineered materials, such as metamaterials, phononic crystals, and metasurfaces, has opened new frontiers in wave control. Our research group explores the fundamental principles and advanced techniques for harnessing structural periodicity to manipulate wave propagation for diverse applications in sensing, energy harvesting, and space technology. By leveraging the unique properties of these periodic structures, we demonstrate how they can be used to enhance ultrasonic sensing and nondestructive testing, improve the efficiency of energy harvesters, and develop innovative solutions for space applications. The first part of my talk will focus on gradient index phononic crystal (GRIN-PC) lenses conforming pipe-like structures. Conformal GRIN-PC lenses are designed by tailoring unit cell geometry according to a specific refractive index profile. We explore the focusing of multi-mode guided waves at the desired locations (i.e. sensor nodes) along the pipe structure to address the attenuation problem in long-range pipelines. Then, I will explain how we exploit the negative refraction property of phononic crystals for designing a super lens. Unlike GRIN-PC lenses, which have at least minimum wavelength resolution as their natural limit, negative refraction-based PC lenses can potentially overcome the diffraction limit, which is highly favorable in medical imaging or other applications requiring localized wave intensity in areas smaller than a square wavelength. The second part of my talk will deal with reconfigurable metasurfaces for full wavefront control with an emphasis on energy harvesting of low frequency elastic waves. We fully analyze and design the elastic metasurfaces by tailoring the phase gradient of individual unit structures for different wave functions and present theoretical findings along with experimental validation. The last part of my talk will highlight the potential of metamaterials in space applications, such as novel in-space manufacturable extended solar arrays and antennas with high precision and mass efficiency.

Contact: Silas Alben

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]]>The US political arena is generally a bleak mix of distressing and aggravating, particularly in the current highly polarized climate, but that distress only increases the need to honestly and scientifically understand the forces at play in ideological space, and the polarization offers emergent simplicity and thus a unique opportunity for mathematical modeling. This talk will share some recent and ongoing attempts to visualize and understand the current political landscape, as well as some quantitative patterns in political psychology and the modern information ecosystem. These recently-gathered data inform a mechanistic dynamical model of ideological drift, allowing theory to extrapolate the complex implications of micro-scale data to macro-scale outcomes---while iteratively improving and suggesting further data-gathering efforts to corner remaining uncertainty. The first waves of results from this perspective provide some remarkable insights, providing some hope of understanding and productively informing political messaging and algorithmic design for a more reasonable political future.

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]]>Rogue waves or freak waves are spatially-localized disturbances of a background field that are also temporally localized. In the setting of the focusing nonlinear Schrödinger equation, which is a universal model for the complex amplitude of a wave packet in a general one-dimensional weakly nonlinear and strongly dispersive setting that includes water waves and nonlinear optics as special cases, a special exact solution exhibiting rogue-wave character was found by D. H. Peregrine in 1983. Since then, with the help of complete integrability, Peregrine’s solution has been generalized to a family of solutions of arbitrary “order” where more parameters appear in the solution as the order increases. These parameters can be adjusted to maximize the amplitude of the rogue wave for a given order. This talk will describe several recent results concerning such maximal-amplitude rogue wave solutions in the limit that the order increases without bound. For instance, it turns out that there is a limiting structure in a suitable near-field scaling of the peak of the rogue wave; this structure is a novel exact solution of the focusing nonlinear Schrödinger equation — the “rogue wave of infinite order” — that is also connected with the hierarchy of the third Painlevé equation. This is joint work with Deniz Bilman and Liming Ling.

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Contact: Evgeniy Khain (Oakland University)

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Contact: Robert Krasny.

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