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1. Elastic stabilization of an intrinsically unstable hyperbolic flow–structure interaction on the 3D half-space

   https://doi.org/10.1142/S0218202523500124  

   Balakrishna, Abhishek ; Lasiecka, Irena ; Webster, Justin T. ( March 2023 , Mathematical Models and Methods in Applied Sciences)

   The strong asymptotic stabilization of 3D hyperbolic dynamics is achieved by a damped 2D elastic structure. The model is a Neumann wave-type equation with low regularity coupling conditions given in terms of a nonlinear von Karman plate. This problem is motivated by the elimination of aeroelastic instability (sustained oscillations of bridges, airfoils, etc.) in engineering applications. Empirical observations indicate that the subsonic wave-plate system converges to equilibria. Classical approaches which decouple the plate and wave dynamics have fallen short. Here, we operate on the model as it appears in the engineering literature with no regularization and achieve stabilization by microlocalizing the Neumann boundary data for the wave equation (given through the plate dynamics). We observe a compensation by the plate dynamics precisely where the regularity of the 3D Neumann wave is compromised (in the characteristic sector). 

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2. Stability analysis of coupled structural acoustics PDE models under thermal effects and with no additional dissipation

   https://doi.org/10.1002/mana.201700489  

   Avalos, George ; Geredeli, Pelin G. ( November 2018 , Mathematische Nachrichten)

   In this study we consider a coupled system of partial differential equations (PDE's) which describes a certain structural acoustics interaction. One component of this PDE system is a wave equation, which serves to model the interior acoustic wave medium within a given three dimensional chamber Ω. This acoustic wave equation is coupled on a boundary interface Γ₀to a two dimensional system of thermoelasticity: this thermoelastic PDE is composed in part of a structural beam or plate equation, which governs the vibrations of flexible wall portion Γ₀of the chamber Ω. Moreover, this elastic dynamics is coupled to a heat equation which also evolves on Γ₀, and which imparts a thermal damping onto the entire structural acoustic system. As we said, the interaction between the wave and thermoelastic PDE components takes place on the boundary interface Γ₀, and involves coupling boundary terms which are above the level of finite energy. We analyze the stability properties of this coupled structural acoustics PDE model, in the absence of any additive feedback dissipation on the hard walls Γ₁of the boundary. Under a certain geometric assumption on Γ₁, an assumption which has appeared in the literature in connection with structural acoustic flow, and which allows for the invocation of a recently derived microlocal boundary trace estimate, we show that classical solutions of this thermally damped structural acoustics PDE decay uniformly to zero, with a rational rate of decay.

    

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3. Streaming-enhanced flow-mediated transport

   https://doi.org/10.1017/jfm.2019.643  

   Parthasarathy, Tejaswin ; Chan, Fan Kiat ; Gazzola, Mattia ( November 2019 , Journal of Fluid Mechanics)

   We investigate the ability of an active body (master) to manipulate a passive object (slave) purely via contactless flow-mediated mechanisms, motivated by potential applications in microfluidic devices and medicine (drug delivery purposes). We extend prior works on active–passive cylinder pairs by superimposing periodic oscillations to the master’s linear motion. In a viscous fluid, such oscillations produce an additional viscous streaming field, which is leveraged for enhancing slave transport. We see that superimposing oscillations robustly improves transport across a range of Reynolds numbers. Comparison with results without oscillations highlights the flow mechanisms at work, which we capitalize on to design (master) geometries for augmented transport. These principles are found to extend to three-dimensional active–passive shapes as well. 

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4. Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

   https://doi.org/10.1098/rsta.2019.0095  

   Sebek, Michael ; Kawamura, Yoji ; Nott, Ashley M. ; Kiss, István Z. ( December 2019 , Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’. 

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5. Synchronized oscillations, traveling waves, and jammed clusters induced by steric interactions in active filament arrays

   https://doi.org/10.1039/D0SM01162B  

   Chelakkot, Raghunath ; Hagan, Michael F. ; Gopinath, Arvind ( February 2021 , Soft Matter)

   null (Ed.)

   Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. The mechanisms underlying this collective response and the essential ingredients for stable synchronization remain a mystery. Inspired by how these biological entities integrate elasticity with molecular motor activity to generate sustained oscillations, a number of synthetic active filament systems have been developed that mimic oscillations of these biological active filaments. Here, we describe the collective dynamics and stable spatiotemporal patterns that emerge in such biomimetic multi-filament arrays, under conditions where steric interactions may impact or dominate the collective dynamics. To focus on the role of steric interactions, we study the system using Brownian dynamics, without considering long-ranged hydrodynamic interactions. The simulations treat each filament as a connected chain of self-propelling colloids. We demonstrate that short-range steric inter-filament interactions and filament roughness are sufficient – even in the absence of inter-filament hydrodynamic interactions – to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns. We first analyze the collective dynamics of two- and three-filament clusters and identify parameter ranges in which steric interactions lead to synchronized oscillations and strongly occluded states. Generalizing these results to large one-dimensional arrays, we find rich emergent behaviors, including traveling metachronal waves, and modulated wavetrains that are controlled by the interplay between the array geometry, filament activity, and filament elasticity. Interestingly, the existence of metachronal waves is non-monotonic with respect to the inter-filament spacing. We also find that the degree of filament roughness significantly affects the dynamics – specifically, filament roughness generates a locking-mechanism that transforms traveling wave patterns into statically stuck and jammed configurations. Taken together, simulations suggest that short-ranged steric inter-filament interactions could combine with complementary hydrodynamic interactions to control the development and regulation of oscillatory collective patterns. Furthermore, roughness and steric interactions may be critical to the development of jammed spatially periodic states; a spatiotemporal feature not observed in purely hydrodynamically interacting systems. 

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