Showing papers by "John W. M. Bush published in 2022"

Aerodynamics in the beautiful game

Abstract: We consider the aerodynamics of football, specifically, the interaction between a ball in flight and the ambient air. Doing so allows one to account for the characteristic range and trajectories of balls in flight, as well as their anomalous deflections as may be induced by striking the ball either with or without spin. The dynamics of viscous boundary layers is briefly reviewed, its critical importance on the ball trajectories highlighted. The Magnus effect responsible for the anomalous curvature of spinning balls is seen to depend critically on the surface roughness of the ball, the sign of the Magnus force reversing for smooth balls. The origins of the fluttering of balls struck with nearly no spin is also discussed. Particular attention is given to categorizing and providing aerodynamic rationale for the various free kick styles.

Real surreal trajectories in pilot-wave hydrodynamics

Abstract: In certain instances, the particle paths predicted by Bohmian mechanics are thought to be at odds with classical intuition. A striking illustration arises in the interference experiments envisaged by Englert, Scully, Süssmann, and Walther, which lead the authors to claim that the Bohmian trajectories cannot be real and so must be “surreal.” Through a combined experimental and numerical study, we here demonstrate that individual trajectories in the hydrodynamic pilot-wave system exhibit the key features of their surreal Bohmian counterparts. These real surreal classical trajectories are rationalized in terms of the system’s non-Markovian pilot-wave dynamics. Our study thus makes clear that the designation of Bohmian trajectories as surreal is based on misconceptions concerning the limitations of classical dynamics and a lack of familiarity with pilot-wave hydrodynamics.

Hydrodynamic superradiance in wave-mediated cooperative tunneling

Abstract: Superradiance and subradiance occur in quantum optics when the emission rate of photons from multiple atoms is enhanced and diminished, respectively, owing to interaction between neighboring atoms. We here demonstrate a classical analog thereof in a theoretical model of droplets walking on a vibrating bath. Two droplets are confined to identical two-level systems, a pair of wells between which the drops may tunnel, joined by an intervening coupling cavity. The resulting classical superradiance is rationalized in terms of the system's non-Markovian, pilot-wave dynamics.

The Stability of a Hydrodynamic Bravais Lattice

Abstract: We present the results of a theoretical investigation of the stability and collective vibrations of a two-dimensional hydrodynamic lattice comprised of millimetric droplets bouncing on the surface of a vibrating liquid bath. Using the theoretical model, we derive the linearized equations of motion describing the dynamics of a generic Bravais lattice, as encompasses all possible tilings of parallelograms in an infinite plane-filling array. Focusing on square and triangular lattice geometries, we demonstrate that for relatively low driving accelerations of the bath, only a subset of inter-drop spacings exist for which stable lattices may be achieved. The range of stable spacings is prescribed by the structure of the underlying wavefield. As the driving acceleration is increased progressively, the initially stationary lattices destabilize into coherent oscillatory motion. Our analysis yields both the instability threshold and the wavevector and polarization of the most unstable vibrational mode. The non-Markovian nature of the droplet dynamics renders the stability analysis of the hydrodynamic lattice more rich and subtle than that of its solid state counterpart.

A platform for investigating Bell correlations in pilot-wave hydrodynamics

Abstract: Since its discovery in 2005, the hydrodynamic pilot-wave system has provided a concrete macroscopic realization of wave-particle duality and concomitant classical analogs of a growing list of quantum effects. The question naturally arises as to whether this system might support statistical states that violate Bell's inequality, and so yield a classical analog of quantum entanglement. We here introduce a new platform for addressing this question, a numerical model of coupled bipartite tunneling in the hydrodynamic pilot-wave system. We demonstrate that, under certain conditions, the Bell inequality is violated in a static Bell test owing to correlations induced by the wave-mediated coupling between the two subsystems. The establishment of non-factorizable states with two spatially separated classical particles introduces the possibility of novel forms of quantum-inspired classical computing.

MIT Open Access Articles Natural drinking strategies

Abstract: We examine the fluid mechanics of drinking in nature. We classify the drinking strategies of a broad range of creatures according to the principal forces involved, and present physical pictures for each style. Simple scaling arguments are developed and tested against existing data. While suction is the most common drinking strategy, various alternative styles have evolved among creatures whose morphological, physiological and environmental constraints preclude it. Particular attention is given to creatures small relative to the capillary length, whose drinking styles rely on relatively subtle interfacial effects. We also discuss attempts to rationalize various drinking strategies through consideration of constrained optimization problems. Some biomimetic applications are discussed.

MIT Open Access Articles Thermal delay of drop coalescence

Abstract: We present the results of a combined experimental and theoretical study of drop coalescence in the presence of an initial temperature difference ∆T 0 between a drop and a bath of the same liquid. We characterize experimentally the dependence of the residence time before coalescence on ∆T 0 for silicone oils with different viscosities. Delayed coalescence arises above a critical temperature difference ∆T c that depends on the fluid viscosity: for ∆T 0 > ∆T c , the delay time increases as ∆T 2 / 3 0 for all liquids examined. This observed dependence is rationalized theoretically through consideration of the thermocapillary flows generated within the drop, the bath and the intervening air layer.

Pilot-Wave Dynamics: Using Dynamic Mode Decomposition to characterize Bifurcations, Routes to Chaos and Emergent Statistics

Abstract: We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry, and apply the Dynamic mode decomposition (DMD) in order to characterize the evolution of the wave field as the bath’s vibrational acceleration is increased progressively. DMD provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatio-temporal data. The DMD characterization of the wave field yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. Moreover, it provides a low-rank characterization of the bifurcation structure of the pilot wave physics. Specifically, the analysis shows that as the vibrational acceleration is increased, the pilot-wave field undergoes a series of Hopf bifurcations that ultimately lead to a chaotic wave field. The established relation between the mean pilot-wave field and the droplet statistics allows us to characterize the evolution of the emergent statistics with increased vibrational forcing from the evolution of the pilot-wave field. We thus develop a numerical framework with the same basic structure as quantum mechanics, specifically a wave theory that predicts particle statistics.