Tunneling with a hydrodynamic pilot-wave model

Posted by on Oct 17, 2017 in Bibliography, Core Bibliography, Theory Bibliography | 0 comments

ABSTRACT : “Eddi et al. [Phys. Rev Lett. 102, 240401 (2009)] presented experimental results demonstrating the unpredictable tunneling of a classical wave-particle association as may arise when a droplet walking across the surface of a vibrating fluid bath approaches a submerged barrier.We here present a theoreticalmodel that captures the influence of bottom topography on this wave-particle association and so enables us to investigate its interaction 2 with barriers. The coupledwave-droplet dynamics results in unpredictable tunneling events.
As reported in the experiments by Eddi et al. and as is the case in quantum tunneling [Gamow, Nature (London) 122, 805 (1928)], the predicted tunneling probability decreases exponentially with increasing barrier width. In the parameter regimes examined, tunnelingbetween two cavities suggests an underlying stationary ergodic process for the droplet’s position.”

Nachbin, A., Milewski, P. A., & Bush, J. W. (2017). Tunneling with a hydrodynamic pilot-wave model. Physical Review Fluids2(3), 034801


Click to access NachbinMilewskiBush_PRF17.pdf

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Faraday pilot wave dynamics : modelling and computation

Posted by on Apr 10, 2016 in Bibliography, Core Bibliography, Numerical Simulation | 0 comments

Milewski, P. A., Galeano-Rios, C. A., Nachbin, A., & Bush, J. W. (2015). Faraday pilot-wave dynamics: modelling and computation. Journal of Fluid Mechanics, 778, 361-388.

A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue of a resonant interaction with its own wave field. This system represents the first known example of  pilot-wave system of the form envisaged by Louis de Broglie in his double-solution pilot-wave theory. We here develop a fluid model of pilot-wave hydrodynamics by coupling recent models of the droplet’s bouncing dynamics with a more realistic model of weakly viscous quasi-potential wave generation and evolution. The resulting model is the first to capture a number of features reported in experiment, including the rapid transient wave generated during impact, the Doppler effect and walker–walker interactions.

faraday pilot wave dynamics modelling and computation


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Video Lesson – 07/06/2013 – Hydrodynamic Modelling of Pilot-Wave and boucing droplet coupling in a Faraday Problem

Posted by on Jul 21, 2014 in Blog, On the web, Videos | 0 comments

“Recent experiments by two groups, Yves Couder (Paris) and John 
Bush (MIT) have shown experimentally that droplets will bounce on the 
surface of a vertically vibrated bath (instead of coalescing with it), 
generating a Faraday-type wavefield at every bounce. From this state, a 
pitchfork symmetry breaking bifurcation leads to a “walking” state whereby 
the bouncing droplet is “guided” by the self-generated wavefield – the 
droplet’s pilot wave. Once this state is achieved a large array of 
interesting dynamics ensues with surprising analogies to quantum 
mechanical behaviour. We will present a coupled particle-fluid model that 
can can be used simulate the dynamics of this problem. This is joint work 
with John Bush, Andre Nachbin (IMPA) and Carlos Galeano (IMPA)”

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