A hydrodynamic analog to the optical Talbot effect may be realized on the surface of a vertically shaken fluid bath when a periodic array of pillars protrudes from the fluid surface. When the pillar spacing is twice or one and a half times the Faraday wavelength, we observe repeated images of the pillars projected in front of the array. Sloshing inter-pillar ridges act as sources of Faraday waves, giving rise to self-images. Here, we explore the emergence of Faraday-Talbot patterns when the sloshing ridges between pillars have alternating phases. We present a simple model of linear wave superposition and use it to calculate the expected self-image locations, comparing them to experimental observations. We explore how alternating phase sources affect the Faraday-Talbot patterns for linear and circular arrays of pillars, where curvature allows for magnification and demagnification of the self-imaging pattern. The use of an underlying wavefield is a subject of current interest in hydrodynamic quantum analog experiments, as it may provide a means to trap walking droplets.
Skip Nav Destination
Article navigation
September 2018
Research Article|
September 11 2018
Faraday-Talbot effect: Alternating phase and circular arrays
Special Collection:
Hydrodynamic Quantum Analogs
N. Sungar;
N. Sungar
a)
1
Department of Physics, California Polytechnic State University
, San Luis Obispo, California 93407, USA
Search for other works by this author on:
J. P. Sharpe;
J. P. Sharpe
1
Department of Physics, California Polytechnic State University
, San Luis Obispo, California 93407, USA
Search for other works by this author on:
J. J. Pilgram
;
J. J. Pilgram
1
Department of Physics, California Polytechnic State University
, San Luis Obispo, California 93407, USA
Search for other works by this author on:
J. Bernard;
J. Bernard
1
Department of Physics, California Polytechnic State University
, San Luis Obispo, California 93407, USA
Search for other works by this author on:
L. D. Tambasco
L. D. Tambasco
2
Department of Mathematics, Massachusetts Institute of Technology
, Cambridge, Massachusetts 02139, USA
Search for other works by this author on:
a)
Email: nsungar@calpoly.edu
Chaos 28, 096101 (2018)
Article history
Received:
March 29 2018
Accepted:
July 05 2018
Citation
N. Sungar, J. P. Sharpe, J. J. Pilgram, J. Bernard, L. D. Tambasco; Faraday-Talbot effect: Alternating phase and circular arrays. Chaos 1 September 2018; 28 (9): 096101. https://doi.org/10.1063/1.5031442
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Pay-Per-View Access
$40.00
Citing articles via
Sex, ducks, and rock “n” roll: Mathematical model of sexual response
K. B. Blyuss, Y. N. Kyrychko
Nonlinear model reduction from equations and data
Cecilia Pagliantini, Shobhit Jain
Focus on the disruption of networks and system dynamics
Peng Ji, Jan Nagler, et al.
Related Content
Analysis of a scheme for de-magnified Talbot lithography
J. Vac. Sci. Technol. B (November 2011)
A causal look into the quantum Talbot effect
J. Chem. Phys. (June 2007)
Observation of the Talbot effect with water waves
Am. J. Phys. (January 2019)
Bouncing droplet dynamics above the Faraday threshold
Chaos (September 2018)
Improving the resolution and throughput of achromatic Talbot lithography
J. Vac. Sci. Technol. B (September 2018)