Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/3041
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dc.contributor.advisorFort, Emmanuelen_US
dc.contributor.authorSURABHI K Sen_US
dc.date.accessioned2019-05-30T06:51:16Z
dc.date.available2019-05-30T06:51:16Z
dc.date.issued2019-04en_US
dc.identifier.urihttp://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/3041-
dc.descriptionThis project aiMS to experimentally analyse the analogy between Ising machine and bouncing droplets by looking at their dynamics and interaction. We develop a novel technique to produce reproducible drops (0.64 mm in diameter). We fully characterize the period doubling transition for one droplet and its associated wave field emission. This gives new insight for further analysis involving looking at the Fourier components of the wave field and understanding how droplets reach the ground state. We study the interaction and relative phase selection for a two droplets systeMS and showed that it finds the minimum energy state of the conformational space depending on their mutual interaction. Finally, we show some examples of more complex sets of interacting 9 droplets which also attain ground states. These results show that interacting droplets contain many features of an Ising machine and can perform relevant optimization calculations. The full experimental characterizations can now be used to perform realistic simulations and to develop an Ising model based on this system.en_US
dc.description.abstractThis project’s larger goal involves devising an experimental method to investigate links between a lattice of bouncing drops and the Ising machine. The coupling between droplets plays a crucial role in this aspect and the work carried out here encapsulates some major features pertaining to this interaction between droplets. An Ising machine is an artificial system of spins based on the Ising model, which describes the energy of a set of interacting constituent spin like elements with bi-stable states. Combinatorial optimization problems are a large class of problems which involve optimizing a certain quantity from a set of discrete elements and they can be mapped to the Hamiltonian function of the Ising model. These problems belong to the class of NP-hard problems for which computational complexity grows as a power law with each new added element. The purpose of building an Ising machine is to provide an architecture which can efficiently solve such problems by finding the ground state of its constituent elements. Previously, interacting coupled parametric oscillators have been proposed as a possible implementation of an Ising machine. The ground state can be efficiently determined by slowly increasing the excitation until each oscillator reaches a bi-stable state which is determined by its interactions with the other oscillators. A set of bouncing droplets on a vertically vibrated bath is a good candidate for an Ising machine. Each droplet can be considered as a parametrical oscillator which is controlled by the vibration of the bath. These droplets undergo period doubling above a given excitation threshold which defines a bi-stable state defined by their phase. These ‘artificial spins’ interact with each other through the waves that they emit on the bath. This interaction can be tuned by changing the distances between droplets.en_US
dc.description.sponsorshipESPCI Paris and CNRS, Franceen_US
dc.language.isoenen_US
dc.subject2019
dc.subjectBouncing droplet dynamics Ising Machine Max-Cut NP-Harden_US
dc.titleWave mediated interaction in a lattice of bouncing dropsen_US
dc.typeThesisen_US
dc.type.degreeBS-MSen_US
dc.contributor.departmentDept. of Physicsen_US
dc.contributor.registration20141095en_US
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