Twin vortex computer in fluid flow

Abstract

Fluids exist universally in nature and technology. Among the many types of fluid flows is the well-known vortex shedding, which takes place when a fluid flows past a bluff body. Diverse types of vortices can be found in this flow as the Reynolds number increases. In this study, we reveal that these vortices can be employed for conducting certain types of computation. The results from computational fluid dynamics simulations showed that optimal computational performance is achieved near the critical Reynolds number, where the flow exhibits a twin vortex before the onset of the Kármán vortex shedding associated with the Hopf bifurcation. It is revealed that as the Reynolds number increases toward the bifurcation point, the input sensitivity of the twin vortex motion also increases, suggesting the modality of information processing within the system. Our finding paves a novel path to understand the relationship between fluid dynamics and its computational capability.

A shape optimization problem constrained with the Stokes equations to address maximization of vortices

“…Furthermore, the visual observations on the emergence of the twin-vortex are not enough to give a good conclusion with regards to the memory capacity of the physical reservoir computer. With this, one can investigate even further and try some more tests as carried out in [13].…”

“…As mentioned before, the generation of twin-vortices gives a possible application of our shape optimization problem to a branch of machine learning known as physical reservoir computing. According to K. Goto et al, [13], the length of the long diameter of the twin vortices has a correlation with the memory capacity -as defined in the aforementioned reference -of the physical reservoir computer. With our previous observations, we can naively conjecture that the shapes generated by the implementations above will cause a better memory capacity for the physical reservoir computer.…”

“…Introduction. The study of fluid dynamics is among the most active areas in mathematics, physics, engineering, and most recently in information theory [13]. An interesting area in this field is the study of turbulent flows and on controlling the emergence of such phenomenon [7,10,30].Even though turbulence represents chaos, harnessing it in a controlled manner can be useful, for instance, in optimal mixing problems.…”

“…An interesting area in this field is the study of turbulent flows and on controlling the emergence of such phenomenon [7,10,30].Even though turbulence represents chaos, harnessing it in a controlled manner can be useful, for instance, in optimal mixing problems. Among these studies is [8] where an optimal stirring strategy to maximize mixing is studied, while in [24] the authors studied the best type of input functions that will provide a better mixing in the fluid.Recently, K. Goto et al [13] utilized the generation of vortices in the fluid for information processing tasks. In the said literature, the authors found out that the…”

“…Recently, K. Goto et al [13] utilized the generation of vortices in the fluid for information processing tasks. In the said literature, the authors found out that the…”