Group 2 2014 - Revision history

Faraday2014: /* Analysis of Results */

2014-12-12T22:46:25Z

Analysis of Results

← Older revision		Revision as of 18:46, 12 December 2014
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	[[File:WaveOnset.jpg \| thumb \| 300px \| Pattern formation at the onset of the waves. These dots occur in the middle of convection nodes, where particles collide.]]		[[File:WaveOnset.jpg \| thumb \| 300px \| Pattern formation at the onset of the waves. These dots occur in the middle of convection nodes, where particles collide.]]


	Of the two functions derived from each video, the luminosity function is the key one; the forcing function merely contextualizes it. The total luminosity reflected by the fluid is an interesting metric because of the way the particles within the rheoscopic fluid behave. These particles are tiny flakes, like fish scales, which align with the fluid flow. In a still fluid, they are oriented randomly. In a fluid with 2D flow perpendicular to the line of sight, the majority of the particles align parallel to the flow such that light shone from above will not reflect toward the observer i.e. the particles have the flat face towards the observer. Further, in areas of the flow with high sheer or curl (as in the center of a convection node), these particles collide and "tumble," and thus reflect light toward the observer. With this information about the way the particles behave in the fluid, we can decipher both what we see occurring in the videos, and the structure of the luminosity function.		Of the two functions derived from each video, the luminosity function is the key one; the forcing function merely contextualizes it. The total luminosity reflected by the fluid is an interesting metric because of the way the particles within the rheoscopic fluid behave. These particles are tiny flakes, like fish scales, which align with the fluid flow. In a still fluid, they are oriented randomly. In a fluid with 2D flow perpendicular to the line of sight, the majority of the particles align parallel to the flow such that light shone from above will not reflect toward the observer i.e. the particles have the flat face towards the observer. Further, in areas of the flow with high sheer or curl (as in the center of a convection node), these particles collide and "tumble," and thus reflect light toward the observer. With this information about the way the particles behave in the fluid, we can decipher both what we see occurring in the videos, and the structure of the luminosity function.
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	[[File:WaveGraph378.jpg \| thumb \| 300px \| Luminosity function (top) and forcing amplitude (bottom) at .378 g. Yellow: convection "dots" first appear; Red: Surface waves form; Green: "Dots" fall and fade out.]]		[[File:WaveGraph378.jpg \| thumb \| 300px \| Luminosity function (top) and forcing amplitude (bottom) at .378 g. Yellow: convection "dots" first appear; Red: Surface waves form; Green: "Dots" fall and fade out.]]


	=Conclusion=		=Conclusion=

Faraday2014: /* Methodology */

2014-12-12T22:45:42Z

Methodology

← Older revision		Revision as of 18:45, 12 December 2014
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	===Experiment Videos===		===Experiment Videos===
	<videoflash>kRBP7rz2KTk~~&index=3&list=UUTT5_sfMeq7I7tATTt-WrJg~~</videoflash>		<videoflash>kRBP7rz2KTk</videoflash>

	<videoflash>xYonD_TS0_0~~&index=2&list=UUTT5_sfMeq7I7tATTt-WrJg~~</videoflash>		<videoflash>xYonD_TS0_0</videoflash>

	<videoflash>XQLX90sTQ2M~~&list=UUTT5_sfMeq7I7tATTt-WrJg&index=1~~</videoflash>		<videoflash>XQLX90sTQ2M</videoflash>

	=Data Analysis=		=Data Analysis=

Faraday2014: /* Methodology */

2014-12-12T22:43:29Z

Methodology

← Older revision		Revision as of 18:43, 12 December 2014
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	For each trial we began by mixing the fluid to homogeneity, and allowing a moment for the flows of the stirring to damp out. Once the fluid appeared on camera to be still and uniform, we turned on the shaker table, and quickly turned up the amplitude to our target amplitude for the trial. After reaching the target amplitude, we would not adjust the forcing function until the fluid had undergone the Faraday instability and settled into a steady oscillation. Once the fluid had reached a steady state (judged qualitatively by the profile of the forcing function and the images from the camera), we turned off the forcing function and allowed the waveform to damp out. We recorded the whole process with a highs-peed camera for each trial, and then saved the video. This video was the data we collected, and all other metrics were derived from it during post-processing.		For each trial we began by mixing the fluid to homogeneity, and allowing a moment for the flows of the stirring to damp out. Once the fluid appeared on camera to be still and uniform, we turned on the shaker table, and quickly turned up the amplitude to our target amplitude for the trial. After reaching the target amplitude, we would not adjust the forcing function until the fluid had undergone the Faraday instability and settled into a steady oscillation. Once the fluid had reached a steady state (judged qualitatively by the profile of the forcing function and the images from the camera), we turned off the forcing function and allowed the waveform to damp out. We recorded the whole process with a highs-peed camera for each trial, and then saved the video. This video was the data we collected, and all other metrics were derived from it during post-processing.

			===Experiment Videos===
			<videoflash>kRBP7rz2KTk&index=3&list=UUTT5_sfMeq7I7tATTt-WrJg</videoflash>

			<videoflash>xYonD_TS0_0&index=2&list=UUTT5_sfMeq7I7tATTt-WrJg</videoflash>

			<videoflash>XQLX90sTQ2M&list=UUTT5_sfMeq7I7tATTt-WrJg&index=1</videoflash>

	=Data Analysis=		=Data Analysis=

Faraday2014: /* Introduction */

2014-12-12T22:38:19Z

Introduction

← Older revision		Revision as of 18:38, 12 December 2014
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	=Introduction=		=Introduction=
	First observed by Michael Faraday in 1831 ~~\cite{Fpaper}~~, Faraday waves are surface instabilities that arise in a fluid undergoing vertical oscillations above a critical amplitude and/or frequency. Faraday himself measured that the resulting surface wave frequency was equal to half the driving frequency. Above this critical amplitude/frequency the fluid surface can exhibit an incredible variety of patterns as well as spatial and temporal chaos and combinations of the two, attracting the attention of mathematicians and physicists alike. The pattern symmetries and critical values are highly dependent on boundary conditions, and the properties of the fluid itself (for example viscosity and surface tension).		First observed by Michael Faraday in 1831, Faraday waves are surface instabilities that arise in a fluid undergoing vertical oscillations above a critical amplitude and/or frequency. Faraday himself measured that the resulting surface wave frequency was equal to half the driving frequency. Above this critical amplitude/frequency the fluid surface can exhibit an incredible variety of patterns as well as spatial and temporal chaos and combinations of the two, attracting the attention of mathematicians and physicists alike. The pattern symmetries and critical values are highly dependent on boundary conditions, and the properties of the fluid itself (for example viscosity and surface tension).

	Beyond the mere satisfaction of mathematical curiosity, Faraday waves have several practical applications and made contributions to other areas of physics. They play a role in the amplification of earthquakes through looser sediments ~~\cite{Equake}~~ and can allow one to deposit thin films of material in a desired pattern because small particles in the fluid are pulled towards amplitude; such a skill has interesting applications in creating more precise optical instruments ~~\cite{nanofilm}~~. In the field of quantum mechanics, Faraday waves have been observed in Bose-Einstein Condensates ~~\cite{BEC}~~ and there is a curious analogy one can make between a probability wave distribution in quantum mechanics and a the chaotic motion of a 'walking' droplet guided by a precisely tuned Faraday wave ~~\cite{Walkers}~~. When confined to a circular container, an oil droplet can be made to bounce on a water surface supporting a Faraday wave within a small range of driving frequency and amplitude ~~\cite{bouncingdrop}~~. Within an even narrower parameter range, the Faraday wave can guide the oil droplet in a random walk across the surface. This results in a probability distribution for the droplet reminiscent of the wave function of an atom confined in a similar circular geometry. The particle/wave guide pair also exhibits many effects similar to those predicted by quantum physics such as tunneling and bears a striking resemblance to wave/particle duality on a macroscopic level. These similarities have left many speculating that there may be a hidden variable theory for quantum mechanics that mimics the pilot wave in the walking droplet experiment ~~\cite{Bush2014}~~.		Beyond the mere satisfaction of mathematical curiosity, Faraday waves have several practical applications and made contributions to other areas of physics. They play a role in the amplification of earthquakes through looser sediments and can allow one to deposit thin films of material in a desired pattern because small particles in the fluid are pulled towards amplitude; such a skill has interesting applications in creating more precise optical instruments. In the field of quantum mechanics, Faraday waves have been observed in Bose-Einstein Condensates and there is a curious analogy one can make between a probability wave distribution in quantum mechanics and a the chaotic motion of a 'walking' droplet guided by a precisely tuned Faraday wave. When confined to a circular container, an oil droplet can be made to bounce on a water surface supporting a Faraday wave within a small range of driving frequency and amplitude. Within an even narrower parameter range, the Faraday wave can guide the oil droplet in a random walk across the surface. This results in a probability distribution for the droplet reminiscent of the wave function of an atom confined in a similar circular geometry. The particle/wave guide pair also exhibits many effects similar to those predicted by quantum physics such as tunneling and bears a striking resemblance to wave/particle duality on a macroscopic level. These similarities have left many speculating that there may be a hidden variable theory for quantum mechanics that mimics the pilot wave in the walking droplet experiment.

	=Methodology=		=Methodology=

Faraday2014: /* References */

2014-12-12T22:34:03Z

References

@@ Line 62: / Line 62: @@
 | journal = Philosophical Transactions of the Royal Society (London
 | volume  = 121
 | year    = 1831
 | pages   = 299–318
 }}

PatrickChang at 22:32, 12 December 2014

2014-12-12T22:32:25Z

← Older revision		Revision as of 18:32, 12 December 2014
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	Members: Bollenbacher, Chambers, Cunningham, Putzel		Members: Bollenbacher, Chambers, Cunningham, Putzel

	[[Media:Faraday.pdf\|Final ~~Paper~~]]		[[Media:Faraday.pdf\|Final Report]]

	=Introduction=		=Introduction=

PatrickChang at 22:28, 12 December 2014

2014-12-12T22:28:30Z

← Older revision		Revision as of 18:28, 12 December 2014
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	Members: Bollenbacher, Chambers, Cunningham, Putzel		Members: Bollenbacher, Chambers, Cunningham, Putzel

			[[Media:Faraday.pdf\|Final Paper]]

	=Introduction=		=Introduction=

Faraday2014: /* References */

2014-12-12T22:21:27Z

References

← Older revision		Revision as of 18:21, 12 December 2014
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	=References=		=References=
	{{Citation		{{Citation
	\| last = ~~Hill~~		\| last = Faraday
	\| first = ~~Marvin S~~.		\| first = M.
	\| title = ~~Joseph Smith~~ and ~~the 1826~~		\| title = On a peculiar class of acoustical figures; and on certain forms assumed by a group of particles upon vibrating elastic surfaces
	~~Trial: New Evidence and New~~		\| journal = Philosophical Transactions of the Royal Society (London
	~~Difficulties~~		\| volume = 121
	\| journal = ~~BYU Studies~~
	\| volume = 12
	\| issue = 2		\| issue = 2
	\| year = ~~1976~~		\| year = 1831
	\| pages = ~~1–8~~		\| pages = 299–318
	}}		}}

Faraday2014: /* References */

2014-12-12T22:19:15Z

References

← Older revision		Revision as of 18:19, 12 December 2014
Line 54:		Line 54:

	=References=		=References=
			{{Citation
			\| last = Hill
			\| first = Marvin S.
			\| title = Joseph Smith and the 1826
			Trial: New Evidence and New
			Difficulties
			\| journal = BYU Studies
			\| volume = 12
			\| issue = 2
			\| year = 1976
			\| pages = 1–8
			}}

Faraday2014 at 21:41, 12 December 2014

2014-12-12T21:41:36Z

← Older revision		Revision as of 17:41, 12 December 2014
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	After tracking these two surfaces, we were able to pull out both the forcing function and the total reflected luminosity within the fluid. We factored out the surface reflections and the visible meniscus of the fluid by chopping off a small buffer zone on the top and bottom of the region. These two functions were the major results of the current work, and proved to be quite illuminating.		After tracking these two surfaces, we were able to pull out both the forcing function and the total reflected luminosity within the fluid. We factored out the surface reflections and the visible meniscus of the fluid by chopping off a small buffer zone on the top and bottom of the region. These two functions were the major results of the current work, and proved to be quite illuminating.

			[[File:WaveAnalysis.jpg \| thumb \| 300px \| Top: raw image; Middle: surface tracking; Bottom: region of integration for luminosity function]]

	===Analysis of Results===		===Analysis of Results===

			[[File:WaveOnset.jpg \| thumb \| 300px \| Pattern formation at the onset of the waves. These dots occur in the middle of convection nodes, where particles collide.]]


	Of the two functions derived from each video, the luminosity function is the key one; the forcing function merely contextualizes it. The total luminosity reflected by the fluid is an interesting metric because of the way the particles within the rheoscopic fluid behave. These particles are tiny flakes, like fish scales, which align with the fluid flow. In a still fluid, they are oriented randomly. In a fluid with 2D flow perpendicular to the line of sight, the majority of the particles align parallel to the flow such that light shone from above will not reflect toward the observer i.e. the particles have the flat face towards the observer. Further, in areas of the flow with high sheer or curl (as in the center of a convection node), these particles collide and "tumble," and thus reflect light toward the observer. With this information about the way the particles behave in the fluid, we can decipher both what we see occurring in the videos, and the structure of the luminosity function.		Of the two functions derived from each video, the luminosity function is the key one; the forcing function merely contextualizes it. The total luminosity reflected by the fluid is an interesting metric because of the way the particles within the rheoscopic fluid behave. These particles are tiny flakes, like fish scales, which align with the fluid flow. In a still fluid, they are oriented randomly. In a fluid with 2D flow perpendicular to the line of sight, the majority of the particles align parallel to the flow such that light shone from above will not reflect toward the observer i.e. the particles have the flat face towards the observer. Further, in areas of the flow with high sheer or curl (as in the center of a convection node), these particles collide and "tumble," and thus reflect light toward the observer. With this information about the way the particles behave in the fluid, we can decipher both what we see occurring in the videos, and the structure of the luminosity function.
Line 38:		Line 43:

	As the amplitude of the forcing increases, the profile of the luminosity function changes, especially in the early stages of onset. At higher forcing amplitude, the amplitude of the oscillations in the luminosity function grow much larger than in the lower amplitude case. While this makes the graphs look quite different at first glance, the behavior of the mean and relative amplitude is the same.		As the amplitude of the forcing increases, the profile of the luminosity function changes, especially in the early stages of onset. At higher forcing amplitude, the amplitude of the oscillations in the luminosity function grow much larger than in the lower amplitude case. While this makes the graphs look quite different at first glance, the behavior of the mean and relative amplitude is the same.

	~~[[File:WaveAnalysis.jpg \| thumb \| 300px \| Top: raw image; Middle: surface tracking; Bottom: region of integration for luminosity function]]~~


	~~[[File:WaveOnset.jpg \| thumb \| 300px \| Pattern formation at the onset of the waves. These dots occur in the middle of convection nodes, where particles collide.]]~~

	[[File:WaveGraph378.jpg \| thumb \| 300px \| Luminosity function (top) and forcing amplitude (bottom) at .378 g. Yellow: convection "dots" first appear; Red: Surface waves form; Green: "Dots" fall and fade out.]]		[[File:WaveGraph378.jpg \| thumb \| 300px \| Luminosity function (top) and forcing amplitude (bottom) at .378 g. Yellow: convection "dots" first appear; Red: Surface waves form; Green: "Dots" fall and fade out.]]

	[[File:WaveGraph378.jpg \| thumb \| 300px \| Luminosity function (top) and forcing amplitude (bottom) at .378 g. Yellow: convection "dots" first appear; Red: Surface waves form; Green: "Dots" fall and fade out.]]

	=Conclusion=		=Conclusion=