Gunner and James

Abstract

PHISICS Trim.mp4

Background

In 2014, Dr. Alfred Hübler designed an experiment with which he explored Complex Systems: "Stability and Conductivity of self assembled wires in a transverse electrical field." He explored the minutia of this complex system, and said later in an article, titled "Inhibitory nodes in self-assembling networks mimic the human brain," that this system puts us one step closer to designing "engineered brains." In this experiment, since we were unable to find any proven explanation for this phenomenon, we proposed a theory of our own. We then tested an aspect of this theory using conductance of various metals, and then found results which supported, but did not prove our proposition. But before talking about our results, we must discuss the terminology used in the original study.

Self Assembling Wires

Stainless steel ball bearings, with a conductivity of 1.32 Siemens/m and resistance of 76.0 Ohms, in a variety of sizes ranging from 2mm to 1mm. Our experiment controlled for size, keeping ball bearings a constant 1mm, and added additional runs with Copper ball bearings, with a conductivity of 58.7 Siemens/m resistance of 1.68 Ohms.

Transverse Electrical Field

A petri-dish with a layer of castor oil, polarized through a metal edge as an anode, and a live wire in the center as a cathode. The castor oil, a dielectric substance, insulates the charge running through the ball bearings and slows their trajectory as they move to the negatively charged exterior of the petri-dish

Emergent Patterns and Findings of Dr. Hübler

An astounding mix of organized trends and chaos was found in the original study. One particular trend: 22% of ball bearings were end nodes, and 22% were branch nodes. Some emergent patterns were also observed in the study, patterns which we can be found in our own data.

The Van de Graaff Generator

A Van de Graaff generator is a device which can produce a high, constant flow of static electricity. Inside the generator, a belt is spun around a wheel and axle, stealing electrons from a roll of Teflon. The belt is positively charged from this interaction, and carries this charge up to a metal orb. Through different speeds of spinning, a variety of charges can be produced. The Van de Graaff used in this experiment also had a ground socket at its base.

Lichtenberg Figures

Lichtenberg figures are patterns found after some electrical discharge in an insulating material as a result of the natural patterns of branching electrons. Lightning and its resulting patterns after striking wood or skin demonstrate naturally occurring Lichtenberg figures, and our self building wires provide a similar pattern.

*Warning: The third photo may not be for the faint of heart.

Experimental Design

Physical Study

We replicated the original experiment, using both copper and stainless steel ball bearings. Our experiment used a Van de Graaff generator as a power source, and held the positively charged wire using an insulated glove and insulated prongs. The experiment was run ten times for each material, for a total of 20 runs. After each run, the ball bearings were reorganized back into the center using a scoopula. Videos of the runs were analyzed using the video software "Davinci Resolve," and the time data was graphed and analyzed in excel.

Materials

1000 copper ball bearings (1mm)
1000 stainless steel ball bearings (1mm)
2 clear plastic petri-dishes
Castor oil
Aluminum foil
Van De graaff generator
Clip-end copper wire (Anode)
Prong-end copper wire (Cathode)
Electrical tape
Recording Device (smartphone)

Theoretical Explanation

From research and theorizing, we came to the agreement that the movement of these ball bearings was dictated by the passage of a positive or negative electrical charge through them. As is described in basic electrostatics, like charges repel, and opposite charges attract. Due to the like charges of all the ball bearings and the opposing charge between the ball bearings and the aluminum rim of the petri dish, the ball bearings would logically travel away from each other and towards the outer edge of the petri dish. Furthermore, as the ball bearings contact one another, their charge passes further from the center until it eventually escapes through the castor oil, so the bridges formed by the bearings between the cathode and anode of the power supply are similarly easy to explain. However, the trait of this phenomenon we struggled to grasp was the observed Lichtenburg-esque forks in the bearing trees. After contemplating this trait for some time and seeking the advice of Mr. Copeland, we realized that these forks are likely caused by the path the electrons take after reaching the ends of the bearing chains.

As the induced electric charge runs through chains of ball bearings, it is passed from one bearing to the next when two bearings come in contact. Electricity always takes the path of least resistance, and since both stainless steel and copper possess significantly higher conductivity properties than castor oil, the electric charge logically passes through the chain of bearings for as long a distance as possible. However, once the charge reaches the ball bearing furthest from the center of the pile, the charge begins to travel through the dialectic castor oil and falls into line with the high-entropy Lichtenburg travel patterns associated with unguided electric charge transfer. In simpler terms, once reaching the end of the ball bearing chain, the charge randomly travels from the bearings to the rim of the petri dish. It’s similar to how the spark on a grill or stove never travels between the lighter and burner in a straight line. Rather it moves in a random, arc-like shape. Of course, these arcs are slowed down by the presence of the castor oil, and the “trail” they leave in the oil by polarizing it as they pass draws the ball bearings along the path the arc took. Therefore, the chains created by the bearings form into Lichtenburg-esque branches which straighten out once they connect the two terminals of the power supply.

Computer Simulation

We struggled with the idea of confirming or denying our conceptual understanding of how these self-assembling wires functioned. Therefore, we decided that modeling the process with a computer would allow us to better grasp the concepts at play and determine if the ideal scenario we crafted played out in real life.

Simulating this entire process was a massive process, however, so we elected to start from the ground up with our real-life emulations. The first step we took was designing a physics engine capable of calculating electrostatic forces between two objects and adjusting the accelerations, velocities, and positions of the objects accordingly. Thus, we created two particle objects which each held a charge, mass, position, velocity, and acceleration, and used the below equation to calculate the electric force between the two particles.

This equation, named Coulomb's Law, returns the electric force between two bodies if given their net charge and distance apart. Thus, after dealing with some trigonometric complexities, we successfully calculate the direction and magnitude of electric force vectors for each of the two bodies, calculated their accelerations, modified their velocities, and updated their positions before redrawing the next frame. The next step of our process was developing this concept to react to many different bodies. And after adjusting our code to calculate accelerations and all related metrics from a single net force vector, developing a process for calculating a net force vector from the myriad of electric forces acting, adding in neutral oxygen and nitrogen molecules, and building in positive and negative terminals for our cathode and anode, the sim began to look like this.

In the video, the gray lines represent the path electrons have taken, the blue dots represent neutral oxygen molecules, and the boxes on the sides of the screen were our power supply terminal connections. In this simulation, black is negative and red is positive.

With additional time to pursue this project, we would continue to develop spark-making features (the physics of which we learned from this Walter Lewin Lecture) and eventually attempt building a proper simulation for the entire process of self-assembling wires.

Side by Side Data

DYO Video.mov

Results

Stainless Steel

Fewer initial branches and more forks. Average circuit completion speed of 16.61 seconds

Copper

More initial branches and similar forking. Average circuit completion speed of 12.61, four seconds faster than steel on average.

Stainless Steel was found to have a slower circuit completion time on average. The average deviation of Stainless Steel was 4.08 with a percent AAD of 24.58%. The average deviation of Copper was 2.14 with a percent AAD of 16.96%.

Stainless Steel

Copper

The photos above highlight a phenotypic phenomena observed in self building wires of different metals. Stainless steel wires form fewer, longer branches from the origin while copper wires are more numerous initially. Branching in the stainless steel system tends to be contained to twofold forks, with the occasional threefold tree. The copper system contains trees with numerous branches.

Discussion

Patterns

As mentioned in the computer simulation section, the phenomenon of self-building wires themselves are a result of positively charged ball bearings repelling one another while simultaneously following the path electrons take in dielectric liquid. Thus, this experiment effectively slows the patterns of lightning which appear in air. The castor oil slows ball bearings, which effectively become like electrons traveling along branching paths.

Speed

Stainless steel has a higher resistance than copper. Thus, we propose the slower circuit completion time in the stainless steel system is a result of the higher voltage needed to induce similar charges and thus similar movement on stainless steel ball bearings relative to copper ones. The difference in density of materials, where an increase in the mass of ball bearings of identical volume could result in a decreased acceleration is a non-factor. Copper has a higher density than stainless steel, so we would suspect copper to have a slower acceleration than stainless steel, and thus have a slower circuit completion time. Our results disprove this theory.

Branching

We propose copper has more branches as a result of its higher conductivity. Since copper will hold its charge less, a smaller portion of electrons can generate an effect that would require more for stainless steel. Stainless steel, on the other hand, "binds" electrons to the path of least resistance more than copper does as a result of its increased resistance. It requires a higher voltage for an electron to surpass the threshold of resistance in stainless steel and create a new branch. Thus, copper creates a sort of "electrical freedom," which allows electrons to branch off at higher rates.

Conclusion

PHYSICS CONCLUSION Trim.mp4

Resources

https://en.wikipedia.org/wiki/Lichtenberg_figure

Lichtenberg Figures

https://www.nature.com/articles/srep15044.pdf

Self assembling wires original article

http://www.cs.unc.edu/~geom/LIGHTNING/lightning.pdf

Lightning simulation paper

https://www.frostphysics.org/electric-charge.html

Charges explanation

https://www.theworldmaterial.com/density-of-metals/

Density of Copper and Stainless Steel

https://www.tibtech.com/conductivite.php?lang=en_US

Conductivity/Resistance of Copper and Stainless Steel

https://www.youtube.com/watch?v=PeHWqr9dz3c&t=176s

Original Video on Self-Assembling wires

https://www.youtube.com/watch?v=2NKJ3x-iOAU