1:45 PM - 3:15 PM
[O11-P32] Application of entropy and random knot theory in entanglement of string objects: influence of electrostatic forces.
Keywords:random knot theory, entropy
OBJECTIVE
Focusing on the tangling phenomenon of wired earphones, which is a common phenomenon in daily life, this study aims to verify whether this phenomenon can be explained based on the law of increasing entropy. We also attempt to model the entanglement phenomenon by applying the random knot theory. Furthermore, we will consider the influence of electrostatic forces on this phenomenon and conduct a more detailed analysis.
DATA AND METHODOLOGY
Experimental Method
In this study, string-like objects (wired earphones) are placed under different conditions, and changes in entanglement over time are observed. The following procedure was used to conduct the experiment.
Two 125-cm wired earphones were placed at 2-cm intervals and vibrated for 40 seconds.
Change the placement interval to 5 cm and conduct the same experiment.
Change the wired earphones to PP strings and conduct the same experiment.
To equalize the effect of the vibration, a piece of paper was placed under the wire object, and the paper was vibrated at a constant amplitude. The experiment was performed 5 times in each condition and the number of entanglements was recorded as an integer value.
Experimental Apparatus
Wired earphone (total length 125 cm, flexible material)
PP string (used to compare different stiffnesses)
Paper (used to give equal vibrations to several wired earphones)
Recording camera (used for detailed analysis of the entanglement)
RESULTS
For the first 8 seconds, each earpiece vibrated independently, but after 10 seconds, one location began to tangle. Thereafter, entanglement increased exponentially with each passing second, and finally 9 locations were observed to become entangled.
When the distance between the earphones was increased to 5 cm, the time at which entanglement began was delayed, but a similar pattern was eventually observed.
In the experiment with the PP string, no entanglement occurred over time.
These results suggest that the ease of entanglement of string-like objects strongly depends on their flexibility and electrostatic properties.
DISCUSSION
Relevance to the Law of Increasing Entropy: The entanglement phenomenon of wired earphones is considered to be related to the law of increasing entropy, since the entanglement changes irreversibly from an orderly state (low entropy) to a tangled state (high entropy). The increase in the number of entanglements with time confirms that the rate of entropy increase is exponential.
Relevance to Wire Electricity: Static electricity can accumulate on the surface of wired earphones, which may promote the attraction of different parts and increase the entanglement susceptibility. Considering Coulomb's law of force, one would expect that the greater the surface charge density of an earphone, the more likely it is to become entangled. In light of the experimental results of this study, this hypothesis is supported.
Relation to the Random Knot Theory: The random knot theory states that the higher the degree of freedom of the string, the higher the probability of entanglement. The results of this study also suggest that this theory is valid, as entanglement occurred more frequently in wired earphones with a higher degree of freedom and did not occur in PP strings with a higher degree of rigidity.
REFERENCES
J. Lowell and A. C. Rose-Innes, “Contact Electrification,” Advances in Physics, Vol. 29, pp. 947–1023, 1980.
E. S. Matsusaka, H. Maruyama, T. Matsuyama, and M. Ghadiri, “Triboelectric charging of powders: A review,” Chemical Engineering Science, Vol. 65, No. 22, pp. 5781–5807, 2010.
Technical Information Center “SEKIGIN,” Second Law of Thermodynamics, http://sekigin.jp/science/phys/phys_04_02.html
Translated by deepl
Focusing on the tangling phenomenon of wired earphones, which is a common phenomenon in daily life, this study aims to verify whether this phenomenon can be explained based on the law of increasing entropy. We also attempt to model the entanglement phenomenon by applying the random knot theory. Furthermore, we will consider the influence of electrostatic forces on this phenomenon and conduct a more detailed analysis.
DATA AND METHODOLOGY
Experimental Method
In this study, string-like objects (wired earphones) are placed under different conditions, and changes in entanglement over time are observed. The following procedure was used to conduct the experiment.
Two 125-cm wired earphones were placed at 2-cm intervals and vibrated for 40 seconds.
Change the placement interval to 5 cm and conduct the same experiment.
Change the wired earphones to PP strings and conduct the same experiment.
To equalize the effect of the vibration, a piece of paper was placed under the wire object, and the paper was vibrated at a constant amplitude. The experiment was performed 5 times in each condition and the number of entanglements was recorded as an integer value.
Experimental Apparatus
Wired earphone (total length 125 cm, flexible material)
PP string (used to compare different stiffnesses)
Paper (used to give equal vibrations to several wired earphones)
Recording camera (used for detailed analysis of the entanglement)
RESULTS
For the first 8 seconds, each earpiece vibrated independently, but after 10 seconds, one location began to tangle. Thereafter, entanglement increased exponentially with each passing second, and finally 9 locations were observed to become entangled.
When the distance between the earphones was increased to 5 cm, the time at which entanglement began was delayed, but a similar pattern was eventually observed.
In the experiment with the PP string, no entanglement occurred over time.
These results suggest that the ease of entanglement of string-like objects strongly depends on their flexibility and electrostatic properties.
DISCUSSION
Relevance to the Law of Increasing Entropy: The entanglement phenomenon of wired earphones is considered to be related to the law of increasing entropy, since the entanglement changes irreversibly from an orderly state (low entropy) to a tangled state (high entropy). The increase in the number of entanglements with time confirms that the rate of entropy increase is exponential.
Relevance to Wire Electricity: Static electricity can accumulate on the surface of wired earphones, which may promote the attraction of different parts and increase the entanglement susceptibility. Considering Coulomb's law of force, one would expect that the greater the surface charge density of an earphone, the more likely it is to become entangled. In light of the experimental results of this study, this hypothesis is supported.
Relation to the Random Knot Theory: The random knot theory states that the higher the degree of freedom of the string, the higher the probability of entanglement. The results of this study also suggest that this theory is valid, as entanglement occurred more frequently in wired earphones with a higher degree of freedom and did not occur in PP strings with a higher degree of rigidity.
REFERENCES
J. Lowell and A. C. Rose-Innes, “Contact Electrification,” Advances in Physics, Vol. 29, pp. 947–1023, 1980.
E. S. Matsusaka, H. Maruyama, T. Matsuyama, and M. Ghadiri, “Triboelectric charging of powders: A review,” Chemical Engineering Science, Vol. 65, No. 22, pp. 5781–5807, 2010.
Technical Information Center “SEKIGIN,” Second Law of Thermodynamics, http://sekigin.jp/science/phys/phys_04_02.html
Translated by deepl