Proton channeling through long chiral carbon nanotubes: The rainbow route to equilibration
Abstract
In this work we investigate the rainbows appearing in channeling of 1 GeV protons through the long (11, 9) single-wall carbon nanotubes. The nanotube length is varied from 10 to 500 pm. The angular distributions of channeled protons are computed using the numerical solution of the proton equations of motion in the transverse plane and the Monte Carlo method. The rainbows are identified as the rings in the angular distributions, which correspond to the extrema of the proton deflection functions. Each rainbow is characterized by a sharp decrease of the proton yield on its large angle side. As the nanotube length increases, the number of rainbows increases and the average distance between them decreases in an easily predictable way. When the average distance between the rainbows becomes smaller than the resolution of the angular distribution, one cannot distinguish between the adjacent rainbows, and the angular distribution becomes equilibrated. We call this route to equilibration the rai...nbow route to equilibration. This work is a demonstration of how a simple one-dimensional bound dynamic system can exhibit a complex collective behavior.
Keywords:
channeling / nanotubes / rainbowsSource:
Physics Letters A, 2008, 372, 38, 6003-6007
DOI: 10.1016/j.physleta.2008.08.005
ISSN: 0375-9601
WoS: 000259626700015
Scopus: 2-s2.0-50149098212
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Institution/Community
VinčaTY - JOUR AU - Petrović, Srđan M. AU - Telečki, Igor N. AU - Borka, Duško AU - Nešković, Nebojša B. PY - 2008 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3529 AB - In this work we investigate the rainbows appearing in channeling of 1 GeV protons through the long (11, 9) single-wall carbon nanotubes. The nanotube length is varied from 10 to 500 pm. The angular distributions of channeled protons are computed using the numerical solution of the proton equations of motion in the transverse plane and the Monte Carlo method. The rainbows are identified as the rings in the angular distributions, which correspond to the extrema of the proton deflection functions. Each rainbow is characterized by a sharp decrease of the proton yield on its large angle side. As the nanotube length increases, the number of rainbows increases and the average distance between them decreases in an easily predictable way. When the average distance between the rainbows becomes smaller than the resolution of the angular distribution, one cannot distinguish between the adjacent rainbows, and the angular distribution becomes equilibrated. We call this route to equilibration the rainbow route to equilibration. This work is a demonstration of how a simple one-dimensional bound dynamic system can exhibit a complex collective behavior. T2 - Physics Letters A T1 - Proton channeling through long chiral carbon nanotubes: The rainbow route to equilibration VL - 372 IS - 38 SP - 6003 EP - 6007 DO - 10.1016/j.physleta.2008.08.005 ER -
@article{ author = "Petrović, Srđan M. and Telečki, Igor N. and Borka, Duško and Nešković, Nebojša B.", year = "2008", abstract = "In this work we investigate the rainbows appearing in channeling of 1 GeV protons through the long (11, 9) single-wall carbon nanotubes. The nanotube length is varied from 10 to 500 pm. The angular distributions of channeled protons are computed using the numerical solution of the proton equations of motion in the transverse plane and the Monte Carlo method. The rainbows are identified as the rings in the angular distributions, which correspond to the extrema of the proton deflection functions. Each rainbow is characterized by a sharp decrease of the proton yield on its large angle side. As the nanotube length increases, the number of rainbows increases and the average distance between them decreases in an easily predictable way. When the average distance between the rainbows becomes smaller than the resolution of the angular distribution, one cannot distinguish between the adjacent rainbows, and the angular distribution becomes equilibrated. We call this route to equilibration the rainbow route to equilibration. This work is a demonstration of how a simple one-dimensional bound dynamic system can exhibit a complex collective behavior.", journal = "Physics Letters A", title = "Proton channeling through long chiral carbon nanotubes: The rainbow route to equilibration", volume = "372", number = "38", pages = "6003-6007", doi = "10.1016/j.physleta.2008.08.005" }
Petrović, S. M., Telečki, I. N., Borka, D.,& Nešković, N. B.. (2008). Proton channeling through long chiral carbon nanotubes: The rainbow route to equilibration. in Physics Letters A, 372(38), 6003-6007. https://doi.org/10.1016/j.physleta.2008.08.005
Petrović SM, Telečki IN, Borka D, Nešković NB. Proton channeling through long chiral carbon nanotubes: The rainbow route to equilibration. in Physics Letters A. 2008;372(38):6003-6007. doi:10.1016/j.physleta.2008.08.005 .
Petrović, Srđan M., Telečki, Igor N., Borka, Duško, Nešković, Nebojša B., "Proton channeling through long chiral carbon nanotubes: The rainbow route to equilibration" in Physics Letters A, 372, no. 38 (2008):6003-6007, https://doi.org/10.1016/j.physleta.2008.08.005 . .