fluctuation theorem application on 2-d granular materials configurations
DESCRIPTION
Fluctuation theorem is tested for case of 2-d Brazil nut effect through entropy definition using concept of contactopyTRANSCRIPT
![Page 1: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/1.jpg)
Fluctuation Theorem Application on 2-D Granular Materials Configurations
S. Viridi, S. N. Khotimah, Novitrian, Widayani
Nuclear Physics and Biophysics Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia
Solo, Indonesia, 16 September 2014 12nd International Conference on Advanced
Materials Science and Technology (ICAMST)
![Page 2: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/2.jpg)
Outline
• Fluctuation theorem• Brazil nut effect• 2-d artificial configuration• Observation• Summary
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 2
![Page 3: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/3.jpg)
Fluctuation theorem
• One of the FTs states that (Seifert, 2005)
which holds for finite length of time δt for entropy change Δs
• Constraints: steady state of constant force and constant temperature
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 3
sesp
sp
![Page 4: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/4.jpg)
Fluctuation theorem (cont.)
• Second law of thermodynamics predicts that the entropy of an isolated system should tend to increase until it reaches equilibrium
• This theorem tells us that reverse process, where entropy decrease, could have high probability to happen
• It violates the law (in small scale during finite length of time)
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 4
![Page 5: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/5.jpg)
Brazil nut effect (BNE)
• Mixture of two different size of granular materials under vibration will produce seggreation larger grains on top, smaller grains on the bottom
• It holds also for only single intruder• It is observed in two- and three-dimension
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 5
![Page 6: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/6.jpg)
Brazil nut effect (BNE) (cont.)
• It has also the reverse BNE (RBNE) as reported (Hong et al., 2001)
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 6
![Page 7: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/7.jpg)
Brazil nut effect (BNE) (cont.)
• There is a crossover condition
BNE: ●, RBNE: ▪
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 7
![Page 8: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/8.jpg)
2-d artificial configuration
• It is based on real observation• Configuration are set artificially (Viridi et al.,
2014)• Time series of intruder and granular bed can
be analyzed
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 8
![Page 9: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/9.jpg)
2-d artificial configuration (cont.)
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 9
![Page 10: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/10.jpg)
Observation
• Number of contacts between grains are observed
• It is named as contactopy (Herrmann, 1993)Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 10
![Page 11: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/11.jpg)
Observation (cont.)
• Potential energy
• Contact energy
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 11
N
iig trgmtU
1
N
i
N
jijc ttU
1 1
sign
![Page 12: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/12.jpg)
Observation (cont.)
• Overlap between grains (Schäfer et al., 1996)
• Temperature T = mgDα • Entropy
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 12
trtrDDt jijiij
2
1,0max
tUttUT
s 1
![Page 13: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/13.jpg)
Observation (cont.)
• Center of mass posi-tion for mA/mB = 1
• Intruder movementseems to violateMPEP
• Change of COM forthe whole systemagrees with MPEP
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 13
![Page 14: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/14.jpg)
Observation (cont.)
• For mA/mB = 1, γ = 1, and α = 8
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 14
![Page 15: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/15.jpg)
Summary
• BNE obey second law of thermodynamics• RBNE has small probability to occur• FT does not violate second law of
thermodynamics for chosen parameters (mA/mB = 1, γ = 1, and α = 8)
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 15
![Page 16: Fluctuation Theorem Application on 2-D Granular Materials Configurations](https://reader034.vdocuments.us/reader034/viewer/2022052600/558942ded8b42ad9188b45c4/html5/thumbnails/16.jpg)
THANK YOU
Solo, Indonesia, 16 September 2014
2nd International Conference on Advanced Materials Science and Technology (ICAMST) 16