TY  - JOUR
AU  - Zeković, Slobodan
AU  - Muniyappan, Annamalai
AU  - Zdravković, Slobodan
AU  - Kavitha, Louis
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5904
AB  - We show how Jacobian elliptic functions (JEFs) can be used to solve ordinary differential equations (ODEs) describing the nonlinear dynamics of microtubules (MTs). We demonstrate that only one of the JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kink-type soliton moves along MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.
T2  - Chinese Physics B
T1  - Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules
VL  - 23
IS  - 2
DO  - 10.1088/1674-1056/23/2/020504
ER  - 

@article{
author = "Zeković, Slobodan and Muniyappan, Annamalai and Zdravković, Slobodan and Kavitha, Louis",
year = "2014",
abstract = "We show how Jacobian elliptic functions (JEFs) can be used to solve ordinary differential equations (ODEs) describing the nonlinear dynamics of microtubules (MTs). We demonstrate that only one of the JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kink-type soliton moves along MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.",
journal = "Chinese Physics B",
title = "Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules",
volume = "23",
number = "2",
doi = "10.1088/1674-1056/23/2/020504"
}

Zeković, S., Muniyappan, A., Zdravković, S.,& Kavitha, L.. (2014). Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules. in Chinese Physics B, 23(2).
https://doi.org/10.1088/1674-1056/23/2/020504

Zeković S, Muniyappan A, Zdravković S, Kavitha L. Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules. in Chinese Physics B. 2014;23(2).
doi:10.1088/1674-1056/23/2/020504 .

Zeković, Slobodan, Muniyappan, Annamalai, Zdravković, Slobodan, Kavitha, Louis, "Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules" in Chinese Physics B, 23, no. 2 (2014),
https://doi.org/10.1088/1674-1056/23/2/020504 . .

TY  - JOUR
AU  - Kavitha, L.
AU  - Muniyappan, A.
AU  - Prabhu, A.
AU  - Zdravković, Slobodan
AU  - Jayanthi, S.
AU  - Gopi, D.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5231
AB  - Non-linear localization phenomena in biological lattices have attracted a steadily growing interest and their existence has been predicted in a wide range of physical settings. We investigate the non-linear proton dynamics of a hydrogen-bonded chain in a semi-classical limit using the coherent state method combined with a Holstein-Primakoff bosonic representation. We demonstrate that even a weak inherent discreteness in the hydrogen-bonded (HB) chain may drastically modify the dynamics of the non-linear system, leading to instabilities that have no analog in the continuum limit. We suggest a possible localization mechanism of polarization oscillations of protons in a hydrogen-bonded chain through modulational instability analysis. This mechanism arises due to the neighboring proton-proton interaction and coherent tunneling of protons along hydrogen bonds and/or around heavy atoms. We present a detailed analysis of modulational instability, and highlight the role of the interaction strength of neighboring protons in the process of bioenergy localization. We perform molecular dynamics simulations and demonstrate the existence of nanoscale discrete breather (DB) modes in the hydrogen-bonded chain. These highly localized and long-lived non-linear breather modes may play a functional role in targeted energy transfer in biological systems.
T2  - Journal of Biological Physics
T1  - Nano breathers and molecular dynamics simulations in hydrogen-bonded chains
VL  - 39
IS  - 1
SP  - 15
EP  - 35
DO  - 10.1007/s10867-012-9283-7
ER  - 

@article{
author = "Kavitha, L. and Muniyappan, A. and Prabhu, A. and Zdravković, Slobodan and Jayanthi, S. and Gopi, D.",
year = "2013",
abstract = "Non-linear localization phenomena in biological lattices have attracted a steadily growing interest and their existence has been predicted in a wide range of physical settings. We investigate the non-linear proton dynamics of a hydrogen-bonded chain in a semi-classical limit using the coherent state method combined with a Holstein-Primakoff bosonic representation. We demonstrate that even a weak inherent discreteness in the hydrogen-bonded (HB) chain may drastically modify the dynamics of the non-linear system, leading to instabilities that have no analog in the continuum limit. We suggest a possible localization mechanism of polarization oscillations of protons in a hydrogen-bonded chain through modulational instability analysis. This mechanism arises due to the neighboring proton-proton interaction and coherent tunneling of protons along hydrogen bonds and/or around heavy atoms. We present a detailed analysis of modulational instability, and highlight the role of the interaction strength of neighboring protons in the process of bioenergy localization. We perform molecular dynamics simulations and demonstrate the existence of nanoscale discrete breather (DB) modes in the hydrogen-bonded chain. These highly localized and long-lived non-linear breather modes may play a functional role in targeted energy transfer in biological systems.",
journal = "Journal of Biological Physics",
title = "Nano breathers and molecular dynamics simulations in hydrogen-bonded chains",
volume = "39",
number = "1",
pages = "15-35",
doi = "10.1007/s10867-012-9283-7"
}

Kavitha, L., Muniyappan, A., Prabhu, A., Zdravković, S., Jayanthi, S.,& Gopi, D.. (2013). Nano breathers and molecular dynamics simulations in hydrogen-bonded chains. in Journal of Biological Physics, 39(1), 15-35.
https://doi.org/10.1007/s10867-012-9283-7

Kavitha L, Muniyappan A, Prabhu A, Zdravković S, Jayanthi S, Gopi D. Nano breathers and molecular dynamics simulations in hydrogen-bonded chains. in Journal of Biological Physics. 2013;39(1):15-35.
doi:10.1007/s10867-012-9283-7 .

Kavitha, L., Muniyappan, A., Prabhu, A., Zdravković, Slobodan, Jayanthi, S., Gopi, D., "Nano breathers and molecular dynamics simulations in hydrogen-bonded chains" in Journal of Biological Physics, 39, no. 1 (2013):15-35,
https://doi.org/10.1007/s10867-012-9283-7 . .