Dynamical models of molecular chains and efficient integration algorithms
Chains of point masses and chains of rigid bodies are used to model biological polymers. To investigate their dynamics we propose a method which allows an efficient realization of the constraints jointly with a simple and accurate integration of the free rigid body motion. The method is quite effect...
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| Vydáno v: | Communications in nonlinear science & numerical simulation Ročník 14; číslo 2; s. 593 - 612 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.02.2009
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| ISSN: | 1007-5704, 1878-7274 |
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| Abstract | Chains of point masses and chains of rigid bodies are used to model biological polymers. To investigate their dynamics we propose a method which allows an efficient realization of the constraints jointly with a simple and accurate integration of the free rigid body motion. The method is quite effective to evolute the geodesic flow of a rigid body chain and the global performance depends on the computational complexity of the algorithms used to compute the interaction forces. Our approach is suitable to describe a chain of rigid bodies immersed in a thermal bath. In the method we propose, the constraints are realized by hard springs whose elastic constant is set to maximize the energy dissipation rate of a Runge–Kutta integrator scheme. Moreover the use of local Lagrangian coordinates is introduced using the possibility of a continuous change of chart, such that the distance from the coordinate singularities is the highest possible. For a chain of point masses the numerical results are checked with another method where the constraints are exactly realized by means of Lagrangian coordinates. When the chain is subject to regular interactions potentials plus a thermal bath the exact and approximate constraints realization provide comparable results. |
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| AbstractList | Chains of point masses and chains of rigid bodies are used to model biological polymers. To investigate their dynamics we propose a method which allows an efficient realization of the constraints jointly with a simple and accurate integration of the free rigid body motion. The method is quite effective to evolute the geodesic flow of a rigid body chain and the global performance depends on the computational complexity of the algorithms used to compute the interaction forces. Our approach is suitable to describe a chain of rigid bodies immersed in a thermal bath. In the method we propose, the constraints are realized by hard springs whose elastic constant is set to maximize the energy dissipation rate of a Runge-Kutta integrator scheme. Moreover the use of local Lagrangian coordinates is introduced using the possibility of a continuous change of chart, such that the distance from the coordinate singularities is the highest possible. For a chain of point masses the numerical results are checked with another method where the constraints are exactly realized by means of Lagrangian coordinates. When the chain is subject to regular interactions potentials plus a thermal bath the exact and approximate constraints realization provide comparable results. |
| Author | Rambaldi, Sandro Turchetti, Giorgio Bazzani, Armando Benedetti, Carlo Rossi, Luca |
| Author_xml | – sequence: 1 givenname: Armando surname: Bazzani fullname: Bazzani, Armando organization: Centro Interdipartimentale Galvani, Università di Bologna, Italy – sequence: 2 givenname: Carlo surname: Benedetti fullname: Benedetti, Carlo email: benedetti@bo.infn.it organization: Dipartimento di Fisica, Università di Bologna, Via Irnerio 46, 40126, Bologna, Italy – sequence: 3 givenname: Sandro surname: Rambaldi fullname: Rambaldi, Sandro organization: Centro Interdipartimentale Galvani, Università di Bologna, Italy – sequence: 4 givenname: Luca surname: Rossi fullname: Rossi, Luca organization: Dipartimento di Fisica, Università di Bologna, Via Irnerio 46, 40126, Bologna, Italy – sequence: 5 givenname: Giorgio surname: Turchetti fullname: Turchetti, Giorgio organization: Centro Interdipartimentale Galvani, Università di Bologna, Italy |
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| Cites_doi | 10.1002/(SICI)1096-987X(199709)18:12<1463::AID-JCC4>3.0.CO;2-H 10.1002/(SICI)1096-987X(19980115)19:1<102::AID-JCC9>3.0.CO;2-T 10.1103/PhysRevE.48.1469 10.1126/science.282.5389.740 10.1146/annurev.physchem.48.1.545 10.1103/RevModPhys.75.23 10.1016/j.plrev.2004.03.001 10.1073/pnas.87.9.3526 10.1039/b605744f 10.1007/s10569-006-9037-6 10.1103/RevModPhys.72.259 |
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| Snippet | Chains of point masses and chains of rigid bodies are used to model biological polymers. To investigate their dynamics we propose a method which allows an... |
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| SubjectTerms | Algorithms Biological Computer simulation Flipping rule Hard springs Mathematical models Molecular chains Nonlinear dynamics Rigid-body dynamics Rigidity constraints Runge-Kutta method Runge–Kutta Thermal baths |
| Title | Dynamical models of molecular chains and efficient integration algorithms |
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