Symplectic quaternion scheme for biophysical molecular dynamics

Keywords

Quaternion, Integrator, Symplectic geometry, Hamiltonian (control theory), Symplectic integrator

References

• On the classical statistical mechanics of non-Hamiltonian systemsMark E. Tuckerman, Christopher J. Mundy, Glenn Martyna — 1999
• Reversible molecular dynamics for rigid bodies and hybrid Monte CarloNobuyuki Matubayasi, Masaru Nakahara — 1999
• Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculationsHans Christian Andersen — 1983
• On the representatation of orientation spaceDenis J. Evans — 1977
• On the product of semi-groups of operatorsH. F. Trotter — 1959
• A symplectic method for rigid-body molecular simulationAyla Kol, Brian B. Laird, Benedict Leimkuhler — 1997
• Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-range InteractionsHelmut Grubmüller, Helmut Heller, Andreas Windemuth — 1991
• Non-Hamiltonian molecular dynamics: Generalizing Hamiltonian phase space principles to non-Hamiltonian systemsMark E. Tuckerman, Yi Liu, Giovanni Ciccotti — 2001
• Symplectic Numerical Integrators in Constrained Hamiltonian SystemsBenedict Leimkuhler, Robert D. Skeel — 1994
• Reversible multiple time scale molecular dynamicsMark E. Tuckerman, B. J. Berne, Glenn Martyna — 1992
• Thermodynamic Properties of the Williams, OPLS-AA, and MMFF94 All-Atom Force Fields for Normal AlkanesBin Chen, Marcus G. Martin, J. Ilja Siepmann — 1998
• Blue Gene: A vision for protein science using a petaflop supercomputerFrances Allen, George Almási, Wanda Andreoni — 2001
• Understanding Modern Molecular Dynamics: Techniques and ApplicationsMark E. Tuckerman, Glenn Martyna — 2000
• All-atom empirical potential for molecular modeling and dynamics studies of proteins.Alexander D. MacKerell, Donald Bashford, M. Bellott — 1998
• Exploiting multiple levels of parallelism in Molecular Dynamics based calculations via modern techniques and software paradigms on distributed memory computersMark E. Tuckerman, Dawn A. Yarne, Shane O. Samuelson — 2000
• Computer Simulation of LiquidsMichael P. Allen, Dominic J. Tildesley — 1988
• Higher-order hybrid Monte Carlo algorithms.Michael Creutz, Andreas Gocksch — 1989
• Modern geometry--methods and applicationsBoris Dubrovin, A. T. Fomenko, S. P. Novikov — 1984
• Exponential Operators and Parameter Differentiation in Quantum PhysicsR. M. Wilcox — 1967
• Symplectic splitting methods for rigid body molecular dynamicsAndreas Dullweber, Benedict Leimkuhler, Robert I. McLachlan — 1997

Cited by

• Explicit symplectic integrators of molecular dynamics algorithms for rigid-body molecules in the canonical, isobaric-isothermal, and related ensembles.Чипига Александр Федорович — 2007
• Ice Ih-Water Interfacial Free Energy of Simple Water Models with Full Electrostatic Interactions.Joaquín María García de Dios — 2012
• Calculating ice–water interfacial free energy by molecular simulationRichard W. Handel — 2009
• Self assembly problems of anisotropic particles in soft matterS. Glotzer, C. L. Phillips — 2012
• Explicit, Multi-Map Symplectic Integrator for Three -Body Classical Trajectory Studies in Hyperspherical CoordinatesPaul Burkhardt — 2004
• A new force field for H2S and its binary and ternary mixtures with CO2 and CH4Andrew N. Owen, Caroline Desgranges, Jérôme Delhommelle — 2015
• A technique for calculating particle systems containing rigid and soft partsNima Nouri, Saeed Ziaei‐Rad — 2015
• Comparison of Replica-Permutation Molecular Dynamics Simulations with and without Detailed Balance ConditionHiroaki Nishizawa, Hisashi Okumura — 2015
• Elements of naturality in dynamical simulation frameworks for Hamiltonian, thermostatic, and Lindbladian ows on classical and quantum state-spacesJohn A. Sidles, Joseph L. Garbini, Jonathan Jacky — 2010
• Development of accurate and efficient models for biological moleculesJohnny C. Wu — 2011
• Investigating water and framework dynamics in pillared MOFsNicholas C. Burtch, David Dubbeldam, Krista S. Walton — 2015
• Coarse-Grained Modelling of DNA and DNA Self-AssemblyThomas E. Ouldridge — 2012
• Field response and switching times in biaxial nematics.Roberto Berardi, Luca Muccioli, Claudio Zannoni — 2008
• Molecular dynamics simulation of quasi-two-dimensional water clusters on ice nucleation protein.Daisuke Murakami, Kenji Yasuoka — 2012
• Ring polymer dynamics in curved spaces.Sarah Wolf, E. Curotto — 2012
• Semiquantal molecular dynamics simulations of hydrogen-bond dynamics in liquid water using multi-dimensional Gaussian wave packets.Junichi Ono, Koji Ando — 2012
• Time reversible and symplectic integrators for molecular dynamics simulations of rigid molecules.Hiqmet Kamberaj, Robert J. Low, Maureen P. Neal — 2005
• Numerical implementation of the exact dynamics of free rigid bodiesRamses van Zon, Jeremy Schofield — 2006
• Substrate directed self-assembly of anisotropic nanoparticlesTarak K. Patra, Parul Katiyar, Jayant K. Singh — 2015
• Predictive supracolloidal helices from patchy particlesRuohai Guo, Jian Mao, Xu‐Ming Xie — 2014

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