Non-equilibrium by molecular dynamics: a dynamical approach

References

• Metropolis N, Rosenbluth AW, Rosenbluth MN, et al. Equation of state calculations by fast computing machines. J. Chem. Phys. 1953;21:1087–1092.
   Web of Science ®Google Scholar
• Wood WW, Parker FR. Monte Carlo equation of state of molecules interacting with the Lennard-Jones potential. I. J. Chem. Phys. 1957;27:720–733.
   Web of Science ®Google Scholar
• Alder BJ, Wainwright TE. Phase transition for a hard sphere system. J. Chem. Phys. 1957;27:1208–1209.
   Web of Science ®Google Scholar
• Rahman A. Correlations in the motion of atoms in liquid argon. Phys. Rev. 1964;136:A405–A411.
   Web of Science ®Google Scholar
• Levesque D, Verlet L. Computer ‘Experiments’ on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 1967;159:98–103.
   Web of Science ®Google Scholar
• Van Hove L. Correlations in space and time and born approximation scattering in systems of interacting particles. Phys. Rev. 1954;95:249–262.
   Web of Science ®Google Scholar
• Onsager L. Reciprocal relations in irreversible processes. I. Phys. Rev. 1931;37:405–426.
   Google Scholar
• Kubo R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 1957;12:570–586.
   Google Scholar
• Alder BJ, Gass DM, Wainwright TE. Studies in molecular dynamics VIII. The transport coefficients for a hard-sphere fluid. J. Chem. Phys. 1970;53:3813–3826.
   Web of Science ®Google Scholar
• Levesque D, Verlet L. Computer ‘Experiments’ on classical fluids. III. time-dependent self-correlation functions. Phys. Rev. A. 1970;2:2514–2528.
   Web of Science ®Google Scholar
• Levesque D, Kürkijarvi J, Verlet L. Computer ‘Experiments’ on classical fluids. IV. Transport properties and time-correlation functions of the Lennard-Jones liquid near its triple point. Phys. Rev. A. 1970;2:2514–2528.
   Web of Science ®Google Scholar
• Kadanoff LP, Martin PC. Hydrodynamic equations and correlation functions. Ann. Phys. 1963;24:419–469.
   Web of Science ®Google Scholar
• Zwanzig R. Time-correlation functions and transport coefficients in Statistical Mechanics. Annual Rev. Phys. Chem. 1965;16:67–102.
   Web of Science ®Google Scholar
• Kubo R. The fluctuation-dissipation theorem. Rep. Prog. Phys. 1966;29:255–284.
   Web of Science ®Google Scholar
• Ciccotti G, Jacucci G. Direct computation of dynamical response by molecular dynamics: the mobility of a charged Lennard-Jones particle. Phys. Rev. Lett. 1975;35:789–792.
   Web of Science ®Google Scholar
• Ciccotti G, Jacucci G, McDonald IR. Transport properties of molten alkali halides. Phys. Rev. A. 1976;13:426–436.
   Web of Science ®Google Scholar
• Ciccotti G, Jacucci G, McDonald IR. Thermal response to a weak external field. J. Phys. C. 1978;11:L509–L513.
   Web of Science ®Google Scholar
• Ciccotti G, Jacucci G, McDonald IR. ‘Thought-experiments’ by molecular dynamics. J. Stat. Phys. 1979;21:1–22.
   Web of Science ®Google Scholar
• Chandler D. Statistical mechanics of isomerization dynamics in liquids and the transition state approximation. J. Chem. Phys. 1978;68:2959–2970.
   Web of Science ®Google Scholar
• Carter EA, Ciccotti G, Hynes JT, et al. Constrained reaction coordinate dynamics for the simulation of rare events. Chem. Phys. Lett. 1989;156:472–477.
   Web of Science ®Google Scholar
• Ciccotti G, Ferrario M, Hynes JT, et al. Dynamics of ion pair interconversion in a polar solvent. J. Chem. Phys. 1990;93:7137–7147.
   Web of Science ®Google Scholar
• Ciccotti G, Kapral R, Sergi A. Non-equilibrium molecular dynamics. In: Yip S,editor. Handbook of materials modeling. Vol. I, Methods and model. Berlin Heidelberg: Springer; 2005. p. 1–17.
   Google Scholar
• Hartmann C, Schütte C, Ciccotti G. On the linear response of mechanical systems with constraints. J. Chem. Phys. 2010;132:111103.
   PubMed Web of Science ®Google Scholar
• Mountain RD. Spectral distribution of scattered light in a simple fluid. Rev. Modern Phys. 1966;38:205–214.
   Google Scholar
• Alder BJ, Wainwright TE. Decay of the velocity autocorrelation function. Phys Rev. A. 1970;1:18–21.
   Web of Science ®Google Scholar
• Mugnai ML, Caprara S, Ciccotti G, et al. Transient hydrodynamical behavior by dynamical nonequilibrium molecular dynamics: The formation of convective cells. J. Chem. Phys. 2009;131:064106.
   Web of Science ®Google Scholar
• Orlandini S, Meloni S, Ciccotti G. Hydrodynamics from Statistical Mechanics: combined dynamical-NEMD and conditional sampling to relax an interface between two immiscible liquids. Phys. Chem. Chem. Phys. 2011;13:13177–13181.
   PubMed Web of Science ®Google Scholar
• Pourali M, Meloni S, Magaletti F, et al. Relaxation of a steep density gradient in a simple fluid: Comparison between atomistic and continuum modeling. J. Chem. Phys. 2014;141:154107.
   PubMed Web of Science ®Google Scholar
• Ryckaert JP, Ciccotti G, Berendsen HJC. Numerical integration of the Cartesian equation of motion of a system with constraints: molecular dynamics of N-alkanes. J. Comput. Phys. 1977;23:327–341.
   Web of Science ®Google Scholar
• Goldstein H, Poole C, Safko J. Classical mechanics. 3rd ed. Boston (MA): Addison-Wesley; 2001.
   Google Scholar
• Andersen HC. Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 1980;72:2384–2393.
   Web of Science ®Google Scholar
• Nose S. Constant temperature molecular-dynamics methods. Prog. Theor. Phys. Suppl. 1991;103:1–46.
   Google Scholar
• Tuckerman ME, Liu Y, Ciccotti G, et al. Non-Hamiltonian molecular dynamics: generalizing Hamiltonian phase space principles to non-Hamiltonian systems. J. Chem. Phys. 2001;115:1678–1702.
   Web of Science ®Google Scholar
• Ciccotti G, Ferrario M. Dynamical non-equilibrium molecular dynamics. Entropy. 2014;16:233–257.
   Web of Science ®Google Scholar
• Tuckerman ME, Mundy CJ, Martyna GJ. Nosé-Hoover chains: the canonical ensemble via continuous dynamics. J. Chem. Phys. 1992;97:2635–2643.
   Web of Science ®Google Scholar
• Ciccotti G. Molecular dynamics simulation of non equilibrium phenomena and rare dynamical events. In: Meyer M, Pontikis V,editors. Computer simulation in material science. NATO ASI series E, applied sciences. Dordrecht: Kluwer Academic Publishers; 1991. p. 119–137.
   Google Scholar
• Jackson JL, Mazur P. On the statistical mechanics derivation of the correlation formula for the viscosity. Physica. 1964;30:2295–2304.
   Google Scholar
• Luttinger JM. Theory of thermal transport coefficients. Phys. Rev. 1964;135:A1505–A1514.
   Google Scholar
• Maragliano L, Fischer A, Vanden-Eijnden E, et al. String method in collective variables: minimum free energy paths and isocommittor surfaces. J. Chem. Phys. 2006;125:024106.
   PubMed Web of Science ®Google Scholar
• Tenenbaum A, Ciccotti G, Gallico R. Stationary nonequilibrium states by molecular dynamics. Fourier’s law. Phys. Rev. A. 1982;25:2778–2787.
   Web of Science ®Google Scholar
• Massobrio C, Ciccotti G. Lennard-Jones triple-point conductivity via weak external fields. Phys. Rev. A. 1984;30:3191–3197.
   Web of Science ®Google Scholar
• Bellemans A, Ryckaert JP, Ciccotti G, et al. The shear rate dependence of the viscosity of simple fluids by molecular dynamics. Phys. Rev. Lett. 1988;60:128–131.
   PubMed Web of Science ®Google Scholar
• Ciccotti G, Pierleoni C, Ryckaert JP. Theoretical foundation and rheological application of non-equilibrium molecular dynamics. In: Mareschal M, Holian BL, editors. Microscopic simulation of complex hydrodynamics phenomena. New York (NY): Plenum Press; 1992. p. 25–45.
   Google Scholar
• Paolini GV, Ciccotti G, Massobrio C. Non-linear thermal response of a LJ fluid near its triple point. Phys. Rev. A. 1986;34:1355–1362.
   Web of Science ®Google Scholar
• Palla PL, Pierleoni C, Ciccotti G. Bulk viscosity of the Lennard-Jones system at the triple point by dynamical nonequilibrium molecular dynamics. Phys. Rev. E. 2008;78:021204.
   Web of Science ®Google Scholar
• Erpenbeck JJ, Wood WW. Molecular dynamics calculations of shear viscosity time-correlation functions for hard spheres. J. Stat. Phys. 1981;24:455–468.
   Web of Science ®Google Scholar
• Marchio S. Confronto di meccanismi di interdiffusione binaria: simulazione atomistica vs. continuo [A comparison of interdiffusion mechanisms in binary systems: atomistic vs continuum simulations] [Master’s thesis]. Rome: Università di Roma- Sapienza; 2015.
   Google Scholar
• Hoover WG, Ashurst WT. Nonequilibrium molecular dynamics. In: Eyring H, Henderson D, editors. Theoretical chemistry: advances and perspectives. New York (NY): Academic Press; 1975. p. 1–51.
   Google Scholar
• Ashurst WT, Hoover WG. Dense-fluid shear viscosity via nonequilibrium molecular dynamics. Phys. Rev. A. 1975;11:658–678.
   Web of Science ®Google Scholar
• Evans DJ, Morris GP. Statistical mechanics of nonequilibrium liquids. 2nd ed. Camberra: ANU E Press; 2007.
   Google Scholar
• Singer K, Singer JV, Fincham D. Determination of the shear viscosity of atomic liquids by nonequilibrium molecular dynamics molecular-dynamics study. Mol. Phys. 1980;40:515–519.
   Web of Science ®Google Scholar
• Allen MP, Kivelson D. Non equilibrium molecular dynamics simulation and generalised hydrodynamics of transverse modes in molecular fluids. Mol. Phys. 1981;44:945–965.
   Web of Science ®Google Scholar
• Heyes DM. Self-diffusion and shear viscosity of simple fluids. A molecular-dynamics study. J. Chem. Soc., Faraday Trans. 1983;2:1741–1758.
   Google Scholar
• Hoover WG, Ciccotti G, Paolini GV, et al. Lennard-Jones triple-point conductivity via weak external fields: additional calculations. Phys. Rev. A. 1985;32:3765–3767.
   Web of Science ®Google Scholar
• Paolini GV, Ciccotti G. Cross thermotransport in liquid mixtures by nonequilibrium molecular dynamics. Phys. Rev. A. 1987;35:5156–5166.
   PubMed Web of Science ®Google Scholar
• Pierleoni C, Ciccotti G, Bernu B. Thermal conductivity of the classical one-component plasma by non-equilibrium molecular-dynamics. Europhys. Lett. 1987;4:1115–1120.
   Google Scholar
• Morriss GP, Evans DJ. Application of transient correlation functions to shear flow far from equilibrium. Phys. Rev. A. 1987;35:792–797.
   PubMed Web of Science ®Google Scholar
• Gosling EM, McDonald IR, Singer K. On the calculation by molecular dynamics of the shear viscosity of a simple fluid. Mol. Phys. 1973;26:1475–1484.
   Web of Science ®Google Scholar
• Ferrario M, Ciccotti G, Holian BL, et al. Shear rate dependence of the viscosity of the Lennard-Jones liquid at the triple point. Phys. Rev. A. 1991;44:6936–6939.
   PubMed Web of Science ®Google Scholar
• Evans DJ, Morriss GP, Hood LM. On the number dependence of viscosity in three dimensional fluids. Mol. Phys. 1989;68:637–646.
   Web of Science ®Google Scholar
• Heyes DM. Shear thinning and thickening of the Lennard-Jones liquid. A molecular dynamics study. J. Chem. Soc., Faraday Trans. 1986;2(82):1365–1383.
   Google Scholar
• Eu BC. Shear-rate dependence of viscosity for simple fluids. Phys. Lett. A. 1983;96:29–32.
   Web of Science ®Google Scholar
• Ladd AJ. Equations of motion for non-equilibrium molecular dynamics simulations of viscous flow in molecular fluids. Mol. Phys. 1984;53:459–463.
   Web of Science ®Google Scholar
• Lees AW, Edwards F. The computer study of transport process under extreme conditions. J. Phys. C. 1972;5:1921–1929.
   Web of Science ®Google Scholar
• Evans DJ, Morris GP. Shear thickening and turbulence in simple fluids. Phys. Rev. Lett. 1986;56:2172–2175.
   PubMed Web of Science ®Google Scholar
• Pierleoni C, Ryckaert JP. Non-Newtonian viscosity of atomic fluids in shear and shear-free flows. Phys. Rev. A. 1991;44:5314–5317.
   PubMed Web of Science ®Google Scholar
• Ryckaert JP, Bellemans A, Ciccotti G, et al. Evaluation of transport coefficients of simple fluids by molecular dynamics: comparison of Green-Kubo and nonequilibrium approaches for shear viscosity. Phys. Rev A. 1988;39:259–267.
   Web of Science ®Google Scholar
• Hounkonnou MN, Pierleoni C, Ryckaert JP. Liquid chlorine in shear and elongational flows: a nonequilibrium molecular dynamics study. J. Chem. Phys. 1992;97:9335–9344.
   Web of Science ®Google Scholar
• Todd BD. Application of transient-time correlation functions to nonequilibrium molecular-dynamics simulations of elongational flow. Phys. Rev. E. 1997;56:6723–6728.
   Web of Science ®Google Scholar
• Todd BD. Nonlinear response theory for time-periodic elongational flows. Phys. Rev. E. 1998;58:4587–4593.
   Web of Science ®Google Scholar
• Ryckaert JP, Pierleoni C. Polymer solutions in flow: a non-equilibrium molecular dynamics approach. In: Nguyen T, Kausch HH, editors. Flexible polymer chains in elongational flow. Berlin Heidelberg: Springer; 1999. p. 5–40.
   Google Scholar
• Todd BD, Daivis PJ. Homogeneous non-equilibrium molecular dynamics simulations of viscous flow: techniques and applications. Mol. Simul. 2007;33:189–229.
   Web of Science ®Google Scholar
• Hunt TA, Todd BD. Diffusion of linear polymer melts in shear and extensional flows. J. Chem. Phys. 2009;131:054904.
   Web of Science ®Google Scholar
• Hartkamp R, Bernardi S, Todd BD. Transient-time correlation function applied to mixed shear and elongational flows. J. Chem. Phys. 2012;136:064105.
   Web of Science ®Google Scholar
• Kraynik A, Reinelt D. Extensional motions of spatially periodic lattices. Int. J. Multiphase Flow. 1992;18:1045–1059.
   Web of Science ®Google Scholar
• Hunt TA, Todd BD. On the Arnold cat map and periodic boundary conditions for planar elongational flow. Mol. Phys. 2003;101:3445–3454.
   Web of Science ®Google Scholar
• Adams DJ. Gran canonical ensemble Monte Carlo for a Lennard-Jones fluid. Mol. Phys. 1975;29:307–311.
   Web of Science ®Google Scholar
• Rowley LA, Nicholson D, Parsonage NG. Monte Carlo Grand canonical ensemble calculation in a gas-liquid transition region for 12–6 argon. J. Comp. Phys. 1975;17:401–414.
   Web of Science ®Google Scholar
• Frenkel D, Smit B. Understanding molecular simulation. From algorithms to applications. London: Academic Press; 1996.
   Google Scholar
• Irving JH, Kirkwood JG. The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 1950;18:817–829.
   Web of Science ®Google Scholar
• Torrie G, Valleau J. Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J. Comput. Phys. 1977;23:187–199.
   Web of Science ®Google Scholar
• Martyna GJ, Klein ML, Tuckerman ME. Nosé-Hoover chains: the canonical ensemble via continuous dynamics. J. Chem. Phys. 1992;97:2635–2643.
   Web of Science ®Google Scholar
• Weeks JD, Chandler D, Andersen HC. Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 1971;54:5237–5247.
   Web of Science ®Google Scholar
• Callen HB. Thermodynamics: an introduction to the physical theories of equilibrium thermostatics and irreversible thermodynamics. New York (NY): Wiley; 1960.
   Google Scholar