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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 13: Continue reading Chapter 6 Modern example of analysis using Lagrangian and Hamiltonian formalisms. Lagrangian picture. Hamiltonian picture. J. Chem. Physics 72 2384-2393 (1980).

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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

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  1. PHY 711 Classical Mechanics and Mathematical Methods • 10-10:50 AM MWF Olin 103 • Plan for Lecture 13: • Continue reading Chapter 6 • Modern example of analysis using Lagrangian and Hamiltonian formalisms PHY 711 Fall 2012 -- Lecture 12

  2. PHY 711 Fall 2012 -- Lecture 12

  3. PHY 113 A Fall 2012 -- Lecture 12

  4. PHY 113 A Fall 2012 -- Lecture 12

  5. PHY 113 A Fall 2012 -- Lecture 12

  6. Lagrangian picture Hamiltonian picture PHY 711 Fall 2012 -- Lecture 12

  7. J. Chem. Physics 72 2384-2393 (1980) PHY 711 Fall 2012 -- Lecture 12

  8. “Molecular dynamics” is a subfield of computational physics focused on analyzing the motions of atoms in fluids and solids with the goal of relating the atomistic and macroscopic properties of materials. Ideally molecular dynamics calculations can numerically realize the statistical mechanics viewpoint. PHY 711 Fall 2012 -- Lecture 12

  9. rij From this Lagrangian, can find the 3N coupled 2nd order differential equations of motion and/or find the corresponding Hamiltonian, representing the system at constant energy, volume, and particle number N (N,V,E ensemble). PHY 711 Fall 2012 -- Lecture 12

  10. PHY 711 Fall 2012 -- Lecture 12

  11. H. C. Andersen wanted to adapt the formalism for modeling an (N,V,E) ensemble to one which could model a system at constant pressure (P). P V constant P constant, V variable PHY 711 Fall 2012 -- Lecture 12

  12. PV contribution to potential energy kinetic energy of “balloon” PHY 711 Fall 2012 -- Lecture 12

  13. PHY 711 Fall 2012 -- Lecture 12

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