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Description

Theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Energy models, from classical potentials to first-principles approaches. Density-functional theory and the total-energy pseudopotential method. Errors and accuracy of quantitative predictions. Thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations. Free energies and phase transitions. Fluctuations and transport properties. Coarse-graining approaches and mesoscale models. Theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Energy models, from classical potentials to first-principles approaches. Density-functional theory and the total-energy pseudopotential method. Errors and accuracy of quantitative predictions. Thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations. Free energies and phase transitions. Fluctuations and transport properties. Coarse-graining approaches and mesoscale models.Subjects

atomistic computer simulations | atomistic computer simulations | Density-functional theory | Density-functional theory | total-energy pseudopotential method | total-energy pseudopotential method | Thermodynamic ensembles | Thermodynamic ensembles | Monte Carlo sampling | Monte Carlo sampling | molecular dynamics simulations | molecular dynamics simulations | Free energies | Free energies | phase transitions | phase transitions | Coarse-graining approaches | Coarse-graining approaches | mesoscale models | mesoscale modelsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course uses the theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Specific topics include: energy models from classical potentials to first-principles approaches; density functional theory and the total-energy pseudopotential method; errors and accuracy of quantitative predictions: thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations; free energy and phase transitions; fluctuations and transport properties; and coarse-graining approaches and mesoscale models. The course employs case studies from industrial applications of advanced materials to nanotechnology. Several laboratories will give students direct experience with simulations of classical force fields, electronic-structure app This course uses the theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Specific topics include: energy models from classical potentials to first-principles approaches; density functional theory and the total-energy pseudopotential method; errors and accuracy of quantitative predictions: thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations; free energy and phase transitions; fluctuations and transport properties; and coarse-graining approaches and mesoscale models. The course employs case studies from industrial applications of advanced materials to nanotechnology. Several laboratories will give students direct experience with simulations of classical force fields, electronic-structure appSubjects

simulation | simulation | computer simulation | computer simulation | atomistic computer simulations | atomistic computer simulations | Density-functional theory | Density-functional theory | DFT | DFT | Hartree-Fock | Hartree-Fock | total-energy pseudopotential | total-energy pseudopotential | thermodynamics | thermodynamics | thermodynamic ensembles | thermodynamic ensembles | quantum mechanics | quantum mechanics | first-principles | first-principles | Monte Carlo sampling | Monte Carlo sampling | molecular dynamics | molecular dynamics | finite temperature | finite temperature | Free energies | Free energies | phase transitions | phase transitions | Coarse-graining | Coarse-graining | mesoscale model | mesoscale model | nanotube | nanotube | alloy | alloyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata3.20 Materials at Equilibrium (SMA 5111) (MIT) 3.20 Materials at Equilibrium (SMA 5111) (MIT)

Description

Material covered in this course includes the following topics: Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams Computation of phase diagrams Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions Applications to phase stability and properties of mixtures Computational modeling Interfaces This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5111 (Materials at Equilibrium). Material covered in this course includes the following topics: Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams Computation of phase diagrams Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions Applications to phase stability and properties of mixtures Computational modeling Interfaces This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5111 (Materials at Equilibrium).Subjects

thermodynamics | thermodynamics | mechanical | mechanical | electromagnetic and electrochemical systems | electromagnetic and electrochemical systems | phase diagrams | phase diagrams | Statistical thermodynamics | Statistical thermodynamics | microscopic and macroscopic properties | microscopic and macroscopic properties | ensembles | ensembles | gases | gases | crystal lattices | crystal lattices | phase transitions | phase transitions | phase stability | phase stability | properties of mixtures | properties of mixtures | Computational modeling | Computational modeling | Interfaces | Interfaces | mechanical | electromagnetic and electrochemical systems | mechanical | electromagnetic and electrochemical systems | Computational modeling; Interfaces | Computational modeling; Interfaces | mechanical systems | mechanical systems | electromagnetic systems | electromagnetic systems | electrochemical systems | electrochemical systems | laws of thermodynamics | laws of thermodynamics | solutions | solutions | microscopic properties | microscopic properties | macroscopic properties | macroscopic propertiesLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course discusses phase transitions in Earth's interior. Phase transitions in Earth materials at high pressures and temperatures cause the seismic discontinuities and affect the convections in the Earth's interior. On the other hand, they enable us to constrain temperature and chemical compositions in the Earth's interior. However, among many known phase transitions in mineral physics, only a few have been investigated in seismology and geodynamics. This course reviews important papers about phase transitions in mantle and core materials. This course discusses phase transitions in Earth's interior. Phase transitions in Earth materials at high pressures and temperatures cause the seismic discontinuities and affect the convections in the Earth's interior. On the other hand, they enable us to constrain temperature and chemical compositions in the Earth's interior. However, among many known phase transitions in mineral physics, only a few have been investigated in seismology and geodynamics. This course reviews important papers about phase transitions in mantle and core materials.Subjects

Earth | Earth | mantle | mantle | phase transitions | phase transitions | transition zone | transition zone | post-spinel transition | post-spinel transition | seismic discontinuities | seismic discontinuities | D'' discontinuity | D'' discontinuity | D'' anisotropy | D'' anisotropy | post-perovskite transition and spin transition | post-perovskite transition and spin transitionLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata14.15J Networks (MIT) 14.15J Networks (MIT)

Description

Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form a Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form aSubjects

networks | networks | crowds | crowds | markets | markets | highly connected world | highly connected world | social networks | social networks | economic networks | economic networks | power networks | power networks | communication networks | communication networks | game theory | game theory | graph theory | graph theory | branching processes | branching processes | random graph models | random graph models | rich get richer phenomena | rich get richer phenomena | power laws | power laws | small worlds | small worlds | Erd?s-Renyi graphs | Erd?s-Renyi graphs | degree distributions | degree distributions | phase transitions | phase transitions | connectedness | connectedness | and giant component | and giant component | link analysis | link analysis | web search | web search | navigation | navigation | decentralized search | decentralized search | preferential attachment | preferential attachment | epidemics | epidemics | diffusion through networks | diffusion through networks | SIR | SIR | (susceptible | (susceptible | infected | infected | removed) | removed) | SIS | SIS | susceptible) | susceptible) | strategies | strategies | payoffs | payoffs | normal forms | normal forms | Nash equilibrium | Nash equilibrium | traffic networks | traffic networks | negative externalities | negative externalities | Braess' paradox | Braess' paradox | potential games | potential games | myopic behavior | myopic behavior | fictitious play | fictitious play | repeated games | repeated games | prisoner's dilemma | prisoner's dilemma | cooperation | cooperation | perfect information | perfect information | imperfect information | imperfect information | positive externalities | positive externalities | strategic complements | strategic complements | path dependence | path dependence | diffusion of innovation | diffusion of innovation | contagion pheonomena | contagion pheonomena | Bayes's rule | Bayes's rule | Bayesian Nash equilibrium | Bayesian Nash equilibrium | first price auctions | first price auctions | second price auctions | second price auctions | social learning | social learning | Bayesian learning | Bayesian learning | copying | copying | herding | herding | herd behavior | herd behavior | informational cascades | informational cascades | decisions | decisions | social choice | social choice | Condorcet jury theorem | Condorcet jury theorem | political economy | political economyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata3.20 Materials at Equilibrium (SMA 5111) (MIT)

Description

Material covered in this course includes the following topics: Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams Computation of phase diagrams Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions Applications to phase stability and properties of mixtures Computational modeling Interfaces This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5111 (Materials at Equilibrium).Subjects

thermodynamics | mechanical | electromagnetic and electrochemical systems | phase diagrams | Statistical thermodynamics | microscopic and macroscopic properties | ensembles | gases | crystal lattices | phase transitions | phase stability | properties of mixtures | Computational modeling | Interfaces | mechanical | electromagnetic and electrochemical systems | Computational modeling; Interfaces | mechanical systems | electromagnetic systems | electrochemical systems | laws of thermodynamics | solutions | microscopic properties | macroscopic propertiesLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata3.320 Atomistic Computer Modeling of Materials (MIT)

Description

Theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Energy models, from classical potentials to first-principles approaches. Density-functional theory and the total-energy pseudopotential method. Errors and accuracy of quantitative predictions. Thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations. Free energies and phase transitions. Fluctuations and transport properties. Coarse-graining approaches and mesoscale models.Subjects

atomistic computer simulations | Density-functional theory | total-energy pseudopotential method | Thermodynamic ensembles | Monte Carlo sampling | molecular dynamics simulations | Free energies | phase transitions | Coarse-graining approaches | mesoscale modelsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form aSubjects

networks | crowds | markets | highly connected world | social networks | economic networks | power networks | communication networks | game theory | graph theory | branching processes | random graph models | rich get richer phenomena | power laws | small worlds | Erd?s-Renyi graphs | degree distributions | phase transitions | connectedness | and giant component | link analysis | web search | navigation | decentralized search | preferential attachment | epidemics | diffusion through networks | SIR | (susceptible | infected | removed) | SIS | susceptible) | strategies | payoffs | normal forms | Nash equilibrium | traffic networks | negative externalities | Braess' paradox | potential games | myopic behavior | fictitious play | repeated games | prisoner's dilemma | cooperation | perfect information | imperfect information | positive externalities | strategic complements | path dependence | diffusion of innovation | contagion pheonomena | Bayes's rule | Bayesian Nash equilibrium | first price auctions | second price auctions | social learning | Bayesian learning | copying | herding | herd behavior | informational cascades | decisions | social choice | Condorcet jury theorem | political economyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata3.320 Atomistic Computer Modeling of Materials (SMA 5107) (MIT)

Description

This course uses the theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Specific topics include: energy models from classical potentials to first-principles approaches; density functional theory and the total-energy pseudopotential method; errors and accuracy of quantitative predictions: thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations; free energy and phase transitions; fluctuations and transport properties; and coarse-graining approaches and mesoscale models. The course employs case studies from industrial applications of advanced materials to nanotechnology. Several laboratories will give students direct experience with simulations of classical force fields, electronic-structure appSubjects

simulation | computer simulation | atomistic computer simulations | Density-functional theory | DFT | Hartree-Fock | total-energy pseudopotential | thermodynamics | thermodynamic ensembles | quantum mechanics | first-principles | Monte Carlo sampling | molecular dynamics | finite temperature | Free energies | phase transitions | Coarse-graining | mesoscale model | nanotube | alloyLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata12.581 Phase Transitions in the Earth's Interior (MIT)

Description

This course discusses phase transitions in Earth's interior. Phase transitions in Earth materials at high pressures and temperatures cause the seismic discontinuities and affect the convections in the Earth's interior. On the other hand, they enable us to constrain temperature and chemical compositions in the Earth's interior. However, among many known phase transitions in mineral physics, only a few have been investigated in seismology and geodynamics. This course reviews important papers about phase transitions in mantle and core materials.Subjects

Earth | mantle | phase transitions | transition zone | post-spinel transition | seismic discontinuities | D'' discontinuity | D'' anisotropy | post-perovskite transition and spin transitionLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata3.20 Materials at Equilibrium (SMA 5111) (MIT)

Description

Material covered in this course includes the following topics: Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams Computation of phase diagrams Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions Applications to phase stability and properties of mixtures Computational modeling Interfaces This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5111 (Materials at Equilibrium).Subjects

thermodynamics | mechanical | electromagnetic and electrochemical systems | phase diagrams | Statistical thermodynamics | microscopic and macroscopic properties | ensembles | gases | crystal lattices | phase transitions | phase stability | properties of mixtures | Computational modeling | Interfaces | mechanical | electromagnetic and electrochemical systems | Computational modeling; Interfaces | mechanical systems | electromagnetic systems | electrochemical systems | laws of thermodynamics | solutions | microscopic properties | macroscopic propertiesLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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