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18.327 Wavelets, Filter Banks and Applications (MIT) 18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications. Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | Discrete-time filters | convolution | convolution | Fourier transform | Fourier transform | owpass and highpass filters | owpass and highpass filters | Sampling rate change operations | Sampling rate change operations | upsampling and downsampling | upsampling and downsampling | ractional sampling | ractional sampling | interpolation | interpolation | Filter Banks | Filter Banks | time domain (Haar example) and frequency domain | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | conditions for alias cancellation and no distortion | perfect reconstruction | perfect reconstruction | halfband filters and possible factorizations | halfband filters and possible factorizations | Modulation and polyphase representations | Modulation and polyphase representations | Noble identities | Noble identities | block Toeplitz matrices and block z-transforms | block Toeplitz matrices and block z-transforms | polyphase examples | polyphase examples | Matlab wavelet toolbox | Matlab wavelet toolbox | Orthogonal filter banks | Orthogonal filter banks | paraunitary matrices | paraunitary matrices | orthogonality condition (Condition O) in the time domain | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | modulation domain and polyphase domain | Maxflat filters | Maxflat filters | Daubechies and Meyer formulas | Daubechies and Meyer formulas | Spectral factorization | Spectral factorization | Multiresolution Analysis (MRA) | Multiresolution Analysis (MRA) | requirements for MRA | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | Refinement equation | iterative and recursive solution techniques | iterative and recursive solution techniques | infinite product formula | infinite product formula | filter bank approach for computing scaling functions and wavelets | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | Orthogonal wavelet bases | connection to orthogonal filters | connection to orthogonal filters | orthogonality in the frequency domain | orthogonality in the frequency domain | Biorthogonal wavelet bases | Biorthogonal wavelet bases | Mallat pyramid algorithm | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | Accuracy of wavelet approximations (Condition A) | vanishing moments | vanishing moments | polynomial cancellation in filter banks | polynomial cancellation in filter banks | Smoothness of wavelet bases | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | convergence of the cascade algorithm (Condition E) | splines | splines | Bases vs. frames | Bases vs. frames | Signal and image processing | Signal and image processing | finite length signals | finite length signals | boundary filters and boundary wavelets | boundary filters and boundary wavelets | wavelet compression algorithms | wavelet compression algorithms | Lifting | Lifting | ladder structure for filter banks | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | lifting form of refinement equationSec | Wavelets and subdivision | Wavelets and subdivision | nonuniform grids | nonuniform grids | multiresolution for triangular meshes | multiresolution for triangular meshes | representation and compression of surfaces | representation and compression of surfaces | Numerical solution of PDEs | Numerical solution of PDEs | Galerkin approximation | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | convergence | Subdivision wavelets for integral equations | Subdivision wavelets for integral equations | Compression and convergence estimates | Compression and convergence estimates | M-band wavelets | M-band wavelets | DFT filter banks and cosine modulated filter banks | DFT filter banks and cosine modulated filter banks | Multiwavelets | Multiwavelets

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3.012 Fundamentals of Materials Science (MIT) 3.012 Fundamentals of Materials Science (MIT)

Description

This course focuses on the fundamentals of structure, energetics, and bonding that underpin materials science. It is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and 3.016 to create a unified introduction to the subject. Topics include: an introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to atomistic and molecular models of materials; the role of electronic bonding in determining the energy, structure, and stability of materials; quantum mechanical descriptions of interacting electrons and atoms; materials phenomena, such as heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism; symmetry properties of molecules and s This course focuses on the fundamentals of structure, energetics, and bonding that underpin materials science. It is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and 3.016 to create a unified introduction to the subject. Topics include: an introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to atomistic and molecular models of materials; the role of electronic bonding in determining the energy, structure, and stability of materials; quantum mechanical descriptions of interacting electrons and atoms; materials phenomena, such as heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism; symmetry properties of molecules and s

Subjects

bonding | bonding | energetics | energetics | structure | structure | antibonding | antibonding | hydrogen | hydrogen | Quantum mechanics | Quantum mechanics | electron | electron | atom | atom | molecule | molecule | molecular dynamics | molecular dynamics | MD | MD | Symmetry properties | Symmetry properties | solid | solid | gas | gas | liquid | liquid | phase | phase | matter; molecular geometry | matter; molecular geometry | complex and disordered materials | complex and disordered materials | thermodynamics | thermodynamics | equilibrium property | equilibrium property | macroscopic behavior | macroscopic behavior | molecular model | molecular model | heat capacity | heat capacity | phase transformation | phase transformation | multiphase equilibria | multiphase equilibria | chemical reaction | chemical reaction | magnetism | magnetism | engineered alloy | engineered alloy | electronic and magnetic material | electronic and magnetic material | ionic solid | ionic solid | network solid | network solid | polymer | polymer | biomaterial | biomaterial | glass | glass | liquid crystal | liquid crystal | LCD | LCD | matter | matter | molecular geometry | molecular geometry

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6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola

Subjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | number states | coherent states | coherent states | and squeezed states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | heterodyne detection | heterodyne detection | and homodyne detection. Second-order nonlinear optics: phasematched interactions | and homodyne detection. Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | generation of squeezed states | photon-twin beams | photon-twin beams | non-classical fourth-order interference | non-classical fourth-order interference | and polarization entanglement. Quantum systems theory: optimum binary detection | and polarization entanglement. Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | and quantum teleportation. | and quantum teleportation.

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8.322 Quantum Theory II (MIT) 8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation. 8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | uncertainty relation | observables | observables | eigenstates | eigenstates | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | quantization | quantization | EM radiation field | EM radiation field | electromagnetic radiation field | electromagnetic radiation field | adiabatic theorem | adiabatic theorem | Berry?s phase | Berry?s phase | many-particle systems | many-particle systems | Dirac equation | Dirac equation | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

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6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following.  Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields.  Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following.  Quantum optics: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; radiation field quantization and quantum field propagation; P-representation and classical fields.  Linear loss and linear amplification: commutator preservation and the Uncertainty Principle; beam splitters; phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection, heterodyne detection, and homodyne detection.&a

Subjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | coherent states | and squeezed states | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields | P-representation and classical fields | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers | phase-insensitive and phase-sensitive amplifiers | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Quantum photodetection: direct detection | heterodyne detection | and homodyne detection | Second-order nonlinear optics: phasematched interactions | Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement | Quantum systems theory: optimum binary detection | Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | quantum teleportation | quantum teleportation

License

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6.453 Quantum Optical Communication (MIT) 6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola

Subjects

Quantum optics: Dirac notation quantum mechanics | Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | harmonic oscillator quantization | number states | number states | coherent states | coherent states | and squeezed states | and squeezed states | radiation field quantization and quantum field propagation | radiation field quantization and quantum field propagation | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | beam splitters | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | heterodyne detection | heterodyne detection | and homodyne detection. Second-order nonlinear optics: phasematched interactions | and homodyne detection. Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | optical parametric amplifiers | generation of squeezed states | generation of squeezed states | photon-twin beams | photon-twin beams | non-classical fourth-order interference | non-classical fourth-order interference | and polarization entanglement. Quantum systems theory: optimum binary detection | and polarization entanglement. Quantum systems theory: optimum binary detection | quantum precision measurements | quantum precision measurements | quantum cryptography | quantum cryptography | and quantum teleportation. | and quantum teleportation.

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3.20 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 properties

License

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22.06 Engineering of Nuclear Systems (MIT) 22.06 Engineering of Nuclear Systems (MIT)

Description

In this course, students explore the engineering design of nuclear power plants using the basic principles of reactor physics, thermodynamics, fluid flow and heat transfer. Topics include reactor designs, thermal analysis of nuclear fuel, reactor coolant flow and heat transfer, power conversion cycles, nuclear safety, and reactor dynamic behavior. In this course, students explore the engineering design of nuclear power plants using the basic principles of reactor physics, thermodynamics, fluid flow and heat transfer. Topics include reactor designs, thermal analysis of nuclear fuel, reactor coolant flow and heat transfer, power conversion cycles, nuclear safety, and reactor dynamic behavior.

Subjects

nuclear power overview | nuclear power overview | accelerators | accelerators | reactor physics review | reactor physics review | thermal parameters | thermal parameters | PWR | PWR | BWR | BWR | reactor design | reactor design | thermal analysis of fuel | thermal analysis of fuel | ideal gas and incompressible fluid models | ideal gas and incompressible fluid models | single phase coolant heat transfer | single phase coolant heat transfer | pure substance model | pure substance model | two-phase coolant flow and heat transfer | two-phase coolant flow and heat transfer | power cycles | power cycles | nuclear safety | nuclear safety

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22.312 Engineering of Nuclear Reactors (MIT) 22.312 Engineering of Nuclear Reactors (MIT)

Description

This course covers the engineering principles of nuclear reactors, emphasizing power reactors. Specific topics include power plant thermodynamics, reactor heat generation and removal (single-phase as well as two-phase coolant flow and heat transfer), and structural mechanics. It also discusses engineering considerations in reactor design. This course covers the engineering principles of nuclear reactors, emphasizing power reactors. Specific topics include power plant thermodynamics, reactor heat generation and removal (single-phase as well as two-phase coolant flow and heat transfer), and structural mechanics. It also discusses engineering considerations in reactor design.

Subjects

power | power | reactors | reactors | thermodynamics | thermodynamics | heat generation and removal | heat generation and removal | coolant flow | coolant flow | single-phase coolant flow | single-phase coolant flow | two-phase coolant flow | two-phase coolant flow | reactor design | reactor design | structural mechanics | structural mechanics

License

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22.312 Engineering of Nuclear Reactors (MIT) 22.312 Engineering of Nuclear Reactors (MIT)

Description

This course covers engineering principles of nuclear reactors, emphasizing power reactors. Topics include power plant thermodynamics, reactor heat generation and removal (single-phase as well as two-phase coolant flow and heat transfer), and structural mechanics. Engineering considerations in reactor design are also covered. The course objective is to understand and model the thermal-hydraulic and mechanical phenomena key to the effective, reliable and safe design and operation of nuclear systems.This course is taught by Prof. Jacopo Buongiorno. More information is available on his Web site. This course covers engineering principles of nuclear reactors, emphasizing power reactors. Topics include power plant thermodynamics, reactor heat generation and removal (single-phase as well as two-phase coolant flow and heat transfer), and structural mechanics. Engineering considerations in reactor design are also covered. The course objective is to understand and model the thermal-hydraulic and mechanical phenomena key to the effective, reliable and safe design and operation of nuclear systems.This course is taught by Prof. Jacopo Buongiorno. More information is available on his Web site.

Subjects

power | power | reactors | reactors | thermodynamics | thermodynamics | heat generation and removal | heat generation and removal | coolant flow | coolant flow | single-phase coolant flow | single-phase coolant flow | two-phase coolant flow | two-phase coolant flow | reactor design | reactor design | structural mechanics | structural mechanics

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22.313J Thermal Hydraulics in Power Technology (MIT) 22.313J Thermal Hydraulics in Power Technology (MIT)

Description

This course covers the thermo-fluid dynamic phenomena and analysis methods for conventional and nuclear power stations. Specific topics include: kinematics and dynamics of two-phase flows; steam separation; boiling, instabilities, and critical conditions; single-channel transient analysis; multiple channels connected at plena; loop analysis including single and two-phase natural circulation; and subchannel analysis. This course covers the thermo-fluid dynamic phenomena and analysis methods for conventional and nuclear power stations. Specific topics include: kinematics and dynamics of two-phase flows; steam separation; boiling, instabilities, and critical conditions; single-channel transient analysis; multiple channels connected at plena; loop analysis including single and two-phase natural circulation; and subchannel analysis.

Subjects

reactor | reactor | nuclear reactor | nuclear reactor | thermal behavior | thermal behavior | hydraulic | hydraulic | hydraulic behavior | hydraulic behavior | heat | heat | modeling | modeling | steam | steam | stability | stability | instability | instability | thermo-fluid dynamic phenomena | thermo-fluid dynamic phenomena | single-heated channel-transient analysis | single-heated channel-transient analysis | Multiple-heated channels | Multiple-heated channels | Loop analysis | Loop analysis | single and two-phase natural circulation | single and two-phase natural circulation | Kinematics | Kinematics | two-phase flows | two-phase flows | subchannel analysis | subchannel analysis | Core thermal analysis | Core thermal analysis

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22.313 Thermal Hydraulics in Nuclear Power Technology (MIT) 22.313 Thermal Hydraulics in Nuclear Power Technology (MIT)

Description

This course covers the thermo-fluid dynamic phenomena and analysis methods for conventional and nuclear power stations. Specific topics include: kinematics and dynamics of two-phase flows; steam separation; boiling, instabilities, and critical conditions; single-channel transient analysis; multiple channels connected at plena; loop analysis including single and two-phase natural circulation; and subchannel analysis.Starting in Spring 2007, this course will be offered jointly in the Departments of Nuclear Science and Engineering, Mechanical Engineering, and Chemical Engineering, and will be titled "Thermal Hydraulics in Power Technology." This course covers the thermo-fluid dynamic phenomena and analysis methods for conventional and nuclear power stations. Specific topics include: kinematics and dynamics of two-phase flows; steam separation; boiling, instabilities, and critical conditions; single-channel transient analysis; multiple channels connected at plena; loop analysis including single and two-phase natural circulation; and subchannel analysis.Starting in Spring 2007, this course will be offered jointly in the Departments of Nuclear Science and Engineering, Mechanical Engineering, and Chemical Engineering, and will be titled "Thermal Hydraulics in Power Technology."

Subjects

reactor | reactor | nuclear reactor | nuclear reactor | thermal behavior | thermal behavior | hydraulic | hydraulic | hydraulic behavior | hydraulic behavior | heat | heat | modeling | modeling | steam | steam | stability | stability | instability | instability | thermo-fluid dynamic phenomena | thermo-fluid dynamic phenomena | single-heated channel-transient analysis | single-heated channel-transient analysis | Multiple-heated channels | Multiple-heated channels | Loop analysis | Loop analysis | single and two-phase natural circulation | single and two-phase natural circulation | Kinematics | Kinematics | two-phase flows | two-phase flows | subchannel analysis | subchannel analysis | Core thermal analysis | Core thermal analysis

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3.40J Physical Metallurgy (MIT) 3.40J Physical Metallurgy (MIT)

Description

This course examines how the presence of 1-, 2- and 3D defects and second phases control the mechanical, electromagnetic and chemical behavior of metals and alloys. It considers point, line and interfacial defects in the context of structural transformations including annealing, spinodal decomposition, nucleation, growth, and particle coarsening. In addition, it concentrates on structure-function relationships, and in particular how grain size, interstitial and substitutional solid solutions, and second-phase particles impact mechanical and other properties. Examples include microelectronic circuitry, magnetic memory and drug delivery applications. This course examines how the presence of 1-, 2- and 3D defects and second phases control the mechanical, electromagnetic and chemical behavior of metals and alloys. It considers point, line and interfacial defects in the context of structural transformations including annealing, spinodal decomposition, nucleation, growth, and particle coarsening. In addition, it concentrates on structure-function relationships, and in particular how grain size, interstitial and substitutional solid solutions, and second-phase particles impact mechanical and other properties. Examples include microelectronic circuitry, magnetic memory and drug delivery applications.

Subjects

1- | 2- and 3D defects | 1- | 2- and 3D defects | second phases | second phases | mechanical | electromagnetic and chemical behavior of metals and alloys | mechanical | electromagnetic and chemical behavior of metals and alloys | point | line and interfacial defects | point | line and interfacial defects | structural transformations | structural transformations | annealing | annealing | spinodal decomposition | spinodal decomposition | nucleation | nucleation | growth | growth | particle coarsening | particle coarsening | structure-function relationships | structure-function relationships | grain size | grain size | interstitial and substitutional solid solutions | interstitial and substitutional solid solutions | second-phase particles | second-phase particles | microelectronic circuitry | microelectronic circuitry | magnetic memory | magnetic memory | drug delivery applications | drug delivery applications | 3.40 | 3.40 | 22.71 | 22.71

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22.312 Engineering of Nuclear Reactors (MIT) 22.312 Engineering of Nuclear Reactors (MIT)

Description

Engineering principles of nuclear reactors, emphasizing power reactors. Topics include power plant thermodynamics, reactor heat generation and removal (single-phase as well as two-phase coolant flow and heat transfer), structural mechanics, and engineering considerations in reactor design. Engineering principles of nuclear reactors, emphasizing power reactors. Topics include power plant thermodynamics, reactor heat generation and removal (single-phase as well as two-phase coolant flow and heat transfer), structural mechanics, and engineering considerations in reactor design.

Subjects

power | power | nuclear reactor | nuclear reactor | energy | energy | thermodynamics | thermodynamics | heat generation and removal | heat generation and removal | coolant flow | coolant flow | single-phase coolant flow | single-phase coolant flow | two-phase coolant flow | two-phase coolant flow | reactor design | reactor design | structural mechanics | structural mechanics

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22.313 Thermal Hydraulics in Nuclear Power Technology (MIT) 22.313 Thermal Hydraulics in Nuclear Power Technology (MIT)

Description

Advanced topics emphasizing thermo-fluid dynamic phenomena and analysis methods. Single-heated channel-transient analysis. Multiple-heated channels connected at plena. Loop analysis including single and two-phase natural circulation. Kinematics and dynamics of two-phase flows with energy addition. Boiling, instabilities, and critical conditions. Subchannel analysis. Core thermal analysis approaches. Advanced topics emphasizing thermo-fluid dynamic phenomena and analysis methods. Single-heated channel-transient analysis. Multiple-heated channels connected at plena. Loop analysis including single and two-phase natural circulation. Kinematics and dynamics of two-phase flows with energy addition. Boiling, instabilities, and critical conditions. Subchannel analysis. Core thermal analysis approaches.

Subjects

thermo-fluid dynamic phenomena | thermo-fluid dynamic phenomena | Single-heated channel-transient analysis | Single-heated channel-transient analysis | Multiple-heated channels | Multiple-heated channels | Loop analysis | Loop analysis | single and two-phase natural circulation | single and two-phase natural circulation | Kinematics | Kinematics | two-phase flows | two-phase flows | Subchannel analysis | Subchannel analysis | Core thermal analysis | Core thermal analysis | Subchannel analysis. Core thermal analysis | Subchannel analysis. Core thermal analysis

License

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8.321 Quantum Theory I (MIT) 8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | eigenstates | uncertainty relation | uncertainty relation | observables | observables | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

License

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3.012 Fundamentals of Materials Science (MIT) 3.012 Fundamentals of Materials Science (MIT)

Description

This subject describes the fundamentals of bonding, energetics, and structure that underpin materials science. From electrons to silicon to DNA: the role of electronic bonding in determining the energy, structure, and stability of materials. Quantum mechanical descriptions of interacting electrons and atoms. Symmetry properties of molecules and solids. Structure of complex and disordered materials. Introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to molecular models of materials. Develops basis for understanding a broad range of materials phenomena, from heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism. Fundamentals are taught using real-world examples such as engineered all This subject describes the fundamentals of bonding, energetics, and structure that underpin materials science. From electrons to silicon to DNA: the role of electronic bonding in determining the energy, structure, and stability of materials. Quantum mechanical descriptions of interacting electrons and atoms. Symmetry properties of molecules and solids. Structure of complex and disordered materials. Introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to molecular models of materials. Develops basis for understanding a broad range of materials phenomena, from heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism. Fundamentals are taught using real-world examples such as engineered all

Subjects

fundamentals of bonding | energetics | and structure | fundamentals of bonding | energetics | and structure | Quantum mechanical descriptions of interacting electrons and atoms | Quantum mechanical descriptions of interacting electrons and atoms | Symmetry properties of molecules and solids | Symmetry properties of molecules and solids | complex and disordered materials | complex and disordered materials | thermodynamic functions | thermodynamic functions | equilibrium properties | equilibrium properties | macroscopic behavior | macroscopic behavior | molecular models | molecular models | heat capacities | heat capacities | phase transformations | phase transformations | multiphase equilibria | multiphase equilibria | chemical reactions | chemical reactions | magnetism | magnetism | engineered alloys | engineered alloys | electronic and magnetic materials | electronic and magnetic materials | ionic and network solids | ionic and network solids | polymers | polymers | biomaterials | biomaterials | energetics | energetics | structure | structure | materials science | materials science | electrons | electrons | silicon | silicon | DNA | DNA | electronic bonding | electronic bonding | energy | energy | stability | stability | quantum mechanics | quantum mechanics | atoms | atoms | interactions | interactions | symmetry | symmetry | molecules | molecules | solids | solids | complex material | complex material | disorderd materials | disorderd materials | thermodynamic laws | thermodynamic laws | electronic materials | electronic materials | magnetic materials | magnetic materials | ionic solids | ionic solids | network solids | network solids | statistical mechanics | statistical mechanics | microstates | microstates | microscopic complexity | microscopic complexity | entropy | entropy

License

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18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | convolution | Fourier transform | owpass and highpass filters | Sampling rate change operations | upsampling and downsampling | ractional sampling | interpolation | Filter Banks | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | perfect reconstruction | halfband filters and possible factorizations | Modulation and polyphase representations | Noble identities | block Toeplitz matrices and block z-transforms | polyphase examples | Matlab wavelet toolbox | Orthogonal filter banks | paraunitary matrices | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | Maxflat filters | Daubechies and Meyer formulas | Spectral factorization | Multiresolution Analysis (MRA) | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | iterative and recursive solution techniques | infinite product formula | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | connection to orthogonal filters | orthogonality in the frequency domain | Biorthogonal wavelet bases | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | vanishing moments | polynomial cancellation in filter banks | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | splines | Bases vs. frames | Signal and image processing | finite length signals | boundary filters and boundary wavelets | wavelet compression algorithms | Lifting | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | Wavelets and subdivision | nonuniform grids | multiresolution for triangular meshes | representation and compression of surfaces | Numerical solution of PDEs | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | Subdivision wavelets for integral equations | Compression and convergence estimates | M-band wavelets | DFT filter banks and cosine modulated filter banks | Multiwavelets

License

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22.312 Engineering of Nuclear Reactors (MIT) 22.312 Engineering of Nuclear Reactors (MIT)

Description

This course covers the engineering principles of nuclear reactors, emphasizing power reactors. Specific topics include power plant thermodynamics, reactor heat generation and removal (single-phase as well as two-phase coolant flow and heat transfer), and structural mechanics. It also discusses engineering considerations in reactor design. This course covers the engineering principles of nuclear reactors, emphasizing power reactors. Specific topics include power plant thermodynamics, reactor heat generation and removal (single-phase as well as two-phase coolant flow and heat transfer), and structural mechanics. It also discusses engineering considerations in reactor design.

Subjects

power | power | reactors | reactors | thermodynamics | thermodynamics | heat generation and removal | heat generation and removal | coolant flow | coolant flow | single-phase coolant flow | single-phase coolant flow | two-phase coolant flow | two-phase coolant flow | reactor design | reactor design | structural mechanics | structural mechanics

License

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.htm

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18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | convolution | Fourier transform | owpass and highpass filters | Sampling rate change operations | upsampling and downsampling | ractional sampling | interpolation | Filter Banks | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | perfect reconstruction | halfband filters and possible factorizations | Modulation and polyphase representations | Noble identities | block Toeplitz matrices and block z-transforms | polyphase examples | Matlab wavelet toolbox | Orthogonal filter banks | paraunitary matrices | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | Maxflat filters | Daubechies and Meyer formulas | Spectral factorization | Multiresolution Analysis (MRA) | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | iterative and recursive solution techniques | infinite product formula | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | connection to orthogonal filters | orthogonality in the frequency domain | Biorthogonal wavelet bases | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | vanishing moments | polynomial cancellation in filter banks | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | splines | Bases vs. frames | Signal and image processing | finite length signals | boundary filters and boundary wavelets | wavelet compression algorithms | Lifting | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | Wavelets and subdivision | nonuniform grids | multiresolution for triangular meshes | representation and compression of surfaces | Numerical solution of PDEs | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | Subdivision wavelets for integral equations | Compression and convergence estimates | M-band wavelets | DFT filter banks and cosine modulated filter banks | Multiwavelets

License

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.htm

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3.071 Amorphous Materials (MIT) 3.071 Amorphous Materials (MIT)

Description

This course discusses the fundamental material science behind amorphous solids, or non-crystalline materials. It covers formation of amorphous solids; amorphous structures and their electrical and optical properties; and characterization methods and technical applications. This course discusses the fundamental material science behind amorphous solids, or non-crystalline materials. It covers formation of amorphous solids; amorphous structures and their electrical and optical properties; and characterization methods and technical applications.

Subjects

glass | glass | amorphous solid | amorphous solid | mechanical and optical properties | mechanical and optical properties | metastable | metastable | silica | silica | ideal crystals | ideal crystals | network formers | network formers | modifiers | modifiers | intermediates | intermediates | alkali silicate glass | alkali silicate glass | amorphous semiconductors | amorphous semiconductors | metallic glass | metallic glass | glass forming theory | glass forming theory | crystallization | crystallization | thermodynamics of nucleation | thermodynamics of nucleation | potential energy landscape | potential energy landscape | Zachariasen’s rules | Zachariasen’s rules | kinetic theory | kinetic theory | network topology theory | network topology theory | laboratory glass transition | laboratory glass transition | glass forming ability parmaters | glass forming ability parmaters | performance metrics | performance metrics | GST phase change alloy | GST phase change alloy | PCM | PCM | phase change memory | phase change memory | data storage | data storage | pitch drop experiment | pitch drop experiment | temperature dependence | temperature dependence | viscous flow | viscous flow | stron v. fragile liquids | stron v. fragile liquids | non- newtonian behavior | non- newtonian behavior | viscometry | viscometry | linear elasticity | linear elasticity | Newtonian viscosity | Newtonian viscosity | elasticity | elasticity | viscosity | viscosity | glass shaping | glass shaping | relaxation | relaxation | mechanical properties | mechanical properties | glass stregthening | glass stregthening | electrical properties | electrical properties | transport properties | transport properties | macroelectronics | macroelectronics | optical properties | optical properties | optical fibers | optical fibers | waveguides | waveguides | amorphous state | amorphous state

License

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6.453 Quantum Optical Communication (MIT)

Description

This course is offered to graduate students and covers topics in five major areas of quantum optical communication: quantum optics, single-mode and two-mode quantum systems, multi-mode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; P-representation and classical fields; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phase-matched interactions; optical parametric amplifiers; generation of squeezed states, photon-twin beams, non-classical fourth-order interference, and pola

Subjects

Quantum optics: Dirac notation quantum mechanics | harmonic oscillator quantization | number states | coherent states | and squeezed states | radiation field quantization and quantum field propagation | P-representation and classical fields. Linear loss and linear amplification: commutator preservation and the Uncertainty Principle | beam splitters | phase-insensitive and phase-sensitive amplifiers. Quantum photodetection: direct detection | heterodyne detection | and homodyne detection. Second-order nonlinear optics: phasematched interactions | optical parametric amplifiers | generation of squeezed states | photon-twin beams | non-classical fourth-order interference | and polarization entanglement. Quantum systems theory: optimum binary detection | quantum precision measurements | quantum cryptography | and quantum teleportation.

License

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8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | observables | eigenstates | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | quantization | EM radiation field | electromagnetic radiation field | adiabatic theorem | Berry?s phase | many-particle systems | Dirac equation | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

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.htm

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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).

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 properties

License

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3.012 Fundamentals of Materials Science (MIT)

Description

This course focuses on the fundamentals of structure, energetics, and bonding that underpin materials science. It is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and 3.016 to create a unified introduction to the subject. Topics include: an introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to atomistic and molecular models of materials; the role of electronic bonding in determining the energy, structure, and stability of materials; quantum mechanical descriptions of interacting electrons and atoms; materials phenomena, such as heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism; symmetry properties of molecules and s

Subjects

bonding | energetics | structure | antibonding | hydrogen | Quantum mechanics | electron | atom | molecule | molecular dynamics | MD | Symmetry properties | solid | gas | liquid | phase | matter; molecular geometry | complex and disordered materials | thermodynamics | equilibrium property | macroscopic behavior | molecular model | heat capacity | phase transformation | multiphase equilibria | chemical reaction | magnetism | engineered alloy | electronic and magnetic material | ionic solid | network solid | polymer | biomaterial | glass | liquid crystal | LCD | matter | molecular geometry

License

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