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22.106 Neutron Interactions and Applications (MIT) 22.106 Neutron Interactions and Applications (MIT)

Description

This course is intended to introduce the student to the concepts and methods of transport theory needed in neutron science applications. This course is a foundational study of the effects of multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department. Stochastic and deterministic simulation techniques will be introduced to the students. This course is intended to introduce the student to the concepts and methods of transport theory needed in neutron science applications. This course is a foundational study of the effects of multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department. Stochastic and deterministic simulation techniques will be introduced to the students.

Subjects

Neutron Interaction | Neutron Interaction | Neutron Elastic Scattering: Thermal Motion | Neutron Elastic Scattering: Thermal Motion | Chemical Binding Effects | Chemical Binding Effects | Particle Simulations I | Particle Simulations I | Monte Carlo Basics Monte Carlo in Statistical Physics and Radiation Transport | Monte Carlo Basics Monte Carlo in Statistical Physics and Radiation Transport | The Neutron Transport Equation | The Neutron Transport Equation | Neutron Slowing Down | Neutron Slowing Down | Neutron Diffusion | Neutron Diffusion | Particle Simulation Methods | Particle Simulation Methods | Basic Molecular Dynamics | Basic Molecular Dynamics | Direct Simulation of Melting | Direct Simulation of Melting | Multiscale Materials Modeling | Multiscale Materials Modeling | Thermal Neutron Scattering | Thermal Neutron Scattering | Dynamic Structure Factor in Neutron Inelastic Scattering | Dynamic Structure Factor in Neutron Inelastic Scattering

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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1.061 Transport Processes in the Environment (MIT) 1.061 Transport Processes in the Environment (MIT)

Description

Includes audio/video content: AV faculty introductions. This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport. Includes audio/video content: AV faculty introductions. This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport.

Subjects

river systems | river systems | lake systems | lake systems | scalar transport in environmental flows | scalar transport in environmental flows | momentum transport in environmental flows | momentum transport in environmental flows | stratification in lakes | stratification in lakes | buoyancy-driven flows | buoyancy-driven flows | settling and coagulation | settling and coagulation | air-water exchange | air-water exchange | bed-water exchange | bed-water exchange | phase partitioning | phase partitioning | dissolution | dissolution | boundary layers | boundary layers | molecular diffusion | molecular diffusion | turbulent diffusion | turbulent diffusion | water transportation | water transportation | advection | advection | aquatic systems | aquatic systems | conservation of mass | conservation of mass | derivation | derivation | Diffusion | Diffusion | dispersion | dispersion | environmental flows | environmental flows | instantaneous point source | instantaneous point source | lakes | lakes | mass | mass | transport | transport | particle transport | particle transport | rivers | rivers | scaling | scaling | turbulence | turbulence | water flow | water flow

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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18.306 Advanced Partial Differential Equations with Applications (MIT) 18.306 Advanced Partial Differential Equations with Applications (MIT)

Description

The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc. The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.

Subjects

partial differential equations (pde) | partial differential equations (pde) | nonlinear pde. Diffusion | nonlinear pde. Diffusion | dispersion | dispersion | Initial and boundary value problems | Initial and boundary value problems | Characteristics and shocks | Characteristics and shocks | Separation of variables | Separation of variables | transform methods | transform methods | Green's functions | Green's functions | Asymptotics | Asymptotics | geometrical theory | geometrical theory | Dimensional analysis | Dimensional analysis | self-similarity | self-similarity | traveling waves | traveling waves | Singular perturbation and boundary layers | Singular perturbation and boundary layers | Solitons | Solitons | Variational methods | Variational methods | Free-boundary problems | Free-boundary problems

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.S096 Topics in Mathematics of Data Science (MIT) 18.S096 Topics in Mathematics of Data Science (MIT)

Description

This is a mostly self-contained research-oriented course designed for undergraduate students (but also extremely welcoming to graduate students) with an interest in doing research in theoretical aspects of algorithms that aim to extract information from data. These often lie in overlaps of two or more of the following: Mathematics, Applied Mathematics, Computer Science, Electrical Engineering, Statistics, and / or Operations Research. This is a mostly self-contained research-oriented course designed for undergraduate students (but also extremely welcoming to graduate students) with an interest in doing research in theoretical aspects of algorithms that aim to extract information from data. These often lie in overlaps of two or more of the following: Mathematics, Applied Mathematics, Computer Science, Electrical Engineering, Statistics, and / or Operations Research.

Subjects

Principal Component Analysis (PCA) | Principal Component Analysis (PCA) | random matrix theory | random matrix theory | spike model | spike model | manifold learning | manifold learning | Diffusion Maps | Diffusion Maps | Sobolev Embedding Theorem | Sobolev Embedding Theorem | Spectral Clustering | Spectral Clustering | Cheeger’s inequality | Cheeger’s inequality | Mesh Theorem | Mesh Theorem | Number Theory | Number Theory | Approximation algorithms | Approximation algorithms | Max-Cut problem | Max-Cut problem | Stochastic Block Model | Stochastic Block Model | Synchronization | Synchronization | inverse problems | inverse problems

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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18.336 Numerical Methods of Applied Mathematics II (MIT) 18.336 Numerical Methods of Applied Mathematics II (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Subjects

Linear systems | Linear systems | Fast Fourier Transform | Fast Fourier Transform | Wave equation | Wave equation | Von Neumann analysis | Von Neumann analysis | Conditions for stability | Conditions for stability | Dissipation | Dissipation | Multistep schemes | Multistep schemes | Dispersion | Dispersion | Group Velocity | Group Velocity | Propagation of Wave Packets | Propagation of Wave Packets | Parabolic Equations | Parabolic Equations | The Du Fort Frankel Scheme | The Du Fort Frankel Scheme | Convection-Diffusion equation | Convection-Diffusion equation | ADI Methods | ADI Methods | Elliptic Equations | Elliptic Equations | Jacobi | Gauss-Seidel and SOR(w) | Jacobi | Gauss-Seidel and SOR(w) | ODEs | ODEs | finite differences | finite differences | spectral methods | spectral methods | well-posedness and stability | well-posedness and stability | boundary and nonlinear instabilities | boundary and nonlinear instabilities | Finite Difference Schemes | Finite Difference Schemes | Partial Differential Equations | Partial Differential Equations

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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18.306 Advanced Partial Differential Equations with Applications (MIT) 18.306 Advanced Partial Differential Equations with Applications (MIT)

Description

This course presents the concepts and techniques for solving partial differential equations (pde), with emphasis on nonlinear pde. This course presents the concepts and techniques for solving partial differential equations (pde), with emphasis on nonlinear pde.

Subjects

partial differential equations (pde) | partial differential equations (pde) | nonlinear pde | nonlinear pde | Diffusion | Diffusion | dispersion | dispersion | Initial and boundary value problems | Initial and boundary value problems | Characteristics and shocks | Characteristics and shocks | Separation of variables | Separation of variables | transform methods | transform methods | Green's functions | Green's functions | Asymptotics | Asymptotics | geometrical theory | geometrical theory | Dimensional analysis | Dimensional analysis | self-similarity | self-similarity | traveling waves | traveling waves | Singular perturbation and boundary layers | Singular perturbation and boundary layers | Solitons | Solitons | Variational methods | Variational methods | Free-boundary problems | Free-boundary problems | fluid dynamics | fluid dynamics | electrical engineering | electrical engineering | mechanical engineering | mechanical engineering | materials science | materials science | quantum mechanics | quantum 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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18.336 Numerical Methods of Applied Mathematics II (MIT) 18.336 Numerical Methods of Applied Mathematics II (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.

Subjects

Linear systems | Linear systems | Fast Fourier Transform | Fast Fourier Transform | Wave equation | Wave equation | Von Neumann analysis | Von Neumann analysis | Conditions for stability | Conditions for stability | Dissipation | Dissipation | Multistep schemes | Multistep schemes | Dispersion | Dispersion | Group Velocity | Group Velocity | Propagation of Wave Packets | Propagation of Wave Packets | Parabolic Equations | Parabolic Equations | The Du Fort Frankel Scheme | The Du Fort Frankel Scheme | Convection-Diffusion equation | Convection-Diffusion equation | ADI Methods | ADI Methods | Elliptic Equations | Elliptic Equations | Jacobi | Gauss-Seidel and SOR(w) | Jacobi | Gauss-Seidel and SOR(w) | ODEs | ODEs | finite differences | finite differences | spectral methods | spectral methods | well-posedness and stability | well-posedness and stability | boundary and nonlinear instabilities | boundary and nonlinear instabilities | Finite Difference Schemes | Finite Difference Schemes | Partial Differential Equations | Partial Differential Equations

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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1.061 Transport Processes in the Environment (MIT) 1.061 Transport Processes in the Environment (MIT)

Description

This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport. This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport.

Subjects

river systems | river systems | lake systems | lake systems | scalar transport in environmental flows | scalar transport in environmental flows | momentum transport in environmental flows | momentum transport in environmental flows | stratification in lakes | stratification in lakes | buoyancy-driven flows | buoyancy-driven flows | settling and coagulation | settling and coagulation | air-water exchange | air-water exchange | bed-water exchange | bed-water exchange | phase partitioning | phase partitioning | dissolution | dissolution | boundary layers | boundary layers | molecular diffusion | molecular diffusion | turbulent diffusion | turbulent diffusion | water transportation | water transportation | advection | advection | aquatic systems | aquatic systems | conservation of mass | conservation of mass | derivation | derivation | Diffusion | Diffusion | dispersion | dispersion | environmental flows | environmental flows | instantaneous point source | instantaneous point source | lakes | lakes | mass | mass | transport | transport | particle transport | particle transport | rivers | rivers | scaling | scaling | turbulence | turbulence | water flow | water flow

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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12.002 Physics and Chemistry of the Terrestrial Planets (MIT) 12.002 Physics and Chemistry of the Terrestrial Planets (MIT)

Description

This course introduces the structure, composition, and physical processes governing the terrestrial planets, including their formation and basic orbital properties. Topics include plate tectonics, earthquakes, seismic waves, rheology, impact cratering, gravity and magnetic fields, heat flux, thermal structure, mantle convection, deep interiors, planetary magnetism, and core dynamics. Suitable for majors and non-majors seeking general background in geophysics and planetary structure. This course introduces the structure, composition, and physical processes governing the terrestrial planets, including their formation and basic orbital properties. Topics include plate tectonics, earthquakes, seismic waves, rheology, impact cratering, gravity and magnetic fields, heat flux, thermal structure, mantle convection, deep interiors, planetary magnetism, and core dynamics. Suitable for majors and non-majors seeking general background in geophysics and planetary structure.

Subjects

Terrestrial Planets | Terrestrial Planets | Disk Accretion | Disk Accretion | Planetary Formation | Planetary Formation | Geochronology | Geochronology | Solar System | Solar System | Elastic stress and strain | Elastic stress and strain | Seismic Waves and wave equation | Seismic Waves and wave equation | Seismology | Seismology | Heat | Heat | Diffusion | Diffusion | Geomagnetism | Geomagnetism | Paleomagnetism | Paleomagnetism | Plate Tectonics | Plate Tectonics | Topography | Topography | Isostasy | Isostasy | Gravity Anomalies | Gravity Anomalies

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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22.106 Neutron Interactions and Applications (MIT) 22.106 Neutron Interactions and Applications (MIT)

Description

This course is a foundational study of the effects of single and multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department - fission, fusion, and RST. Particle simulation methods are introduced to deal with complex processes that cannot be studied only experimentally or by numerical solutions of equations. Treatment will emphasize basic concepts and understanding, as well as showing the underlying scientific connections with current research areas. This course is a foundational study of the effects of single and multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department - fission, fusion, and RST. Particle simulation methods are introduced to deal with complex processes that cannot be studied only experimentally or by numerical solutions of equations. Treatment will emphasize basic concepts and understanding, as well as showing the underlying scientific connections with current research areas.

Subjects

Neutron Interaction | Neutron Interaction | Neutron Elastic Scattering: Thermal Motion | Neutron Elastic Scattering: Thermal Motion | Chemical Binding Effects | Chemical Binding Effects | Particle Simulations I | Particle Simulations I | Monte Carlo Basics Monte Carlo in Statistical Physics and Radiation Transport | Monte Carlo Basics Monte Carlo in Statistical Physics and Radiation Transport | The Neutron Transport Equation | The Neutron Transport Equation | Neutron Slowing Down | Neutron Slowing Down | Neutron Diffusion | Neutron Diffusion | Particle Simulation Methods | Particle Simulation Methods | Basic Molecular Dynamics | Basic Molecular Dynamics | Direct Simulation of Melting | Direct Simulation of Melting | Multiscale Materials Modeling | Multiscale Materials Modeling | Thermal Neutron Scattering | Thermal Neutron Scattering | Dynamic Structure Factor in Neutron Inelastic Scattering | Dynamic Structure Factor in Neutron Inelastic Scattering

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.S096 Topics in Mathematics of Data Science (MIT)

Description

This is a mostly self-contained research-oriented course designed for undergraduate students (but also extremely welcoming to graduate students) with an interest in doing research in theoretical aspects of algorithms that aim to extract information from data. These often lie in overlaps of two or more of the following: Mathematics, Applied Mathematics, Computer Science, Electrical Engineering, Statistics, and / or Operations Research.

Subjects

Principal Component Analysis (PCA) | random matrix theory | spike model | manifold learning | Diffusion Maps | Sobolev Embedding Theorem | Spectral Clustering | ?s inequality | Mesh Theorem | Number Theory | Approximation algorithms | Max-Cut problem | Stochastic Block Model | Synchronization | inverse problems

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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1.061 Transport Processes in the Environment (MIT)

Description

This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport.

Subjects

river systems | lake systems | scalar transport in environmental flows | momentum transport in environmental flows | stratification in lakes | buoyancy-driven flows | settling and coagulation | air-water exchange | bed-water exchange | phase partitioning | dissolution | boundary layers | molecular diffusion | turbulent diffusion | water transportation | advection | aquatic systems | conservation of mass | derivation | Diffusion | dispersion | environmental flows | instantaneous point source | lakes | mass | transport | particle transport | rivers | scaling | turbulence | water flow

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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1.061 Transport Processes in the Environment (MIT)

Description

This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport.

Subjects

river systems | lake systems | scalar transport in environmental flows | momentum transport in environmental flows | stratification in lakes | buoyancy-driven flows | settling and coagulation | air-water exchange | bed-water exchange | phase partitioning | dissolution | boundary layers | molecular diffusion | turbulent diffusion | water transportation | advection | aquatic systems | conservation of mass | derivation | Diffusion | dispersion | environmental flows | instantaneous point source | lakes | mass | transport | particle transport | rivers | scaling | turbulence | water flow

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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12.002 Physics and Chemistry of the Terrestrial Planets (MIT)

Description

This course introduces the structure, composition, and physical processes governing the terrestrial planets, including their formation and basic orbital properties. Topics include plate tectonics, earthquakes, seismic waves, rheology, impact cratering, gravity and magnetic fields, heat flux, thermal structure, mantle convection, deep interiors, planetary magnetism, and core dynamics. Suitable for majors and non-majors seeking general background in geophysics and planetary structure.

Subjects

Terrestrial Planets | Disk Accretion | Planetary Formation | Geochronology | Solar System | Elastic stress and strain | Seismic Waves and wave equation | Seismology | Heat | Diffusion | Geomagnetism | Paleomagnetism | Plate Tectonics | Topography | Isostasy | Gravity Anomalies

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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18.306 Advanced Partial Differential Equations with Applications (MIT)

Description

The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.

Subjects

partial differential equations (pde) | nonlinear pde. Diffusion | dispersion | Initial and boundary value problems | Characteristics and shocks | Separation of variables | transform methods | Green's functions | Asymptotics | geometrical theory | Dimensional analysis | self-similarity | traveling waves | Singular perturbation and boundary layers | Solitons | Variational methods | Free-boundary problems

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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22.106 Neutron Interactions and Applications (MIT)

Description

This course is a foundational study of the effects of single and multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department - fission, fusion, and RST. Particle simulation methods are introduced to deal with complex processes that cannot be studied only experimentally or by numerical solutions of equations. Treatment will emphasize basic concepts and understanding, as well as showing the underlying scientific connections with current research areas.

Subjects

Neutron Interaction | Neutron Elastic Scattering: Thermal Motion | Chemical Binding Effects | Particle Simulations I | Monte Carlo Basics Monte Carlo in Statistical Physics and Radiation Transport | The Neutron Transport Equation | Neutron Slowing Down | Neutron Diffusion | Particle Simulation Methods | Basic Molecular Dynamics | Direct Simulation of Melting | Multiscale Materials Modeling | Thermal Neutron Scattering | Dynamic Structure Factor in Neutron Inelastic Scattering

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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1.061 Transport Processes in the Environment (MIT)

Description

This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport.

Subjects

river systems | lake systems | scalar transport in environmental flows | momentum transport in environmental flows | stratification in lakes | buoyancy-driven flows | settling and coagulation | air-water exchange | bed-water exchange | phase partitioning | dissolution | boundary layers | molecular diffusion | turbulent diffusion | water transportation | advection | aquatic systems | conservation of mass | derivation | Diffusion | dispersion | environmental flows | instantaneous point source | lakes | mass | transport | particle transport | rivers | scaling | turbulence | water flow

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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18.336 Numerical Methods of Applied Mathematics II (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Subjects

Linear systems | Fast Fourier Transform | Wave equation | Von Neumann analysis | Conditions for stability | Dissipation | Multistep schemes | Dispersion | Group Velocity | Propagation of Wave Packets | Parabolic Equations | The Du Fort Frankel Scheme | Convection-Diffusion equation | ADI Methods | Elliptic Equations | Jacobi | Gauss-Seidel and SOR(w) | ODEs | finite differences | spectral methods | well-posedness and stability | boundary and nonlinear instabilities | Finite Difference Schemes | Partial Differential Equations

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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18.306 Advanced Partial Differential Equations with Applications (MIT)

Description

This course presents the concepts and techniques for solving partial differential equations (pde), with emphasis on nonlinear pde.

Subjects

partial differential equations (pde) | nonlinear pde | Diffusion | dispersion | Initial and boundary value problems | Characteristics and shocks | Separation of variables | transform methods | Green's functions | Asymptotics | geometrical theory | Dimensional analysis | self-similarity | traveling waves | Singular perturbation and boundary layers | Solitons | Variational methods | Free-boundary problems | fluid dynamics | electrical engineering | mechanical engineering | materials science | quantum 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 https://ocw.mit.edu/terms/index.htm

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1.061 Transport Processes in the Environment (MIT)

Description

This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport.

Subjects

river systems | lake systems | scalar transport in environmental flows | momentum transport in environmental flows | stratification in lakes | buoyancy-driven flows | settling and coagulation | air-water exchange | bed-water exchange | phase partitioning | dissolution | boundary layers | molecular diffusion | turbulent diffusion | water transportation | advection | aquatic systems | conservation of mass | derivation | Diffusion | dispersion | environmental flows | instantaneous point source | lakes | mass | transport | particle transport | rivers | scaling | turbulence | water flow

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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22.106 Neutron Interactions and Applications (MIT)

Description

This course is intended to introduce the student to the concepts and methods of transport theory needed in neutron science applications. This course is a foundational study of the effects of multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department. Stochastic and deterministic simulation techniques will be introduced to the students.

Subjects

Neutron Interaction | Neutron Elastic Scattering: Thermal Motion | Chemical Binding Effects | Particle Simulations I | Monte Carlo Basics Monte Carlo in Statistical Physics and Radiation Transport | The Neutron Transport Equation | Neutron Slowing Down | Neutron Diffusion | Particle Simulation Methods | Basic Molecular Dynamics | Direct Simulation of Melting | Multiscale Materials Modeling | Thermal Neutron Scattering | Dynamic Structure Factor in Neutron Inelastic Scattering

License

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18.336 Numerical Methods of Applied Mathematics II (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.

Subjects

Linear systems | Fast Fourier Transform | Wave equation | Von Neumann analysis | Conditions for stability | Dissipation | Multistep schemes | Dispersion | Group Velocity | Propagation of Wave Packets | Parabolic Equations | The Du Fort Frankel Scheme | Convection-Diffusion equation | ADI Methods | Elliptic Equations | Jacobi | Gauss-Seidel and SOR(w) | ODEs | finite differences | spectral methods | well-posedness and stability | boundary and nonlinear instabilities | Finite Difference Schemes | Partial Differential Equations

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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