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22.615 MHD Theory of Fusion Systems (MIT) 22.615 MHD Theory of Fusion Systems (MIT)

Description

This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta. This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta.

Subjects

Magnetohydrodynamics | Magnetohydrodynamics | plasma | plasma | transport theory | transport theory | Boltzmann-Maxwell equations | Boltzmann-Maxwell equations | tokamaks | tokamaks | MHD equilibria | MHD equilibria | poloidal field design | poloidal field design | MHD stability theory | MHD stability theory | Energy Principle | Energy Principle | interchange instability | interchange instability | ballooning modes | ballooning modes | second region of stability | second region of stability | external kink modes | external kink modes | MHD instabilities | MHD instabilities

License

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2.700 Principles of Naval Architecture (MIT) 2.700 Principles of Naval Architecture (MIT)

Description

This course presents principles of naval architecture, ship geometry, hydrostatics, calculation and drawing of curves of form, intact and damage stability, hull structure strength calculations and ship resistance. It introduces computer-aided naval ship design and analysis tools. Projects include analysis of ship lines drawings, calculation of ship hydrostatic characteristics, analysis of intact and damaged stability, ship model testing, and hull structure strength calculations. This course presents principles of naval architecture, ship geometry, hydrostatics, calculation and drawing of curves of form, intact and damage stability, hull structure strength calculations and ship resistance. It introduces computer-aided naval ship design and analysis tools. Projects include analysis of ship lines drawings, calculation of ship hydrostatic characteristics, analysis of intact and damaged stability, ship model testing, and hull structure strength calculations.

Subjects

naval architecture | naval architecture | ship geometry | ship geometry | geometry of ships | geometry of ships | ship resistance | ship resistance | flow | flow | hydrostatics | hydrostatics | intact stability | intact stability | damage stability | damage stability | general stability | general stability | hull | hull | hydrostatic | hydrostatic | ship model testing | ship model testing | hull structure | hull structure | Resistance | Resistance | Propulsion | Propulsion | Vibration | Vibration | submarine | submarine | hull subdivision | hull subdivision | midsection | midsection

License

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1.63 Advanced Fluid Dynamics of the Environment (MIT) 1.63 Advanced Fluid Dynamics of the Environment (MIT)

Description

Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year. Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.

Subjects

fluid dynamics | fluid dynamics | fluid motion | fluid motion | Cartesian tensor convention | Cartesian tensor convention | scaling | scaling | approximations | approximations | slow flow | slow flow | Stokes flow | Stokes flow | Oseen | Oseen | spreading | spreading | gravity | gravity | stratified fluid | stratified fluid | boundary layer | boundary layer | high speed flow | high speed flow | jets | jets | thermal plume | thermal plume | pure fluids | pure fluids | porous media | porous media | similarity method of solution | similarity method of solution | shear | shear | stratification | stratification | Orr-Sommerfeld | Orr-Sommerfeld | capillary phenomena | capillary phenomena | bubbles | bubbles | drops | drops | Marangoni instability | Marangoni instability | contact lines | contact lines | geophysical fluid dynamics | geophysical fluid dynamics | coastal flows | coastal flows | wind-induced flows | wind-induced flows | coastal upwelling | coastal upwelling | transient boundary layer | transient boundary layer | buoyancy | buoyancy | convection porous media | convection porous media | dispersion | dispersion | hydrodynamic instability | hydrodynamic instability | Kelvin-Helmholtz instability | Kelvin-Helmholtz instability

License

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2.032 Dynamics (MIT) 2.032 Dynamics (MIT)

Description

This course reviews momentum and energy principles, and then covers the following topics: Hamilton's principle and Lagrange's equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems. This course was originally developed by Professor T. Akylas. This course reviews momentum and energy principles, and then covers the following topics: Hamilton's principle and Lagrange's equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems. This course was originally developed by Professor T. Akylas.

Subjects

motion | motion | momentum | momentum | work-energy principle | work-energy principle | degrees of freedom | degrees of freedom | Lagrange's equations | Lagrange's equations | D'Alembert's principle | D'Alembert's principle | Hamilton's principle | Hamilton's principle | gyroscope | gyroscope | gyroscopic effect | gyroscopic effect | steady motions | steady motions | nature of small deviations | nature of small deviations | natural modes | natural modes | natural frequencies for continuous and lumped parameter systems | natural frequencies for continuous and lumped parameter systems | mode shapes | mode shapes | forced vibrations | forced vibrations | dynamic stability theory | dynamic stability theory | instability | instability

License

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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

License

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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

License

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22.101 Applied Nuclear Physics (MIT) 22.101 Applied Nuclear Physics (MIT)

Description

The topics covered under this course include elements of nuclear physics for engineering students, basic properties of the nucleus and nuclear radiations, quantum mechanical calculations of deuteron bound-state wave function and energy, n-p scattering cross-section, transition probability per unit time and barrier transmission probability. Also explored are binding energy and nuclear stability, interactions of charged particles, neutrons, and gamma rays with matter, radioactive decays, energetics and general cross-section behavior in nuclear reactions. The topics covered under this course include elements of nuclear physics for engineering students, basic properties of the nucleus and nuclear radiations, quantum mechanical calculations of deuteron bound-state wave function and energy, n-p scattering cross-section, transition probability per unit time and barrier transmission probability. Also explored are binding energy and nuclear stability, interactions of charged particles, neutrons, and gamma rays with matter, radioactive decays, energetics and general cross-section behavior in nuclear reactions.

Subjects

Nuclear physics | Nuclear physics | Nuclear reaction | Nuclear reaction | Nucleus | Nucleus | Nuclear radiation | Nuclear radiation | Quantum mechanics | Quantum mechanics | Deuteron bound-state wave function and energy | Deuteron bound-state wave function and energy | n-p scattering cross-section | n-p scattering cross-section | Transition probability per unit time | Transition probability per unit time | Barrier transmission probability | Barrier transmission probability | Binding energy | Binding energy | Nuclear stability | Nuclear stability | Interactions of charged particles neutrons and gamma rays with matter | Interactions of charged particles neutrons and gamma rays with matter | Radioactive decay | Radioactive decay | Energetics | Energetics | nuclear physics | nuclear physics | nuclear reaction | nuclear reaction | nucleus | nucleus | nuclear radiation | nuclear radiation | quantum mechanics | quantum mechanics | deuteron bound-state wave function and energy | deuteron bound-state wave function and energy | transition probability per unit time | transition probability per unit time | barrier transmission probability | barrier transmission probability | nuclear stability | nuclear stability | Interactions of charged particles | Interactions of charged particles | neutrons | neutrons | and gamma rays with matter | and gamma rays with matter | energetics | energetics

License

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18.086 Mathematical Methods for Engineers II (MIT) 18.086 Mathematical Methods for Engineers II (MIT)

Description

Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization. Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.

Subjects

Scientific computing: Fast Fourier Transform | Scientific computing: Fast Fourier Transform | finite differences | finite differences | finite elements | finite elements | spectral method | spectral method | numerical linear algebra | numerical linear algebra | Complex variables and applications | Complex variables and applications | Initial-value problems: stability or chaos in ordinary differential equations | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | wave equation versus heat equation | conservation laws and shocks | conservation laws and shocks | dissipation and dispersion | dissipation and dispersion | Optimization: network flows | Optimization: network flows | linear programming | linear programming | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Optimization: network flows | linear programming | Optimization: network flows | linear programming

License

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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

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1.018J Fundamentals of Ecology (MIT) 1.018J Fundamentals of Ecology (MIT)

Description

This is a basic subject in ecology that seeks to improve the understanding of the flow of energy and materials through ecosystems and the regulation of the distribution and abundance of organisms. The course covers productivity and biogeochemical cycles in ecosystems, trophic dynamics, community structure and stability, competition and predation, evolution and natural selection, population growth and physiological ecology. There is particular emphasis placed on aquatic systems. This is a basic subject in ecology that seeks to improve the understanding of the flow of energy and materials through ecosystems and the regulation of the distribution and abundance of organisms. The course covers productivity and biogeochemical cycles in ecosystems, trophic dynamics, community structure and stability, competition and predation, evolution and natural selection, population growth and physiological ecology. There is particular emphasis placed on aquatic systems.

Subjects

ecology | ecology | flow of energy | flow of energy | flow of materials | flow of materials | ecosystems | ecosystems | distribution and abundance of organisms | distribution and abundance of organisms | productivity cycles | productivity cycles | biogeochemical cycles | biogeochemical cycles | trophic dynamics | trophic dynamics | community structure and stability | community structure and stability | competition and predation | competition and predation | evolution and natural selection | evolution and natural selection | population growth | population growth | physiological ecology | physiological ecology | aquatic systems | aquatic systems | community structure | community structure | community stability | community stability | competition | competition | predation | predation | distribution | distribution | organisms | organisms | evolution | evolution | natural selection | natural selection | energy flow | energy flow | 1.018 | 1.018 | 7.30 | 7.30

License

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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

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18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT)

Description

Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc. Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Nonlinear dynamical systems | Nonlinear dynamical systems | nonlinear waves | nonlinear waves | diffusion | diffusion | stability | stability | characteristics | characteristics | nonlinear steepening | nonlinear steepening | breaking and shock formation | breaking and shock formation | conservation laws | conservation laws | first-order partial differential equations | first-order partial differential equations | finite differences | finite differences | numerical stability | numerical stability | traffic problems | traffic problems | flows in rivers | flows in rivers | internal waves | internal waves | mechanical vibrations | mechanical vibrations

License

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1.63 Advanced Fluid Dynamics of the Environment (MIT)

Description

Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.

Subjects

fluid dynamics | fluid motion | Cartesian tensor convention | scaling | approximations | slow flow | Stokes flow | Oseen | spreading | gravity | stratified fluid | boundary layer | high speed flow | jets | thermal plume | pure fluids | porous media | similarity method of solution | shear | stratification | Orr-Sommerfeld | capillary phenomena | bubbles | drops | Marangoni instability | contact lines | geophysical fluid dynamics | coastal flows | wind-induced flows | coastal upwelling | transient boundary layer | buoyancy | convection porous media | dispersion | hydrodynamic instability | Kelvin-Helmholtz instability

License

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22.615 MHD Theory of Fusion Systems (MIT)

Description

This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta.

Subjects

Magnetohydrodynamics | plasma | transport theory | Boltzmann-Maxwell equations | tokamaks | MHD equilibria | poloidal field design | MHD stability theory | Energy Principle | interchange instability | ballooning modes | second region of stability | external kink modes | MHD instabilities

License

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1.63 Advanced Fluid Dynamics of the Environment (MIT)

Description

Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.

Subjects

fluid dynamics | fluid motion | Cartesian tensor convention | scaling | approximations | slow flow | Stokes flow | Oseen | spreading | gravity | stratified fluid | boundary layer | high speed flow | jets | thermal plume | pure fluids | porous media | similarity method of solution | shear | stratification | Orr-Sommerfeld | capillary phenomena | bubbles | drops | Marangoni instability | contact lines | geophysical fluid dynamics | coastal flows | wind-induced flows | coastal upwelling | transient boundary layer | buoyancy | convection porous media | dispersion | hydrodynamic instability | Kelvin-Helmholtz instability

License

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2.700 Principles of Naval Architecture (MIT)

Description

This course presents principles of naval architecture, ship geometry, hydrostatics, calculation and drawing of curves of form, intact and damage stability, hull structure strength calculations and ship resistance. It introduces computer-aided naval ship design and analysis tools. Projects include analysis of ship lines drawings, calculation of ship hydrostatic characteristics, analysis of intact and damaged stability, ship model testing, and hull structure strength calculations.

Subjects

naval architecture | ship geometry | geometry of ships | ship resistance | flow | hydrostatics | intact stability | damage stability | general stability | hull | hydrostatic | ship model testing | hull structure | Resistance | Propulsion | Vibration | submarine | hull subdivision | midsection

License

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16.31 Feedback Control Systems (MIT) 16.31 Feedback Control Systems (MIT)

Description

This course covers the fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, the student should be able to design controllers using state-space methods and evaluate whether these controllers are robust. This course covers the fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, the student should be able to design controllers using state-space methods and evaluate whether these controllers are robust.

Subjects

linear system response | linear system response | aircraft control | aircraft control | frequency response methods | frequency response methods | Nyquist stability theorem | Nyquist stability theorem | bode plots | bode plots | state-space systems | state-space systems | full-state feedback control | full-state feedback control | open-loop estimators | open-loop estimators | closed-loop estimators | closed-loop estimators | robustness analysis | robustness analysis | small gain theorem | small gain theorem

License

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12.517 Dynamics of Complex Systems: Complexity in Ecology (MIT) 12.517 Dynamics of Complex Systems: Complexity in Ecology (MIT)

Description

In this class we will critically review both classical works and recent literature on complexity in ecology. The emphasis will be on developing quantitative theories in the context of experimental and observational data. We will meet twice weekly for roundtable discussions. In this class we will critically review both classical works and recent literature on complexity in ecology. The emphasis will be on developing quantitative theories in the context of experimental and observational data. We will meet twice weekly for roundtable discussions.

Subjects

complex systems | complex systems | length and time scales | length and time scales | Ecology biodiversity | Ecology biodiversity | ecosystem stability | ecosystem stability | environmental fluctuations | environmental fluctuations | speciation | speciation | extinction | extinction

License

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Dunne, Biplane Dunne, Biplane

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Subjects

uk | uk | england | england | woman | woman | man | man | paris | paris | kent | kent | wings | wings | unitedkingdom | unitedkingdom | philosophy | philosophy | aeroplane | aeroplane | getty | getty | d8 | d8 | riverthames | riverthames | d3 | d3 | graces | graces | d5 | d5 | biplane | biplane | d1 | d1 | eastchurch | eastchurch | notail | notail | d4 | d4 | thechannel | thechannel | gutenberg | gutenberg | churchroad | churchroad | flyingmachine | flyingmachine | thomasmayne | thomasmayne | serialism | serialism | lanternslides | lanternslides | nationallibraryofireland | nationallibraryofireland | dryflyfishing | dryflyfishing | july1910 | july1910 | swaleborough | swaleborough | locationidentified | locationidentified | johnwilliamdunne | johnwilliamdunne | flightmagazine | flightmagazine | dateestablished | dateestablished | thewarintheair | thewarintheair | standfordhill | standfordhill | arcopublishing | arcopublishing | thomasholmesmason | thomasholmesmason | thomashmasonsonslimited | thomashmasonsonslimited | dunnebiplanesstickandstring | dunnebiplanesstickandstring | lieutenantdunne | lieutenantdunne | darlingdownsgazette | darlingdownsgazette | mrhgwells | mrhgwells | april9th1910 | april9th1910 | no5ateastchurch | no5ateastchurch | jane’salltheworld’saircraft1913 | jane’salltheworld’saircraft1913 | fredtjane | fredtjane | villacoublayairfield | villacoublayairfield | earlymilitaryaircraft | earlymilitaryaircraft | taillesssweptwingdesigns | taillesssweptwingdesigns | certifiedinherentlystableaircraft | certifiedinherentlystableaircraft | flyingwingdesign | flyingwingdesign | lateralstability | lateralstability

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16.06 Principles of Automatic Control (MIT) 16.06 Principles of Automatic Control (MIT)

Description

This course introduces the design of feedback control systems as applied to a variety of air and spacecraft systems. Topics include the properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, the Root locus method, Nyquist criterion, frequency-domain design, and state space methods. This course introduces the design of feedback control systems as applied to a variety of air and spacecraft systems. Topics include the properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, the Root locus method, Nyquist criterion, frequency-domain design, and state space methods.

Subjects

classical control systems | classical control systems | feedback control systems | feedback control systems | bode plots | bode plots | time-domain and frequency-domain performance measures | time-domain and frequency-domain performance measures | stability | stability | root locus method | root locus method | nyquist criterion | nyquist criterion | frequency-domain design | frequency-domain design | state space methods | state space methods

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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12.163 Surface Processes and Landscape Evolution (MIT) 12.163 Surface Processes and Landscape Evolution (MIT)

Description

The course offers an introduction to quantitative analysis of geomorphic processes, and examines the interaction of climate, tectonics, and surface processes in the sculpting of Earth's surface. The course offers an introduction to quantitative analysis of geomorphic processes, and examines the interaction of climate, tectonics, and surface processes in the sculpting of Earth's surface.

Subjects

geomorphic processes | geomorphic processes | climate | climate | tectonics | tectonics | surface processes | surface processes | fluvial processes | fluvial processes | hillslope processes | hillslope processes | glacial processes | glacial processes | weathering | weathering | soil formation | soil formation | runoff | runoff | erosion | erosion | slope stability | slope stability | sediment transport | sediment transport | river morphology | river morphology | glacial erosion | glacial erosion | climatic forcings | climatic forcings | tectonic forcings | tectonic forcings | glaciation | glaciation | sea level change | sea level change | uplift | subsidence | uplift | subsidence | post-glacial isostatic rebound | post-glacial isostatic rebound | uplift | subsidence | uplift | subsidence

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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12.802 Wave Motions in the Ocean and Atmosphere (MIT) 12.802 Wave Motions in the Ocean and Atmosphere (MIT)

Description

This course is an introduction to basic ideas of geophysical wave motion in rotating, stratified, and rotating-stratified fluids. Subject begins with general wave concepts of phase and group velocity. It also covers the dynamics and kinematics of gravity waves with a focus on dispersion, energy flux, initial value problems, etc. Also addressed are subject foundation used to study internal and inertial waves, Kelvin, Poincare, and Rossby waves in homogeneous and stratified fluids. Laplace tidal equations are applied to equatorial waves. Other topics include: resonant interactions, potential vorticity, wave-mean flow interactions, and instability. This course is an introduction to basic ideas of geophysical wave motion in rotating, stratified, and rotating-stratified fluids. Subject begins with general wave concepts of phase and group velocity. It also covers the dynamics and kinematics of gravity waves with a focus on dispersion, energy flux, initial value problems, etc. Also addressed are subject foundation used to study internal and inertial waves, Kelvin, Poincare, and Rossby waves in homogeneous and stratified fluids. Laplace tidal equations are applied to equatorial waves. Other topics include: resonant interactions, potential vorticity, wave-mean flow interactions, and instability.

Subjects

geophysical wave motion | geophysical wave motion | rotating | stratified | and rotating-stratified fluids | rotating | stratified | and rotating-stratified fluids | general wave concepts | general wave concepts | phase | phase | group velocity | group velocity | dynamics and kinematics of gravity waves | dynamics and kinematics of gravity waves | dispersion | dispersion | energy flux | energy flux | initial value problems | initial value problems | internal and inertial waves | internal and inertial waves | Kelvin | Kelvin | Poincare | Poincare | and Rossby waves | and Rossby waves | homogeneous and stratified fluids | homogeneous and stratified fluids | Laplace tidal equations | Laplace tidal equations | equatorial waves | equatorial waves | resonant interactions | resonant interactions | potential vorticity | potential vorticity | wave-mean flow interactions | wave-mean flow interactions | instability | instability | 12. Kelvin | Poincare | and Rossby waves | 12. Kelvin | Poincare | and Rossby waves | Kelvin | Poincare | and Rossby waves | Kelvin | Poincare | and Rossby waves | internal gravity waves | internal gravity waves | surface gravity waves | surface gravity waves | rotation | rotation | large-scale hydrostatic motions | large-scale hydrostatic motions | vertical structure equation | vertical structure equation | equatorial ?-plane | equatorial ?-plane | Stratified Quasi-Geostrophic Motion | Stratified Quasi-Geostrophic Motion

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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18.311 Principles of Applied Mathematics (MIT)

Description

Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Nonlinear dynamical systems | nonlinear waves | diffusion | stability | characteristics | nonlinear steepening | breaking and shock formation | conservation laws | first-order partial differential equations | finite differences | numerical stability | traffic problems | flows in rivers | internal waves | mechanical vibrations

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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16.90 Computational Methods in Aerospace Engineering (MIT)

Description

This course provides an introduction to numerical methods and computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques covered include numerical integration of systems of ordinary differential equations; numerical discretization of partial differential equations; and probabilistic methods for quantifying the impact of variability. Specific emphasis is given to finite volume methods in fluid mechanics, and finite element methods in structural mechanics.Acknowledgement: Prof. David Darmofal taught this course in prior years, and created some of the materials found in this OCW site.

Subjects

numerical integration | ODEs | ordinary differential equations | finite difference | finite volume | finite element | discretization | PDEs | partial differential equations | numerical linear algebra | probabilistic methods | optimization | computational methods | aerospace engineering | Monte Carlo | Fourier stability analysis | Matrix stability analysis | Runge-Kutta | convergence | accuracy | stiffness | weighted residual | statistical sampling | sensitivity analysis

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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12.333 Atmospheric and Ocean Circulations (MIT) 12.333 Atmospheric and Ocean Circulations (MIT)

Description

In this course, we will look at many important aspects of the circulation of the atmosphere and ocean, from length scales of meters to thousands of km and time scales ranging from seconds to years. We will assume familiarity with concepts covered in course 12.003 (Physics of the Fluid Earth). In the early stages of the present course, we will make somewhat greater use of math than did 12.003, but the math we will use is no more than that encountered in elementary electromagnetic field theory, for example. The focus of the course is on the physics of the phenomena which we will discuss. In this course, we will look at many important aspects of the circulation of the atmosphere and ocean, from length scales of meters to thousands of km and time scales ranging from seconds to years. We will assume familiarity with concepts covered in course 12.003 (Physics of the Fluid Earth). In the early stages of the present course, we will make somewhat greater use of math than did 12.003, but the math we will use is no more than that encountered in elementary electromagnetic field theory, for example. The focus of the course is on the physics of the phenomena which we will discuss.

Subjects

atmospheric and oceanic phenomena | atmospheric and oceanic phenomena | observations | observations | theoretical interpretations | theoretical interpretations | monsoons | monsoons | El Ni?o | El Ni?o | planetary waves | planetary waves | atmospheric synoptic eddies and fronts | atmospheric synoptic eddies and fronts | gulf stream rings | gulf stream rings | hurricanes | hurricanes | surface and internal gravity waves | surface and internal gravity waves | tides | tides | shallow water gravity waves | shallow water gravity waves | deep water gravity waves | deep water gravity waves | internal gravity waves | internal gravity waves | large-scale motions | large-scale motions | rotating earth | rotating earth | Rossby waves | Rossby waves | planetary scale motions | planetary scale motions | baroclinic instability | baroclinic instability | midlatitude storms | midlatitude storms | equatorial atmosphere | equatorial atmosphere | equatorial ocean | equatorial ocean | southern oscillation | southern oscillation | tropical cyclones | tropical cyclones | typhoons | typhoons

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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