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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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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

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12.802 Wave Motion in the Ocean and the Atmosphere (MIT) 12.802 Wave Motion in the Ocean and the 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. 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.

Subjects

ocean | ocean | atmosphere | atmosphere | wave motion | wave motion | wave kinematics | wave kinematics | gravity waves | gravity waves | Kelvin waves | Kelvin waves | Rossby waves | Rossby waves | wave equation | wave equation | Laplace?s tidal equations | Laplace?s tidal equations | wave-mean flow interactions | wave-mean flow interactions

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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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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8.04 Quantum Physics I (MIT) 8.04 Quantum Physics I (MIT)

Description

Experimental basis of Quantum Physics: photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, De Broglie waves, and wave-particle duality of matter and light. Introduction to wave mechanics: Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states, the Heisenberg uncertainty principle, and zero-point energies. Solutions to Schroedinger's equation in one dimension: transmission and reflection at a barrier, barrier penetration, potential wells, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials, and introduction to hydrogenic systems. Experimental basis of Quantum Physics: photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, De Broglie waves, and wave-particle duality of matter and light. Introduction to wave mechanics: Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states, the Heisenberg uncertainty principle, and zero-point energies. Solutions to Schroedinger's equation in one dimension: transmission and reflection at a barrier, barrier penetration, potential wells, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials, and introduction to hydrogenic systems.

Subjects

quantum physics: photoelectric effect | quantum physics: photoelectric effect | Compton scattering | Compton scattering | photons | photons | Franck-Hertz experiment | Franck-Hertz experiment | the Bohr atom | the Bohr atom | electron diffraction | electron diffraction | deBroglie waves | deBroglie waves | wave-particle duality of matter and light | wave-particle duality of matter and light | wave mechanics: Schroedinger's equation | wave mechanics: Schroedinger's equation | wave functions | wave functions | wave packets | wave packets | probability amplitudes | probability amplitudes | stationary states | stationary states | the Heisenberg uncertainty principle | the Heisenberg uncertainty principle | zero-point energies | zero-point energies | transmission and reflection at a barrier | transmission and reflection at a barrier | barrier penetration | barrier penetration | potential wells | potential wells | simple harmonic oscillator | simple harmonic oscillator | Schroedinger's equation in three dimensions: central potentials | Schroedinger's equation in three dimensions: central potentials | introduction to hydrogenic systems | introduction to hydrogenic systems | De Broglie waves | De Broglie waves

License

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2.034J Nonlinear Dynamics and Waves (MIT) 2.034J Nonlinear Dynamics and Waves (MIT)

Description

This graduate-level course provides a unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems. This graduate-level course provides a unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems.

Subjects

nonlinear oscillations | nonlinear oscillations | wave phenomena | wave phenomena | flow-structure interaction problems | flow-structure interaction problems | nonlinear free and forced vibrations | nonlinear free and forced vibrations | nonlinear resonances | nonlinear resonances | self-excited oscillations | self-excited oscillations | lock-in phenomena | lock-in phenomena | nonlinear dispersive and nondispersive waves | nonlinear dispersive and nondispersive waves | resonant wave interactions | resonant wave interactions | propagation of wave pulses | propagation of wave pulses | nonlinear Schrodinger equation | nonlinear Schrodinger equation | nonlinear long waves and breaking | nonlinear long waves and breaking | theory of characteristics | theory of characteristics | the Korteweg-de Vries equation | the Korteweg-de Vries equation | solitons and solitary wave interactions | solitons and solitary wave interactions | stability of shear flows | stability of shear flows

License

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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

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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.

Subjects

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

License

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6.013 Electromagnetics and Applications (MIT) 6.013 Electromagnetics and Applications (MIT)

Description

This course explores electromagnetic phenomena in modern applications, including wireless communications, circuits, computer interconnects and peripherals, optical fiber links and components, microwave communications and radar, antennas, sensors, micro-electromechanical systems, motors, and power generation and transmission. Fundamentals covered include: quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; resonance; and forces, power, and energy.The instructors of this course extend a general acknowledgment to the many students and instructors who have made major contributions to the 6.013 course materials over the years, and apologize for any residual errors that may remain in these writ This course explores electromagnetic phenomena in modern applications, including wireless communications, circuits, computer interconnects and peripherals, optical fiber links and components, microwave communications and radar, antennas, sensors, micro-electromechanical systems, motors, and power generation and transmission. Fundamentals covered include: quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; resonance; and forces, power, and energy.The instructors of this course extend a general acknowledgment to the many students and instructors who have made major contributions to the 6.013 course materials over the years, and apologize for any residual errors that may remain in these writ

Subjects

electromagnetics | electromagnetics | applications | applications | wireless communications | wireless communications | circuits | circuits | computer interconnects | computer interconnects | peripherals | peripherals | optical fiber links | optical fiber links | microwave | microwave | communications | communications | radar | radar | antennas | antennas | sensors | sensors | micro-electromechanical systems | micro-electromechanical systems | power generation | power generation | power transmission | power transmission | quasistatic solutions | quasistatic solutions | dynamic solutions | dynamic solutions | Maxwell | Maxwell | Maxwell's equations | Maxwell's equations | waves | waves | radiation | radiation | diffraction | diffraction | guided waves | guided waves | unguided waves | unguided waves | resonance | resonance | forces | forces | power | power | energy | energy | microwave communications | microwave communications

License

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22.611J Introduction to Plasma Physics I (MIT) 22.611J Introduction to Plasma Physics I (MIT)

Description

In this course, students will learn about plasmas, the fourth state of matter. The plasma state dominates the visible universe, and is of increasing economic importance. Plasmas behave in lots of interesting and sometimes unexpected ways. The course is intended only as a first plasma physics course, but includes critical concepts needed for a foundation for further study. A solid undergraduate background in classical physics, electromagnetic theory including Maxwell's equations, and mathematical familiarity with partial differential equations and complex analysis are prerequisites. The course introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics, coulomb collisions and transport processes, motion of charged particles in magne In this course, students will learn about plasmas, the fourth state of matter. The plasma state dominates the visible universe, and is of increasing economic importance. Plasmas behave in lots of interesting and sometimes unexpected ways. The course is intended only as a first plasma physics course, but includes critical concepts needed for a foundation for further study. A solid undergraduate background in classical physics, electromagnetic theory including Maxwell's equations, and mathematical familiarity with partial differential equations and complex analysis are prerequisites. The course introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics, coulomb collisions and transport processes, motion of charged particles in magne

Subjects

plasma phenomena | plasma phenomena | energy generation | energy generation | controlled thermonuclear fusion | controlled thermonuclear fusion | astrophysics | astrophysics | Coulomb collisions | Coulomb collisions | transport processes | transport processes | charged particles | charged particles | magnetic fields | magnetic fields | plasma confinement schemes | plasma confinement schemes | MHD models | MHD models | simple equilibrium | simple equilibrium | stability analysis | stability analysis | Two-fluid hydrodynamic plasma models | Two-fluid hydrodynamic plasma models | wave propagation | wave propagation | kinetic theory | kinetic theory | Vlasov plasma model | Vlasov plasma model | electron plasma waves | electron plasma waves | Landau damping | Landau damping | ion-acoustic waves | ion-acoustic waves | streaming instabilities | streaming instabilities | fourth state of matter | fourth state of matter | plasma state | plasma state | visible universe | visible universe | economics | economics | plasmas | plasmas | motion of charged particles | motion of charged particles | two-fluid hydrodynamic plasma models | two-fluid hydrodynamic plasma models | Debye Shielding | Debye Shielding | collective effects | collective effects | charged particle motion | charged particle motion | EM Fields | EM Fields | cross-sections | cross-sections | relaxation | relaxation | fluid plasma descriptions | fluid plasma descriptions | MHD equilibrium | MHD equilibrium | MHD dynamics | MHD dynamics | dynamics in two-fluid plasmas | dynamics in two-fluid plasmas | cold plasma waves | cold plasma waves | magnetic field | magnetic field | microscopic to fluid plasma descriptions | microscopic to fluid plasma descriptions | Vlasov-Maxwell kinetic theory.linear Landau growth | Vlasov-Maxwell kinetic theory.linear Landau growth | kinetic description of waves | kinetic description of waves | instabilities | instabilities | Vlasov-Maxwell kinetic theory | Vlasov-Maxwell kinetic theory | linear Landau growth | linear Landau growth | 22.611 | 22.611 | 6.651 | 6.651 | 8.613 | 8.613

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8.04 Quantum Physics I (MIT) 8.04 Quantum Physics I (MIT)

Description

Includes audio/video content: AV lectures. This course covers the experimental basis of quantum physics. It introduces wave mechanics, Schrödinger's equation in a single dimension, and Schrödinger's equation in three dimensions.It is the first course in the undergraduate Quantum Physics sequence, followed by 8.05 Quantum Physics II and 8.06 Quantum Physics III.  Includes audio/video content: AV lectures. This course covers the experimental basis of quantum physics. It introduces wave mechanics, Schrödinger's equation in a single dimension, and Schrödinger's equation in three dimensions.It is the first course in the undergraduate Quantum Physics sequence, followed by 8.05 Quantum Physics II and 8.06 Quantum Physics III. 

Subjects

quantum physics: photoelectric effect | quantum physics: photoelectric effect | Compton scattering | Compton scattering | photons | photons | Franck-Hertz experiment | Franck-Hertz experiment | the Bohr atom | the Bohr atom | electron diffraction | electron diffraction | deBroglie waves | deBroglie waves | wave-particle duality of matter and light | wave-particle duality of matter and light | wave mechanics: Schroedinger's equation | wave mechanics: Schroedinger's equation | wave functions | wave functions | wave packets | wave packets | probability amplitudes | probability amplitudes | stationary states | stationary states | the Heisenberg uncertainty principle | the Heisenberg uncertainty principle | zero-point energies | zero-point energies | transmission and reflection at a barrier | transmission and reflection at a barrier | barrier penetration | barrier penetration | potential wells | potential wells | simple harmonic oscillator | simple harmonic oscillator | Schroedinger's equation in three dimensions: central potentials | and introduction to hydrogenic systems | Schroedinger's equation in three dimensions: central potentials | and introduction to hydrogenic systems

License

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8.04 Quantum Physics I (MIT) 8.04 Quantum Physics I (MIT)

Description

This course covers the experimental basis of quantum physics, introduces wave mechanics, Schrödinger's equation in a single dimension, and Schrödinger's equation in three dimensions. This course covers the experimental basis of quantum physics, introduces wave mechanics, Schrödinger's equation in a single dimension, and Schrödinger's equation in three dimensions.

Subjects

quantum physics: photoelectric effect | quantum physics: photoelectric effect | Compton scattering | Compton scattering | photons | photons | Franck-Hertz experiment | Franck-Hertz experiment | the Bohr atom | the Bohr atom | electron diffraction | electron diffraction | deBroglie waves | deBroglie waves | wave-particle duality of matter and light | wave-particle duality of matter and light | wave mechanics: Schroedinger's equation | wave mechanics: Schroedinger's equation | wave functions | wave functions | wave packets | wave packets | probability amplitudes | probability amplitudes | stationary states | stationary states | the Heisenberg uncertainty principle | the Heisenberg uncertainty principle | zero-point energies | zero-point energies | transmission and reflection at a barrier | transmission and reflection at a barrier | barrier penetration | barrier penetration | potential wells | potential wells | simple harmonic oscillator | simple harmonic oscillator | Schroedinger's equation in three dimensions: central potentials | Schroedinger's equation in three dimensions: central potentials | and introduction to hydrogenic systems. | and introduction to hydrogenic systems.

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RES.8-005 Vibrations and Waves Problem Solving (MIT) RES.8-005 Vibrations and Waves Problem Solving (MIT)

Description

Includes audio/video content: AV lectures. 8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01 Physics I: Classical Mechanics and 8.02 Physics II: Electricity and Magnetism. Topics include mechanical vibrations and waves, electromagnetic waves, and optics. These Problem Solving Help Videos provide step-by-step solutions to sample problems. Also included is information about how Physics III is typically taught on the MIT campus. Instructor Insights are shared by Professor Wit Busza who has taught Physics III and its associated recitation sessions many times. Professor Busza's insights focus on his approach to problem solving, strategies for supporting students as they solve problems, and common sources of confusion for students i Includes audio/video content: AV lectures. 8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01 Physics I: Classical Mechanics and 8.02 Physics II: Electricity and Magnetism. Topics include mechanical vibrations and waves, electromagnetic waves, and optics. These Problem Solving Help Videos provide step-by-step solutions to sample problems. Also included is information about how Physics III is typically taught on the MIT campus. Instructor Insights are shared by Professor Wit Busza who has taught Physics III and its associated recitation sessions many times. Professor Busza's insights focus on his approach to problem solving, strategies for supporting students as they solve problems, and common sources of confusion for students i

Subjects

vibrations | vibrations | waves | waves | mass on a spring | mass on a spring | LC circuit | LC circuit | simple harmonic motion | simple harmonic motion | harmonic oscillators | harmonic oscillators | damping | damping | coupled oscillators | coupled oscillators | traveling waves | traveling waves | standing waves | standing waves | electromagnetic waves | electromagnetic waves | interference | interference | radiating electromagnetic waves | radiating electromagnetic waves | Quality Factor Q | Quality Factor Q

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5.61 Physical Chemistry (MIT) 5.61 Physical Chemistry (MIT)

Description

This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems -- the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, spectroscopy.AcknowledgementsThe material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW was prepa This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems -- the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, spectroscopy.AcknowledgementsThe material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW was prepa

Subjects

physical chemistry | physical chemistry | quantum mechanics | quantum mechanics | quantum chemistry | quantum chemistry | particles and waves; wave mechanics | particles and waves; wave mechanics | atomic structure | atomic structure | valence orbital | valence orbital | molecular orbital theory | molecular orbital theory | molecular structure | molecular structure | photochemistry | photochemistry | particles and waves | wave mechanics | particles and waves | wave mechanics

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13.811 Advanced Structural Dynamics and Acoustics (MIT) 13.811 Advanced Structural Dynamics and Acoustics (MIT)

Description

This course begins with the foundations of 3D elasticity, fluid and elastic wave equations, elastic and plastic waves in rods and beams, waves in plates, and dynamics and acoustics of cylindrical shells. The course considers acoustic fluids effects such as radiation and scattering by submerged plates and shells, and interaction between structural elements. Finally, it covers the response of plates and shells to high-intensity loads, dynamic plasticity and fracture, and structural damage caused by implosive and impact loads.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. File decompression software, such as Winzip® or StuffIt®, is required to open the .zip files found on this course site. This course begins with the foundations of 3D elasticity, fluid and elastic wave equations, elastic and plastic waves in rods and beams, waves in plates, and dynamics and acoustics of cylindrical shells. The course considers acoustic fluids effects such as radiation and scattering by submerged plates and shells, and interaction between structural elements. Finally, it covers the response of plates and shells to high-intensity loads, dynamic plasticity and fracture, and structural damage caused by implosive and impact loads.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. File decompression software, such as Winzip® or StuffIt®, is required to open the .zip files found on this course site.

Subjects

3D elasticity | 3D elasticity | wave equations | wave equations | elastic wave | elastic wave | plastic wave | plastic wave | plates | plates | shells | shells | cylindrical shells | cylindrical shells | submerged plates and shells | submerged plates and shells | high-intensity load | high-intensity load | dynamic plasticity | dynamic plasticity | fracture | fracture | implosive load | implosive load | impact load | impact load | radiation | radiation | harmonics | harmonics | scattering | scattering | spheres | spheres | waves | waves | cylinders | cylinders | 2.067 | 2.067

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2.016 Hydrodynamics (13.012) (MIT) 2.016 Hydrodynamics (13.012) (MIT)

Description

This course covers the development of the fundamental equations of fluid mechanics and their simplifications for several areas of marine hydrodynamics and the application of these principles to the solution of engineering problems. Topics include the principles of conservation of mass, momentum and energy, lift and drag forces, laminar and turbulent flows, dimensional analysis, added mass, and linear surface waves, including wave velocities, propagation phenomena, and descriptions of real sea waves. Wave forces on structures are treated in the context of design and basic seakeeping analysis of ships and offshore platforms. Geophysical fluid dynamics will also be addressed including distributions of salinity, temperature, and density; heat balance in the ocean; major ocean circulations and This course covers the development of the fundamental equations of fluid mechanics and their simplifications for several areas of marine hydrodynamics and the application of these principles to the solution of engineering problems. Topics include the principles of conservation of mass, momentum and energy, lift and drag forces, laminar and turbulent flows, dimensional analysis, added mass, and linear surface waves, including wave velocities, propagation phenomena, and descriptions of real sea waves. Wave forces on structures are treated in the context of design and basic seakeeping analysis of ships and offshore platforms. Geophysical fluid dynamics will also be addressed including distributions of salinity, temperature, and density; heat balance in the ocean; major ocean circulations and

Subjects

fluid mechanics | fluid mechanics | mass | mass | momentum | momentum | energy | energy | lift | lift | drag | drag | laminar | laminar | turbulent | turbulent | turbulence | turbulence | wave | wave | waves | waves | surface waves | surface waves | current | current | water | water | ocean | ocean | force | force | sea | sea | sea wave | sea wave | ship | ship | propulsion | propulsion | propeller | propeller | fish | fish | swimming | swimming | wind | wind | VIV | VIV | vortex induced vibration | vortex induced vibration | Bernoulli | Bernoulli | D'Allembert | D'Allembert | hydrostatics | hydrostatics | fluid dynamics | fluid dynamics

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2.22 Design Principles for Ocean Vehicles (13.42) (MIT) 2.22 Design Principles for Ocean Vehicles (13.42) (MIT)

Description

The course covers the basic techniques for evaluating the maximum forces and loads over the life of a marine structure or vehicle, so as to be able to design its basic configuration. Loads and motions of small and large structures and their short-term and long-term statistics are studied in detail and many applications are presented in class and studied in homework and laboratory sessions. Issues related to seakeeping of ships are studied in detail. The basic equations and issues of maneuvering are introduced at the end of the course. Three laboratory sessions demonstrate the phenomena studied and provide experience with experimental methods and data processing. This course was originally offered in Course 13 (Ocean Engineering) as 13.42. The course covers the basic techniques for evaluating the maximum forces and loads over the life of a marine structure or vehicle, so as to be able to design its basic configuration. Loads and motions of small and large structures and their short-term and long-term statistics are studied in detail and many applications are presented in class and studied in homework and laboratory sessions. Issues related to seakeeping of ships are studied in detail. The basic equations and issues of maneuvering are introduced at the end of the course. Three laboratory sessions demonstrate the phenomena studied and provide experience with experimental methods and data processing. This course was originally offered in Course 13 (Ocean Engineering) as 13.42.

Subjects

seakeeping | seakeeping | sea keeping | sea keeping | wave | wave | waves | waves | swell | swell | current | current | ship design | ship design | underwater vehicle | underwater vehicle | submarine | submarine | offshore platform | offshore platform | wave spectra | wave spectra | Froude Krylov | Froude Krylov | Fourier transform | Fourier transform | vortex | vortex | vortex induced vibration | vortex induced vibration | wave energy | wave energy | Pierson-Moskowitz spectrum | Pierson-Moskowitz spectrum | Bretschneider spectrum | Bretschneider spectrum | Ochi spectrum | Ochi spectrum | JONSWAP spectrum | JONSWAP spectrum

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2.067 Advanced Structural Dynamics and Acoustics (13.811) (MIT) 2.067 Advanced Structural Dynamics and Acoustics (13.811) (MIT)

Description

This course begins with the foundations of 3D elasticity, fluid and elastic wave equations, elastic and plastic waves in rods and beams, waves in plates, and dynamics and acoustics of cylindrical shells. The course considers acoustic fluids effects such as radiation and scattering by submerged plates and shells, and interaction between structural elements. Finally, it covers the response of plates and shells to high-intensity loads, dynamic plasticity and fracture, and structural damage caused by implosive and impact loads. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.811. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.067. This course begins with the foundations of 3D elasticity, fluid and elastic wave equations, elastic and plastic waves in rods and beams, waves in plates, and dynamics and acoustics of cylindrical shells. The course considers acoustic fluids effects such as radiation and scattering by submerged plates and shells, and interaction between structural elements. Finally, it covers the response of plates and shells to high-intensity loads, dynamic plasticity and fracture, and structural damage caused by implosive and impact loads. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.811. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.067.

Subjects

3D elasticity | 3D elasticity | wave equations | wave equations | elastic wave | elastic wave | plastic wave | plastic wave | plates | plates | shells | shells | cylindrical shells | cylindrical shells | submerged plates and shells | submerged plates and shells | high-intensity load | high-intensity load | dynamic plasticity | dynamic plasticity | fracture | fracture | implosive load | implosive load | impact load | impact load | radiation | radiation | harmonics | harmonics | scattering | scattering | spheres | spheres | waves | waves | cylinders | cylinders

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6.013 Electromagnetics and Applications (MIT) 6.013 Electromagnetics and Applications (MIT)

Description

This course explores electromagnetic phenomena in modern applications, including wireless communications, circuits, computer interconnects and peripherals, optical fiber links and components, microwave communications and radar, antennas, sensors, micro-electromechanical systems, motors, and power generation and transmission. Fundamentals covered include: quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; resonance; and forces, power, and energy.Acknowledgments The instructors would like to thank Robert Haussman for transcribing into LaTeX the problem set and Quiz 2 solutions. This course explores electromagnetic phenomena in modern applications, including wireless communications, circuits, computer interconnects and peripherals, optical fiber links and components, microwave communications and radar, antennas, sensors, micro-electromechanical systems, motors, and power generation and transmission. Fundamentals covered include: quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; resonance; and forces, power, and energy.Acknowledgments The instructors would like to thank Robert Haussman for transcribing into LaTeX the problem set and Quiz 2 solutions.

Subjects

ESD.013 | ESD.013 | electromagnetics | electromagnetics | applications | applications | wireless communications | wireless communications | circuits | circuits | computer interconnects | computer interconnects | peripherals | peripherals | optical fiber links | optical fiber links | microwave communications | microwave communications | radar | radar | antennas | antennas | sensors | sensors | micro-electromechanical systems | micro-electromechanical systems | power generation | power generation | power transmission | power transmission | quasistatic solutions | quasistatic solutions | dynamic solutions | dynamic solutions | Maxwell | Maxwell | Maxwell's equations | Maxwell's equations | waves | waves | radiation | radiation | diffraction | diffraction | guided waves | guided waves | unguided waves | unguided waves | resonance | resonance | forces | forces | power | power | energy | energy

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12.802 Wave Motion in the Ocean and the 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.

Subjects

ocean | atmosphere | wave motion | wave kinematics | gravity waves | Kelvin waves | Rossby waves | wave equation | Laplace?s tidal equations | wave-mean flow interactions

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

Description

This course introduces fundamental concepts in "continuous'' applied mathematics, with an emphasis on nonlinear partial differential equations (PDEs). Topics include linear and nonlinear waves: kinematic waves, method of characteristics, expansion fans, wave breaking, shock dynamics, shock structure; linear and nonlinear diffusion: Green functions, Fourier transform, similarity solutions, boundary layers, Nernst-Planck equations. Applications include traffic flow, gas dynamics, and granular flow. This course introduces fundamental concepts in "continuous'' applied mathematics, with an emphasis on nonlinear partial differential equations (PDEs). Topics include linear and nonlinear waves: kinematic waves, method of characteristics, expansion fans, wave breaking, shock dynamics, shock structure; linear and nonlinear diffusion: Green functions, Fourier transform, similarity solutions, boundary layers, Nernst-Planck equations. Applications include traffic flow, gas dynamics, and granular flow.

Subjects

Linear and nonlinear waves | Linear and nonlinear waves | hyperbolic waves | hyperbolic waves | kinematic waves | kinematic waves | expansion fans | expansion fans | shock dynamics | shock dynamics | shock structure | shock structure | Linear diffusion | Linear diffusion | nonlinear diffusion | nonlinear diffusion | Green functions | Green functions | Fourier transform | Fourier transform | dimensional analysis | dimensional analysis | similarity solutions | similarity solutions | boundary layers | boundary layers | traffic flow | traffic flow | gas dynamics | gas dynamics | tsunamis | tsunamis | heat transfer | heat transfer | ion transport | ion transport | granular flow | granular flow

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12.510 Introduction to Seismology (MIT) 12.510 Introduction to Seismology (MIT)

Description

This graduate level course presents a basic study in seismology and the utilization of seismic waves for the study of Earth's interior. It introduces techniques necessary for understanding of elastic wave propagation in layered media. This graduate level course presents a basic study in seismology and the utilization of seismic waves for the study of Earth's interior. It introduces techniques necessary for understanding of elastic wave propagation in layered media.

Subjects

seismology | seismology | utilization of seismic waves | utilization of seismic waves | Earth's interior | Earth's interior | elastic wave propagation in stratified media | elastic wave propagation in stratified media | synthetic seismograms | synthetic seismograms | WKBJ | WKBJ | mode summation | mode summation | Ray theory | Ray theory | interpretation of travel times | interpretation of travel times | surface wave dispersion in layered media | surface wave dispersion in layered media | Earth's free oscillations | Earth's free oscillations | seismicity | seismicity | earthquake locations | earthquake locations

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13.853 Computational Ocean Acoustics (MIT) 13.853 Computational Ocean Acoustics (MIT)

Description

This course examines wave equations for fluid and visco-elastic media, wave-theory formulations of acoustic source radiation and seismo-acoustic propagation in stratified ocean waveguides, and Wavenumber Integration and Normal Mode methods for propagation in plane-stratified media. Also covered are Seismo-Acoustic modeling of seabeds and ice covers, seismic interface and surface waves in a stratified seabed, Parabolic Equation and Coupled Mode approaches to propagation in range-dependent ocean waveguides, numerical modeling of target scattering and reverberation clutter in ocean waveguides, and ocean ambient noise modeling. Students develop propagation models using all the numerical approaches relevant to state-of-the-art acoustic research. This course examines wave equations for fluid and visco-elastic media, wave-theory formulations of acoustic source radiation and seismo-acoustic propagation in stratified ocean waveguides, and Wavenumber Integration and Normal Mode methods for propagation in plane-stratified media. Also covered are Seismo-Acoustic modeling of seabeds and ice covers, seismic interface and surface waves in a stratified seabed, Parabolic Equation and Coupled Mode approaches to propagation in range-dependent ocean waveguides, numerical modeling of target scattering and reverberation clutter in ocean waveguides, and ocean ambient noise modeling. Students develop propagation models using all the numerical approaches relevant to state-of-the-art acoustic research.

Subjects

Wave equations | Wave equations | fluid and visco-elastic media | fluid and visco-elastic media | Wave-theory formulations | Wave-theory formulations | acoustic source radiation | acoustic source radiation | seismo-acoustic propagation | seismo-acoustic propagation | stratified ocean waveguides | stratified ocean waveguides | Wavenumber Integration | Wavenumber Integration | Normal Mode | Normal Mode | propagation in plane-stratified media | propagation in plane-stratified media | Seismo-Acoustic modeling | Seismo-Acoustic modeling | Seismic interface | Seismic interface | surface waves | surface waves | stratified seabed | stratified seabed | Parabolic Equation | Parabolic Equation | Coupled Mode | Coupled Mode | range-dependent ocean waveguides | range-dependent ocean waveguides | Numerical modeling | Numerical modeling | target scattering | target scattering | reverberation clutter | reverberation clutter | Ocean ambient noise modeling | Ocean ambient noise modeling | Fluid media | Fluid media | visco-elastic media | visco-elastic media | plane-stratified media | plane-stratified media | ice covers | ice covers | 2.068 | 2.068

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2.068 Computational Ocean Acoustics (13.853) (MIT) 2.068 Computational Ocean Acoustics (13.853) (MIT)

Description

This course examines wave equations for fluid and visco-elastic media, wave-theory formulations of acoustic source radiation and seismo-acoustic propagation in stratified ocean waveguides, and Wavenumber Integration and Normal Mode methods for propagation in plane-stratified media. Also covered are Seismo-Acoustic modeling of seabeds and ice covers, seismic interface and surface waves in a stratified seabed, Parabolic Equation and Coupled Mode approaches to propagation in range-dependent ocean waveguides, numerical modeling of target scattering and reverberation clutter in ocean waveguides, and ocean ambient noise modeling. Students develop propagation models using all the numerical approaches relevant to state-of-the-art acoustic research. This course was originally offered in Course 13 ( This course examines wave equations for fluid and visco-elastic media, wave-theory formulations of acoustic source radiation and seismo-acoustic propagation in stratified ocean waveguides, and Wavenumber Integration and Normal Mode methods for propagation in plane-stratified media. Also covered are Seismo-Acoustic modeling of seabeds and ice covers, seismic interface and surface waves in a stratified seabed, Parabolic Equation and Coupled Mode approaches to propagation in range-dependent ocean waveguides, numerical modeling of target scattering and reverberation clutter in ocean waveguides, and ocean ambient noise modeling. Students develop propagation models using all the numerical approaches relevant to state-of-the-art acoustic research. This course was originally offered in Course 13 (

Subjects

Wave equations | Wave equations | fluid and visco-elastic media | fluid and visco-elastic media | Wave-theory formulations | Wave-theory formulations | acoustic source radiation | acoustic source radiation | seismo-acoustic propagation | seismo-acoustic propagation | stratified ocean waveguides | stratified ocean waveguides | Wavenumber Integration | Wavenumber Integration | Normal Mode | Normal Mode | propagation in plane-stratified media | propagation in plane-stratified media | Seismo-Acoustic modeling | Seismo-Acoustic modeling | Seismic interface | Seismic interface | surface waves | surface waves | stratified seabed | stratified seabed | Parabolic Equation | Parabolic Equation | Coupled Mode | Coupled Mode | range-dependent ocean waveguides | range-dependent ocean waveguides | Numerical modeling | Numerical modeling | target scattering | target scattering | reverberation clutter | reverberation clutter | Ocean ambient noise modeling | Ocean ambient noise modeling | Fluid media | Fluid media | visco-elastic media | visco-elastic media | plane-stratified media | plane-stratified media | ice covers | ice covers

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