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Readme file for Web Design and Objects

Description

This readme file contains details of links to all the Web Design and Objects module's material held on Jorum and information about the module as well.

Subjects

ukoer | data oriented dynamic design methods article | data oriented dynamic design methods reading material | data oriented dynamic design methods | data oriented dynamic web design method article | data oriented dynamic web design method reading material | data oriented dynamic web design method | design method article | design method lecture | design method reading material | design method | design methods article | design methods lecture | design methods reading material | design methods | dynamic design method article | dynamic design method lecture | dynamic design methods reading material | dynamic design methods | hypermedia design methods reading material | hypermedia design reading material | hypermedia systems reading material | hypertext application types reading material | live projects reading material | modelling framework reading material | object oriented dynamic design methods and consensus | object oriented dynamic web design method lecture | object oriented dynamic web design method reading material | object oriented dynamic web design method | process/event oriented dynamic design methods lecture | process/event oriented dynamic design methods | robustness diagrams reading material | simple web method website | static web method reading material | static web method task guide | static web method website | static web method | static web methods reading material | static web methods task guide | static web methods website | static web methods | structured detail website | structured overview lecture | structured techniques external website | structured techniques lecture | structured techniques reading material | structured techniques | swm analysis website | swm design detail | systems analysis and design practical | systems analysis and design reading material | systems analysis and design task guide | systems analysis and design website | systems analysis and design | systems analysis reading material | systems analysis task guide | uml lecture | uml reading material | web article | web design and objects article | web design and objects external website | web design and objects introduction lecture | web design and objects introduction reading material | web design and objects introduction task guide | web design and objects introduction website | web design and objects introduction | web design and objects lecture | web design and objects reading material | web design and objects task guide | web design and objects website | web design and objects | web design article | web design external website | web design lecture | web design practical | web design reading material | web design task guide | web design website | web design | web engineering reading material | web external website | web lecture | web method reading material | web method task guide | web method website | web method | web methods reading material | web methods task guide | web methods website | web methods | web object article | web object external website | web object lecture | web object practical | web object reading material | web object task guide | web object website | web object | web objects article | web objects external website | web objects lecture | web objects practical | web objects reading material | web objects task guide | web objects website | web objects | web practical | web reading material | web task guide | web website | web | webml lecture | webml reading material | webml website | webratio website | g530 article | g530 external website | g530 lecture | g530 practical | g530 reading material | g530 task guide | g530 website | g530 | web design and objects practical | web modeling language external website | web modeling language lecture | web modeling language reading material | web modeling language | web modelling language external website | web modelling language lecture | web modelling language reading material | web modelling language | webml external website | webml | Computer science | I100

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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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

License

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

Description

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

Subjects

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

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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8.033 Relativity (MIT) 8.033 Relativity (MIT)

Description

Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay. Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay.

Subjects

Einstein's postulates | Einstein's postulates | consequences for simultaneity | time dilation | length contraction | clock synchronization | consequences for simultaneity | time dilation | length contraction | clock synchronization | Lorentz transformation | Lorentz transformation | relativistic effects and paradoxes | relativistic effects and paradoxes | Minkowski diagrams | Minkowski diagrams | invariants and four-vectors | invariants and four-vectors | momentum | energy and mass | momentum | energy and mass | particle collisions | particle collisions | Relativity and electricity | Relativity and electricity | Coulomb's law | Coulomb's law | magnetic fields | magnetic fields | Newtonian cosmology | Newtonian cosmology | General Relativity | General Relativity | principle of equivalence | principle of equivalence | the Schwarzchild metric | the Schwarzchild metric | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | gravitational red shift | particle trajectories | particle trajectories | light trajectories | light trajectories | invariants | invariants | four-vectors | four-vectors | momentum | momentum | energy | energy | mass | mass | relativistic effects | relativistic effects | paradoxes | paradoxes | electricity | electricity | time dilation | time dilation | length contraction | length contraction | clock synchronization | clock synchronization | Schwarzchild metric | Schwarzchild metric | geodesics | geodesics | Shaprio delay | Shaprio delay | relativistic kinematics | relativistic kinematics | relativistic dynamics | relativistic dynamics | electromagnetism | electromagnetism | hubble expansion | hubble expansion | universe | universe | equivalence principle | equivalence principle | curved space time | curved space time | Ether Theory | Ether Theory | constants | constants | speed of light | speed of light | c | c | graph | graph | pythagorem theorem | pythagorem theorem | triangle | triangle | arrows | arrows

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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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

License

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

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

Description

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

Subjects

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

License

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

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3.23 Electrical, Optical, and Magnetic Properties of Materials (MIT) 3.23 Electrical, Optical, and Magnetic Properties of Materials (MIT)

Description

This class discusses the origin of electrical, magnetic and optical properties of materials, with a focus on the acquisition of quantum mechanical tools. It begins with an analysis of the properties of materials, presentation of the postulates of quantum mechanics, and close examination of the hydrogen atom, simple molecules and bonds, and the behavior of electrons in solids and energy bands. Introducing the variation principle as a method for the calculation of wavefunctions, the course continues with investigation of how and why materials respond to different electrical, magnetic and electromagnetic fields and probes and study of the conductivity, dielectric function, and magnetic permeability in metals, semiconductors, and insulators. A survey of common devices such as transistors, magn This class discusses the origin of electrical, magnetic and optical properties of materials, with a focus on the acquisition of quantum mechanical tools. It begins with an analysis of the properties of materials, presentation of the postulates of quantum mechanics, and close examination of the hydrogen atom, simple molecules and bonds, and the behavior of electrons in solids and energy bands. Introducing the variation principle as a method for the calculation of wavefunctions, the course continues with investigation of how and why materials respond to different electrical, magnetic and electromagnetic fields and probes and study of the conductivity, dielectric function, and magnetic permeability in metals, semiconductors, and insulators. A survey of common devices such as transistors, magn

Subjects

quantum mechanics | quantum mechanics | functional materials | functional materials | magnetic domains | magnetic domains | particle wells | particle wells | spintronics | spintronics | semiconductor engineering | semiconductor engineering | p-n junction | p-n junction | luminescence | luminescence | nanoparticles | nanoparticles | phonons | phonons

License

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12.742 Marine Chemistry (MIT) 12.742 Marine Chemistry (MIT)

Description

Includes audio/video content: AV selected lectures. This course is an introduction to chemical oceanography. It describes reservoir models and residence time, major ion composition of seawater, inputs to and outputs from the ocean via rivers, the atmosphere, and the sea floor. Biogeochemical cycling within the oceanic water column and sediments, emphasizing the roles played by the formation, transport, and alteration of oceanic particles and the effects that these processes have on seawater composition. Cycles of carbon, nitrogen, phosphorus, oxygen, and sulfur. Uptake of anthropogenic carbon dioxide by the ocean. Material presented through lectures and student-led presentation and discussion of recent papers. Includes audio/video content: AV selected lectures. This course is an introduction to chemical oceanography. It describes reservoir models and residence time, major ion composition of seawater, inputs to and outputs from the ocean via rivers, the atmosphere, and the sea floor. Biogeochemical cycling within the oceanic water column and sediments, emphasizing the roles played by the formation, transport, and alteration of oceanic particles and the effects that these processes have on seawater composition. Cycles of carbon, nitrogen, phosphorus, oxygen, and sulfur. Uptake of anthropogenic carbon dioxide by the ocean. Material presented through lectures and student-led presentation and discussion of recent papers.

Subjects

chemical oceanography | chemical oceanography | biogeochemical cycling | biogeochemical cycling | water column processes | water column processes | ocean particles | ocean particles | seawater composition | seawater composition | ocean particle transport | ocean particle transport | carbon | carbon | oxygen | oxygen | nitrogen | nitrogen | phosphorus | phosphorus | sulfur | sulfur | carbon dioxide | carbon dioxide | sediment chemistry | sediment chemistry

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

Description

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

Subjects

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

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

Description

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

Subjects

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

License

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11.479J Water and Sanitation Infrastructure in Developing Countries (MIT) 11.479J Water and Sanitation Infrastructure in Developing Countries (MIT)

Description

This course deals with the principles of infrastructure planning in developing countries, with a focus on appropriate and sustainable technologies for water and sanitation. It also incorporates technical, socio-cultural, public health, and economic factors into the planning and design of water and sanitation systems. Upon completion, students will be able to plan simple, yet reliable, water supply and sanitation systems for developing countries that are compatible with local customs and available human and material resources. Graduate and upper division students from any department who are interested in international development at the grassroots level are encouraged to participate in this interdisciplinary subject. Acknowledgment This course was jointly developed by Earthea Nance and Sus This course deals with the principles of infrastructure planning in developing countries, with a focus on appropriate and sustainable technologies for water and sanitation. It also incorporates technical, socio-cultural, public health, and economic factors into the planning and design of water and sanitation systems. Upon completion, students will be able to plan simple, yet reliable, water supply and sanitation systems for developing countries that are compatible with local customs and available human and material resources. Graduate and upper division students from any department who are interested in international development at the grassroots level are encouraged to participate in this interdisciplinary subject. Acknowledgment This course was jointly developed by Earthea Nance and Sus

Subjects

chemical oceanography | chemical oceanography | biogeochemical cycling | biogeochemical cycling | water column processes | water column processes | ocean particles | ocean particles | seawater composition | seawater composition | ocean particle transport | ocean particle transport | carbon | carbon | oxygen | oxygen | nitrogen | nitrogen | phosphorus | phosphorus | sulfur | sulfur | carbon dioxide | carbon dioxide | sediment chemistry | sediment chemistry

License

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22.105 Electromagnetic Interactions (MIT) 22.105 Electromagnetic Interactions (MIT)

Description

Principles and applications of electromagnetism, starting from Maxwell's equations, with emphasis on phenomena important to nuclear engineering and radiation sciences. Solution methods for electrostatic and magnetostatic fields. Charged particle motion in those fields. Particle acceleration and focussing. Collisions with charged particles and with atoms. Electromagnetic waves, wave emission by accelerated particles, Bremsstrahlung. Compton scattering. Photoionization. Elementary applications to ranging, shielding, imaging, and radiation effects. Principles and applications of electromagnetism, starting from Maxwell's equations, with emphasis on phenomena important to nuclear engineering and radiation sciences. Solution methods for electrostatic and magnetostatic fields. Charged particle motion in those fields. Particle acceleration and focussing. Collisions with charged particles and with atoms. Electromagnetic waves, wave emission by accelerated particles, Bremsstrahlung. Compton scattering. Photoionization. Elementary applications to ranging, shielding, imaging, and radiation effects.

Subjects

electromagnetism | | electromagnetism | | Maxwell's equations | | Maxwell's equations | | electrostatic fields | | electrostatic fields | | magnetostatic fields | | magnetostatic fields | | Charged particle motion | | Charged particle motion | | Particle acceleration | | Particle acceleration | | Electromagnetic waves | | Electromagnetic waves | | Bremsstrahlung | | Bremsstrahlung | | Compton scattering | | Compton scattering | | Photoionization | Photoionization

License

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Astrophysics (MIT) Astrophysics (MIT)

Description

Includes audio/video content: AV selected lectures. Study of physical effects in the vicinity of a black hole as a basis for understanding general relativity, astrophysics, and elements of cosmology. Extension to current developments in theory and observation. Energy and momentum in flat spacetime; the metric; curvature of spacetime near rotating and nonrotating centers of attraction; trajectories and orbits of particles and light; elementary models of the Cosmos. Weekly meetings include an evening seminar and recitation. The last third of the semester is reserved for collaborative research projects on topics such as the Global Positioning System, solar system tests of relativity, descending into a black hole, gravitational lensing, gravitational waves, Gravity Probe B, and more advanced Includes audio/video content: AV selected lectures. Study of physical effects in the vicinity of a black hole as a basis for understanding general relativity, astrophysics, and elements of cosmology. Extension to current developments in theory and observation. Energy and momentum in flat spacetime; the metric; curvature of spacetime near rotating and nonrotating centers of attraction; trajectories and orbits of particles and light; elementary models of the Cosmos. Weekly meetings include an evening seminar and recitation. The last third of the semester is reserved for collaborative research projects on topics such as the Global Positioning System, solar system tests of relativity, descending into a black hole, gravitational lensing, gravitational waves, Gravity Probe B, and more advanced

Subjects

black hole | black hole | general relativity | general relativity | astrophysics | astrophysics | cosmology | cosmology | Energy and momentum in flat spacetime | Energy and momentum in flat spacetime | the metric | the metric | curvature of spacetime near rotating and nonrotating centers of attraction | curvature of spacetime near rotating and nonrotating centers of attraction | trajectories and orbits of particles and light | trajectories and orbits of particles and light | elementary models of the Cosmos | elementary models of the Cosmos | Global Positioning System | Global Positioning System | solar system tests of relativity | solar system tests of relativity | descending into a black hole | descending into a black hole | gravitational lensing | gravitational lensing | gravitational waves | gravitational waves | Gravity Probe B | Gravity Probe B | more advanced models of the Cosmos | more advanced models of the Cosmos | spacetime curvature | spacetime curvature | rotating centers of attraction | rotating centers of attraction | nonrotating centers of attraction | nonrotating centers of attraction | event horizon | event horizon | energy | energy | momentum | momentum | flat spacetime | flat spacetime | metric | metric | trajectories | trajectories | orbits | orbits | particles | particles | light | light | elementary | elementary | models | models | cosmos | cosmos | spacetime | spacetime | curvature | curvature | flat | flat | GPS | GPS | gravitational | gravitational | lensing | lensing | waves | waves | rotating | rotating | nonrotating | nonrotating | centers | centers | attraction | attraction | solar system | solar system | tests | tests | relativity | relativity | general | general | advanced | advanced

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STS.042J Einstein, Oppenheimer, Feynman: Physics in the 20th Century (MIT) STS.042J Einstein, Oppenheimer, Feynman: Physics in the 20th Century (MIT)

Description

This class will study some of the changing ideas within modern physics, ranging from relativity theory and quantum mechanics to solid-state physics, nuclear and elementary particles, and cosmology. These ideas will be situated within shifting institutional, cultural, and political contexts. The overall aim is to understand the changing roles of physics and of physicists over the course of the twentieth century. This class will study some of the changing ideas within modern physics, ranging from relativity theory and quantum mechanics to solid-state physics, nuclear and elementary particles, and cosmology. These ideas will be situated within shifting institutional, cultural, and political contexts. The overall aim is to understand the changing roles of physics and of physicists over the course of the twentieth century.

Subjects

relativity theory | relativity theory | quantum mechanics | quantum mechanics | solid-state physics | solid-state physics | elementary particles | elementary particles | quarks | quarks | cosmology | cosmology | nuclear weapons | nuclear weapons | Maxwell | Maxwell | Mach | Mach | Bohr | Bohr | Heisenberg | Heisenberg | McCarthyism | McCarthyism | Poincar? | Poincar? | Schr?dinger | Schr?dinger | nuclear particles | nuclear particles | physics | physics | 20th century | 20th century | twentieth century | twentieth century | physicists | physicists | institutional | political | cultural context | institutional | political | cultural context | STS.042 | STS.042 | 8.225 | 8.225

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20.462J Molecular Principles of Biomaterials (MIT) 20.462J Molecular Principles of Biomaterials (MIT)

Description

This course covers the analysis and design at a molecular scale of materials used in contact with biological systems, including biotechnology and biomedical engineering. Topics include molecular interactions between bio- and synthetic molecules and surfaces; design, synthesis, and processing approaches for materials that control cell functions; and application of state-of-the-art materials science to problems in tissue engineering, drug delivery, vaccines, and cell-guiding surfaces. This course covers the analysis and design at a molecular scale of materials used in contact with biological systems, including biotechnology and biomedical engineering. Topics include molecular interactions between bio- and synthetic molecules and surfaces; design, synthesis, and processing approaches for materials that control cell functions; and application of state-of-the-art materials science to problems in tissue engineering, drug delivery, vaccines, and cell-guiding surfaces.

Subjects

biomaterials | biomaterials | biomaterial engineering | biomaterial engineering | biotechnology | biotechnology | cell-guiding surface | cell-guiding surface | molecular biomaterials | molecular biomaterials | drug release | drug release | polymers | polymers | pulsatile release | pulsatile release | polymerization | polymerization | polyer erosion | polyer erosion | tissue engineering | tissue engineering | hydrogels | hydrogels | adhesion | adhesion | migration | migration | drug diffusion | drug diffusion | molecular switches | molecular switches | molecular motors | molecular motors | nanoparticles | nanoparticles | microparticles | microparticles | vaccines | vaccines | drug targeting | drug targeting | micro carriers | micro carriers | nano carriers | nano carriers | intracellular drug delivery | intracellular drug delivery | 20.462 | 20.462 | 3.962 | 3.962

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7.341 Designer Immunity: Lessons in Engineering the Immune System (MIT) 7.341 Designer Immunity: Lessons in Engineering the Immune System (MIT)

Description

The immune system is one of the most complex and powerful of human body systems. It is highly dynamic and flexible, yet strictly regulates homeostasis and protects our bodies from both foreign and self-derived challenges. As basic understanding of immune function is growing, researchers are rapidly designing clever and diverse strategies to manipulate immunology to improve human health. In this course, we will explore important advances rooted in engineering principles to harness the power of the immune system, focusing on how engineering has fueled or inspired research concerning (1) vaccines, (2) immunotherapies, and (3) systems immunology. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an The immune system is one of the most complex and powerful of human body systems. It is highly dynamic and flexible, yet strictly regulates homeostasis and protects our bodies from both foreign and self-derived challenges. As basic understanding of immune function is growing, researchers are rapidly designing clever and diverse strategies to manipulate immunology to improve human health. In this course, we will explore important advances rooted in engineering principles to harness the power of the immune system, focusing on how engineering has fueled or inspired research concerning (1) vaccines, (2) immunotherapies, and (3) systems immunology. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an

Subjects

immune system | immune system | immunoengineering | immunoengineering | vaccines | vaccines | immunotherapies | immunotherapies | systems immunology | systems immunology | multivariate profiling | multivariate profiling | regulatory network analyses | regulatory network analyses | vaccine design | vaccine design | immunomodulation | immunomodulation | autoimmunity | autoimmunity | vaccine carriers | vaccine carriers | tolerogenic particle vaccines | tolerogenic particle vaccines | pathogen-mimicking | pathogen-mimicking | lipid nanoparticle vaccines | lipid nanoparticle vaccines

License

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

Description

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

Subjects

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

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13.013J Dynamics and Vibration (MIT) 13.013J Dynamics and Vibration (MIT)

Description

Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms. Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms.

Subjects

umped-parameter models | umped-parameter models | lumped-parameter models | lumped-parameter models | mechanical systems | mechanical systems | Three-dimensional particle kinematics | Three-dimensional particle kinematics | Force-momentum formulation | Force-momentum formulation | Newton-Euler equations | Newton-Euler equations | Work-enery (variational) formulation | Work-enery (variational) formulation | systems particles | systems particles | rigid bodies (indirect method) | rigid bodies (indirect method) | Virtual displacements | Virtual displacements | Lagrange's equations | Lagrange's equations | Linear stability analysis | Linear stability analysis | 1.053J | 1.053J | 13.013 | 13.013 | 1.053 | 1.053

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2.003J Dynamics and Vibration (13.013J) (MIT) 2.003J Dynamics and Vibration (13.013J) (MIT)

Description

Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms. This subject was originally offered in Course 13 (Departm Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-energy (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms. This subject was originally offered in Course 13 (Departm

Subjects

umped-parameter models | umped-parameter models | lumped-parameter models | lumped-parameter models | mechanical systems | mechanical systems | Three-dimensional particle kinematics | Three-dimensional particle kinematics | Force-momentum formulation | Force-momentum formulation | Newton-Euler equations | Newton-Euler equations | Work-enery (variational) formulation | Work-enery (variational) formulation | systems particles | systems particles | rigid bodies (indirect method) | rigid bodies (indirect method) | Virtual displacements | Virtual displacements | Lagrange's equations | Lagrange's equations | Linear stability analysis | Linear stability analysis | 13.013J | 13.013J | 13.013 | 13.013 | 1.053 | 1.053

License

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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

Subjects

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

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8.322 Quantum Theory II (MIT)

Description

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

Subjects

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

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Particle technology and characterisation

Description

This open educational resource was released through the Higher Education Academy Engineering Subject Centre Open Engineering Resources Pilot project. The project was funded by HEFCE and the JISC/HE Academy UKOER programme.

Subjects

ukoer | engscoer | cc-by | engcetl | loughborough university | higher education | learning | loughboroughunioer | engineering | richard holdich | particles | particle technology | spherical diameter | shape factors | specific surface area | size ranges | particle distributions | filtration | Engineering | H000

License

Attribution 2.0 UK: England & Wales Attribution 2.0 UK: England & Wales http://creativecommons.org/licenses/by/2.0/uk/ http://creativecommons.org/licenses/by/2.0/uk/

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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

Subjects

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

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8.033 Relativity (MIT)

Description

Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay.

Subjects

Einstein's postulates | consequences for simultaneity | time dilation | length contraction | clock synchronization | Lorentz transformation | relativistic effects and paradoxes | Minkowski diagrams | invariants and four-vectors | momentum | energy and mass | particle collisions | Relativity and electricity | Coulomb's law | magnetic fields | Newtonian cosmology | General Relativity | principle of equivalence | the Schwarzchild metric | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | particle trajectories | light trajectories | invariants | four-vectors | momentum | energy | mass | relativistic effects | paradoxes | electricity | time dilation | length contraction | clock synchronization | Schwarzchild metric | geodesics | Shaprio delay | relativistic kinematics | relativistic dynamics | electromagnetism | hubble expansion | universe | equivalence principle | curved space time | Ether Theory | constants | speed of light | c | graph | pythagorem theorem | triangle | arrows

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