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So, we can conclude that an ion means an atom with the same number of protons, but a different number of electrons. You have to detect different isotopes by comparing their atomic masses. Anyway, to summarize, an isotope refers to the number of neutrons in an atom; an ion refers to the number of electrons. Human body temperature is about K At what wavelength do humans radiate the most energy? What kind of radiation do we emit? Because humans are made mostly out of really dense matter water, bones, etc.

Fortunately they gave us T in Kelvin already, so we can just plug it in:. Looking on a diagram of the electromagnetic spectrum like the one on p. First of all, to start fusion, the material needs to be very hot. Think about the definition of temperature as the speed with which atoms and molecules in a material are moving around. The hotter the gas, the faster the molecules are going.

This is important because to overcome the force repelling two positive hydrogen nuclei really just two protons so they can fuse, they need to hit each other at huge speeds. Anyway, they have to be really going fast in order that they can get close enough together that an even stronger, attractive force known creatively as the "strong force" pulls them together and they fuse into a helium nucleus. The second condition is that the material has to be very dense. By making the material denser, you increase the probability that the protons will run into each other at all.

So you need something really dense, with lots and lots of nuclei around, before you get enough of them running into each other to get a reasonable rate of fusion. So where in the Sun do these two conditions meet up? As you get closer and closer to the center of the Sun, the amount of stuff pressing inward due to gravity, which wants to make everything collapse into a point at the center gets larger and larger, so the pressure and therefore the density goes up.

The temperature goes up as well - based on what we know about gases, pressure and temperature are proportional to one another. In fact, the temperature at the very center of our Sun is only around 15 million Kelvin, so only right at the center is it hot enough and dense enough for fusion to occur. Convert your answer into degrees Fahrenheit. Note that in Wien's law, the wavelength must be expressed in micrometers not in meters and the temperature is in Kelvin then you can transform Kelvin temperature into Fahrenheit or Celsius.

Also, you were welcome to use the formula from the book, but we warned you that the units were different than the formula we gave you in lecture. What is the wavelength of maximum emission by the surface of Mars? Assume that Mars behaves like a blackbody. Express your answer in both micrometers microns and meters. Assume that all of these gases are present in the Martian atmosphere in concentrations similar to those found on Earth. Water vapor: absorbs mainly at 2.

Methane: absorbs mainly at 2. Nitrous oxide: absorbs mainly at 4. Since the surface of Mars emits infrared radiation with maximum wavelength of emission around 15 m m, carbon dioxide will be a good absorber of the radiation emitted by the planet.

It will radiate some of this energy back to the surface and thus provide a greenhouse effect on Mars. The mass of the ice is exactly kg kilograms. You turn on a heater underneath the tank, and the tank conducts heat from the heater to the ice inside of the tank, melting some of the ice. You need 3. Then you need 1, times as much energy to melt 1, kilograms of ice, or 3.

Once again, you turn on the heater underneath the tank. Hint: the specific heat of liquid water is approximately 1 calorie per gram per degree Celsius, or 4. Note that the change in temperature is 30K. Heat is a measure of the total internal kinetic energy. In 1, kg of water, there are many more molecules than in 50 kg of water, and consequently more total internal kinetic energy, thus more heat.

Although this is not wrong by itself, it is not the correct answer to the question. Convert all your answers into degrees Celsius and degrees Kelvin. April: S. July: S. Convert your answer into meters Hint: one inch equals approximately 2. This is the amount of precipitation received in each city during a typical year.

We did not ask you to compute the average monthly precipitation in each city, but you were not penalized if you did this instead. To convert inches into centimeters, multiply by 2. This gives you Since there are centimeters in one meter, this corresponds to about 1. Don't include too many significant figures in this computation.

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Examples of projects include surveying a lake for millfoil, from a remote controlled aircraft, and then sending out robotic harvesters to clear the invasive growth; and exploration to search for the evidence of life on a moon of Jupiter, with scientists participating through teleoperation and supervisory control of robots.

In person not required. Enrollment limited; preference to freshmen. Prereq: None U Spring units. Provides students with an overview of design for entertainment and play, as well as opportunities in creative product design and community service. Students develop ideas for new toys that serve clients in the community, and work in teams with local sponsors and with experienced mentors on a themed toy design project. Students enhance creativity and experience fundamental aspects of the product development process, including determining customer needs, brainstorming, estimation, sketching, sketch modeling, concept development, design aesthetics, detailed design, and prototyping.

Includes written, visual, and oral communication. Same subject as 1. Students work in small groups, under the guidance of researchers from MIT, to pursue specific aspects of the year's Terrascope problem. Teams design and build prototypes, graphic displays and other tools to communicate their findings and display them in a Bazaar of Ideas open to the MIT community.

Some teams develop particular solutions, others work to provide deeper understanding of the issues, and others focus on ways to communicate these ideas with the general public. Students' work is evaluated by independent experts.

Offers students an opportunity to develop ideas from the fall semester and to work in labs across MIT. Limited to first-year students. Prereq: None U Fall; second half of term units. Project-based introduction to product development and engineering design. Emphasizes key elements of the design process, including defining design problems, generating ideas, and building solutions. Presents a range of design techniques to help students think about, evaluate, and communicate designs, from sketching to physical prototyping, as well as other types of modeling.

Students work both individually and in teams. Enrollment limited; preference to Course 2-A sophomores. Reviews research opportunities and undergraduate major options in Course 2 as well as a variety of career paths pursued by alumni. Subject can count toward the 9-unit discovery-focused credit limit for first year students. Introduction to statics and the mechanics of deformable solids.

Emphasis on the three basic principles of equilibrium, geometric compatibility, and material behavior. Stress and its relation to force and moment; strain and its relation to displacement; linear elasticity with thermal expansion.

Failure modes. Application to simple engineering structures such as rods, shafts, beams, and trusses. Application to biomechanics of natural materials and structures. Socrate, M. Culpepper, D. Parks, K. Prereq: Chemistry GIR and 2. Introduces mechanical behavior of engineering materials, and the use of materials in mechanical design.

Emphasizes the fundamentals of mechanical behavior of materials, as well as design with materials. Major topics: elasticity, plasticity, limit analysis, fatigue, fracture, and creep. Materials selection. Laboratory experiments involving projects related to materials in mechanical design. Enrollment may be limited due to laboratory capacity; preference to Course 2 majors and minors.

Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange's equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems.

Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Vandiver, N. Makris, N. Patrikalakis, T. Peacock, D. Gossard, K. Modeling, analysis, and control of dynamic systems. System modeling: lumped parameter models of mechanical, electrical, and electromechanical systems; interconnection laws; actuators and sensors. Linear systems theory: linear algebra; Laplace transform; transfer functions, time response and frequency response, poles and zeros; block diagrams; solutions via analytical and numerical techniques; stability.

Introduction to feedback control: closed-loop response; PID compensation; steady-state characteristics, root-locus design concepts, frequency-domain design concepts. Laboratory experiments and control design projects. Integrated development of the fundamental principles of thermodynamics, fluid mechanics, and heat transfer, with applications. Focuses on the first and second laws of thermodynamics, mass conservation, and momentum conservation, for both closed and open systems.

Entropy generation and its influence on the performance of engineering systems. Introduction to dimensionless numbers. Introduction to heat transfer: conduction, convection, and radiation. Steady-state and transient conduction. Finned surfaces. The heat equation and the lumped capacitance model. Coupled and uncoupled fluid models. Inviscid flow analysis and Bernoulli equation. Navier-Stokes equation and its solutions. Viscous internal flows, head losses, and turbulence.

Introduction to pipe flows and Moody chart. Prereq: 2. Focuses on the application of the principles of thermodynamics, heat transfer, and fluid mechanics to the design and analysis of engineering systems. Dimensional analysis, similarity, and modeling. Pipe systems: major and minor losses. Laminar and turbulent boundary layers. Boundary layer separation, lift and drag on objects.

Heat transfer associated with laminar and turbulent flow of fluids in free and forced convection in channels and over surfaces. Pure substance model. Heat transfer in boiling and condensation. Thermodynamics and fluid mechanics of steady flow components of thermodynamic plants. Heat exchanger design. Power cycles and refrigeration plants. Design of thermodynamic plants. Analyses for alternative energy systems. Multi-mode heat transfer and fluid flow in thermodynamic plants. Develops students' competence and self-confidence as design engineers.

Emphasis on the creative design process bolstered by application of physical laws. Instruction on how to complete projects on schedule and within budget. Robustness and manufacturability are emphasized. Subject relies on active learning via a major design-and-build project.

Lecture topics include idea generation, estimation, concept selection, visual thinking, computer-aided design CAD , mechanism design, machine elements, basic electronics, technical communication, and ethics. Lab fee. Limited enrollment. Pre-registration required for lab assignment; special sections by lottery only. Partial Lab. Integration of design, engineering, and management disciplines and practices for analysis and design of manufacturing enterprises.

Emphasis is on the physics and stochastic nature of manufacturing processes and systems, and their effects on quality, rate, cost, and flexibility. Topics include process physics and control, design for manufacturing, and manufacturing systems.

Group project requires design and fabrication of parts using mass-production and assembly methods to produce a product in quantity. Six units may be applied to the General Institute Lab Requirement. Satisfies 6 units of Institute Laboratory credit. Chun, J. Hart, S. Kim, J. Liu, W. Seering, D. Students develop an understanding of product development phases and experience working in teams to design and construct high-quality product prototypes. Design process learned is placed into a broader development context.

Primary goals are to improve ability to reason about design alternatives and apply modeling techniques appropriate for different development phases; understand how to gather and process customer information and transform it into engineering specifications; and use teamwork to resolve the challenges in designing and building a substantive product prototype. Instruction and practice in oral communication provided. Enrollment may be limited due to laboratory capacity; preference to Course 2 seniors.

Subject meets with 2. Emphasizes individual initiative, application of fundamental principles, and the compromises inherent in the engineering design process. Culminates in the design of an engineering system, typically a vehicle or other complex system. Includes instruction and practice in written and oral communication through team presentations, design reviews, and written reports.

Students taking graduate version complete additional assignments. Focuses on implementation and operation of engineering systems. Emphasizes system integration and performance verification using methods of experimental inquiry. Students refine their subsystem designs and the fabrication of working prototypes. Includes experimental analysis of subsystem performance and comparison with physical models of performance and with design goals.

Component integration into the full system, with detailed analysis and operation of the complete vehicle in the laboratory and in the field. Includes written and oral reports. Students carry out formal reviews of the overall system design.

Instruction and practice in oral and written communication provided. Covers fundamental principles of fluid mechanics and applications to practical ocean engineering problems. Basic geophysical fluid mechanics, including the effects of salinity, temperature, and density; heat balance in the ocean; large scale flows.

Linear free surface waves, wave forces on floating and submerged structures. Added mass, lift and drag forces on submerged bodies. Includes final project on current research topics in marine hydrodynamics. Design, construction, and testing of field robotic systems, through team projects with each student responsible for a specific subsystem.

Projects focus on electronics, instrumentation, and machine elements. Design for operation in uncertain conditions is a focus point, with ocean waves and marine structures as a central theme. Basic statistics, linear systems, Fourier transforms, random processes, spectra and extreme events with applications in design. Lectures on ethics in engineering practice included. Enrollment may be limited due to laboratory capacity.

Complete cycle of designing an ocean system using computational design tools for the conceptual and preliminary design stages. Team projects assigned, with each student responsible for a specific subsystem. Lectures cover hydrodynamics; structures; power and thermal aspects of ocean vehicles, environment, materials, and construction for ocean use; generation and evaluation of design alternatives.

Focus on innovative design concepts chosen from high-speed ships, submersibles, autonomous vehicles, and floating and submerged deep-water offshore platforms. Chryssostomidis, M. Provides an introduction to thermodynamics, including first law coupled and uncoupled systems, incompressible liquid, ideal gas and second law equilibrium, reversibility and irreversibility.

Explores systems in communication with heat reservoirs; quasi-static processes; and heat engines and refrigeration. Properties of open systems, including mass, energy and entropy transfer. Introduces fundamental processes of heat transfer. Fourier's law. Heat conduction processes including thermal resistance, lumped capacitance, fins, and the heat equation. Elementary convection, including laminar and turbulent boundary layers, internal flow, and natural convection.

Thermal radiation, including Stefan-Boltzmann law, small object in large enclosure, and parallel plates. Basic concepts of heat exchangers. Introduction to principal concepts and methods of fluid mechanics. Pressure, hydrostatics, and buoyancy. Control volume analysis. Mass conservation and momentum conservation for moving fluids. Viscous fluid flows, flow through pipes. Dimensional analysis. Boundary layers, and lift and drag on objects.

Covers elementary programming concepts, including variable types, data structures, and flow control. Provides an introduction to linear algebra and probability. Numerical methods relevant to MechE, including approximation interpolation, least squares, and statistical regression , integration, solution of linear and nonlinear equations, and ordinary differential equations.

Presents deterministic and probabilistic approaches. Uses examples from MechE, particularly from robotics, dynamics, and structural analysis. Frey, F. Hover, N. Introduction to linear algebra and ordinary differential equations ODEs , including general numerical approaches to solving systems of equations. Linear systems of equations, existence and uniqueness of solutions, Gaussian elimination. Initial value problems, 1st and 2nd order systems, forward and backward Euler, RK4.

Eigenproblems, eigenvalues and eigenvectors, including complex numbers, functions, vectors and matrices. Review of momentum principles. Hamilton's principle and Lagrange's equations. Three-dimensional kinematics and dynamics of rigid bodies. Study of steady motions and small deviations therefrom, gyroscopic effects, causes of instability. Free and forced vibrations of lumped-parameter and continuous systems. Nonlinear oscillations and the phase plane.

Nonholonomic systems. Introduction to wave propagation in continuous systems. Akylas, T. Peacock, N. See description under subject 1. A unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems.

Nonlinear free and forced vibrations; nonlinear resonances; self-excited oscillations; lock-in phenomena. Nonlinear dispersive and nondispersive waves; resonant wave interactions; propagation of wave pulses and nonlinear Schrodinger equation.

Nonlinear long waves and breaking; theory of characteristics; the Korteweg-de Vries equation; solitons and solitary wave interactions. Stability of shear flows. Some topics and applications may vary from year to year. Same subject as See description under subject Theoretical concepts and analysis of wave problems in science and engineering with examples chosen from elasticity, acoustics, geophysics, hydrodynamics, blood flow, nondestructive evaluation, and other applications.

Progressive waves, group velocity and dispersion, energy density and transport. Reflection, refraction and transmission of plane waves by an interface. Mode conversion in elastic waves. Rayleigh waves. Waves due to a moving load. Scattering by a two-dimensional obstacle. Reciprocity theorems. Parabolic approximation.

Waves on the sea surface. Capillary-gravity waves. Wave resistance. Radiation of surface waves. Internal waves in stratified fluids. Waves in rotating media. Waves in random media. Introduces the fundamental concepts of acoustics and sensing with waves. Provides a unified theoretical approach to the physics of image formation through scattering and wave propagation in sensing. The linear and nonlinear acoustic wave equation, sources of sound, including musical instruments.

Reflection, refraction, transmission and absorption. Bearing and range estimation by sensor array processing, beamforming, matched filtering, and focusing. Diffraction, bandwidth, ambient noise and reverberation limitations. Scattering from objects, surfaces and volumes by Green's Theorem. Forward scatter, shadows, Babinet's principle, extinction and attenuation.

Ray tracing and waveguides in remote sensing. Applications to acoustic, radar, seismic, thermal and optical sensing and exploration. Students taking the graduate version complete additional assignments. Students taking the graduate version of the subject complete additional assignments.

Fundamentals of solid mechanics applied to the mechanical behavior of engineering materials. Kinematics of deformation, stress, and balance principles. Isotropic linear elasticity and isotropic linear thermal elasticity. Variational and energy methods. Linear viscoelasticity. Small-strain elastic-plastic deformation. Mechanics of large deformation; nonlinear hyperelastic material behavior. Foundations and methods of deformable-solid mechanics, including relevant applications.

Provides base for further study and specialization within solid mechanics, including continuum mechanics, computational mechanics e. Principles and applications of continuum mechanics. Kinematics of deformation. Thermomechanical conservation laws. Stress and strain measures. Constitutive equations including some examples of their microscopic basis. Solution of some basic problems for various materials as relevant in materials science, fluid dynamics, and structural analysis.

Inherently nonlinear phenomena in continuum mechanics. Variational principles. Continuum constitutive models for small and large deformation of elastic- visco plastic solids. Analytical and numerical solution of selected boundary value problems. Applications to deformation processing of metals.

Introduction to the theory and applications of nonlinear and linear elasticity. Strain, stress, and stress-strain relations. Several of the following topics: Spherically and cylindrically symmetric problems. Anisotropic material behavior. Piezoelectric materials. Effective properties of composites. Structural mechanics of beams and plates. Energy methods for structures.

Two-dimensional problems. Stress concentration at cavities, concentrated loads, cracks, and dislocations. Variational methods and their applications; introduction to the finite element method. Introduction to wave propagation. Prereq: None G Fall units. Covers a number of fundamental topics in the emerging field of soft and active materials, including polymer mechanics and physics, poroelasticity, viscoelasticity, and mechanics of electro-magneto-active and other responsive polymers.

Lectures, recitations, and experiments elucidate the basic mechanical and thermodynamic principles underlying soft and active materials. Develops an understanding of the fundamental mechanisms for designing soft materials that possess extraordinary properties, such as stretchable, tough, strong, resilient, adhesive and responsive to external stimuli, from molecular to bulk scales. Applies solid mechanics fundamentals to the analysis of marine, civil, and mechanical structures.

Continuum concepts of stress, deformation, constitutive response and boundary conditions are reviewed in selected examples. The principle of virtual work guides mechanics modeling of slender structural components e. Introduction to elastic stability. Material limits to stress in design.

Variational methods for computational structural mechanics analysis. Stress-strain relations for plate and shell elements. Differential equations of equilibrium. Energy methods and approximate solutions. Bending and buckling of rectangular plates. Post-buckling and ultimate strength of cold formed sections and typical stiffened panels used in aerospace, civil, and mechanical engineering; offshore technology; and ship building. Geometry of curved surfaces. General theory of elastic, axisymmetric shells and their equilibrium equations.

Buckling, crushing and bending strength of cylindrical shells with applications. Propagation of 1-D elastic waves in rods, geometrical and material dispersion. Plane, Rayleigh surface, and 3-D waves. Response of plates and shells to high-intensity loads. Dynamic plasticity and fracture. Application to crashworthiness and impact loading of structures. Design application of analysis developed in 2.

Ship longitudinal strength and hull primary stresses. Ship structural design concepts. Design limit states including plate bending, column and panel buckling, panel ultimate strength, and plastic analysis. Matrix stiffness, and introduction to finite element analysis. Computer projects on the structural design of a midship module. Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, sweeps and generalized cylinders, offsets, blending and filleting surfaces.

Non-linear solvers and intersection problems. Solid modeling: constructive solid geometry, boundary representation, non-manifold and mixed-dimension boundary representation models, octrees. Robustness of geometric computations. Interval methods. Finite and boundary element discretization methods for continuum mechanics problems. Scientific visualization.

Variational geometry. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments. Ordinary differential equation boundary value problems: 2nd-order and 4th-order spatial operators, eigenproblems.

Partial differential equations: elliptic, parabolic, hyperbolic. Strong statement, weak form, minimization principle as appropriate. Rayleigh-Ritz and Galerkin approximation. Numerical interpolation, integration, and differentiation. Finite element method for spatial discretization: formulation, bases and discrete equations, a priori and a posteriori error estimates, sparse solvers, implementation and testing.

Finite difference methods for temporal discretization of mixed initial-boundary value problems. Projects focus on applications in heat transfer and structural analysis. Same subject as 6. See description under subject 6. Variational framework: strong form, weak form, energy. Variational approximation: Rayleigh-Ritz, Galerkin. Finite element method: approximation spaces; discrete equations; solution techniques; implementation; a priori and a posteriori error estimates; SPD eigenproblems.

Components and direct stiffness assembly. Method of lines: heat equation, second-order wave equation. Advanced topics: constrained problems, nonlinear problems, reduced basis methods. Applications: elasticity, heat transfer, acoustics, incompressible flow. Explores the ultimate limits to communication and computation, with an emphasis on the physical nature of information and information processing. Topics include information and computation, digital signals, codes, and compression.

Biological representations of information. Logic circuits, computer architectures, and algorithmic information. Noise, probability, and error correction. The concept of entropy applied to channel capacity and to the second law of thermodynamics. Reversible and irreversible operations and the physics of computation.

Quantum computation. Same subject as 8. Chuang, A. Harrow, S. Lloyd, P. Cross-disciplinary studies in robot mechanics and intelligence. Emphasizes physical understanding of robot kinematics and dynamics, differential motion and energy method, design and control of robotic arms and mobile robots, and actuators, drives, and transmission. Second half of course focuses on algorithmic thinking and computation, computer vision and perception, planning and control for manipulation, localization and navigation, machine learning for robotics, and human-robot systems.

Weekly laboratories include brushless DC motor control, design and fabrication of robotic arms and vehicles, robot vision and navigation, and programming and system integration using Robot Operating System ROS. Group term project builds intelligent robots for specific applications of interest. Coreq: 2. Response of systems to stochastic excitation with design applications. Linear time-invariant systems, convolution, Fourier and Laplace transforms. Probability and statistics. Discrete and continuous random variables, derived distributions.

Stochastic processes, auto-correlation. Stationarity and ergodicity, power spectral density. Systems driven by random functions, Wiener-Khinchine theorem. Sampling and filtering. Short- and long-term statistics, statistics of extremes. Students taking graduate version complete additional assignments and a short-term project. Sapsis, M. Provides training in advanced instrumentation and measurement techniques. Topics include system level design, fabrication and evaluation with emphasis on systems involving concepts and technology from mechanics, optics, electronics, chemistry and biology.

Simulation, modeling and design software. Theory and practice of both linear and nonlinear system identification techniques. Lab sessions include instruction and group project work. No final exam. Develops the fundamentals of feedback control using linear transfer function system models.

Analysis in time and frequency domains. Design in the s-plane root locus and in the frequency domain loop shaping. Describing functions for stability of certain non-linear systems. Extension to state variable systems and multivariable control with observers. Discrete and digital hybrid systems and use of z-plane design. Extended design case studies and capstone group projects. Student taking graduate version complete additional assignments. Rowell, D. Trumper, K. Modeling multidomain engineering systems at a level of detail suitable for design and control system implementation.

Network representation, state-space models; multiport energy storage and dissipation, Legendre transforms; nonlinear mechanics, transformation theory, Lagrangian and Hamiltonian forms; Control-relevant properties. Application examples may include electro-mechanical transducers, mechanisms, electronics, fluid and thermal systems, compressible flow, chemical processes, diffusion, and wave transmission.

Analytical descriptions of state-determined dynamic physical systems; time and frequency domain representations; system characteristics - controllability, observability, stability; linear and nonlinear system responses. Modification of system characteristics using feedback. State observers, Kalman filters. Basic optimization tools. Positive systems. Emphasizes applications to physical systems.

Slotine, K. Youcef-Toumi, N. Same subject as 9. Introduction to nonlinear control and estimation in physical and biological systems. Nonlinear stability theory, Lyapunov analysis, Barbalat's lemma. Feedback linearization, differential flatness, internal dynamics. Sliding surfaces. Adaptive nonlinear control and estimation. Multiresolution bases, nonlinear system identification. Contraction analysis, differential stability theory.

Nonlinear observers. Asynchronous distributed computation and learning. Concurrent synchronization, polyrhythms. Monotone nonlinear systems. Emphasizes application to physical systems robots, aircraft, spacecraft, underwater vehicles, reaction-diffusion processes, machine vision, oscillators, internet , machine learning, computational neuroscience, and systems biology.

Includes term projects. Lays the foundation of adaptive control, and investigates its interconnections with machine learning. Explores fundamental principles of adaptive control, including parameter estimation, recursive algorithms, stability properties, and conditions for convergence. Studies their relationship with machine learning, including the minimization of a performance error and fast convergence. Discusses robustness and regularization in both fields.

Derives conditions of learning and implications of imperfect learning. Examines the trade-off between stability and learning. Focuses throughout the term on dynamic systems and on problems where real-time control is needed. Uses examples from aerospace, propulsion, automotive, and energy systems to elucidate the underlying concepts. Maneuvering motions of surface and underwater vehicles. Derivation of equations of motion, hydrodynamic coefficients.

Memory effects. Linear and nonlinear forms of the equations of motion. Control surfaces modeling and design. Engine, propulsor, and transmission systems modeling and simulation during maneuvering. Stability of motion. Principles of multivariable automatic control. Optimal control, Kalman filtering, loop transfer recovery. Term project: applications chosen from autopilots for surface vehicles; towing in open seas; remotely operated vehicles.

Introduces fundamental concepts and encourages open-ended exploration of the increasingly topical intersection between artificial intelligence and the physical sciences. Energy and information, and their respective optimality conditions are used to define supervised and unsupervised learning algorithms; as well as ordinary and partial differential equations.

Subsequently, physical systems with complex constitutive relationships are drawn from elasticity, biophysics, fluid mechanics, hydrodynamics, acoustics, and electromagnetics to illustrate how machine learning-inspired optimization can approximate solutions to forward and inverse problems in these domains. Provides a broad theoretical basis for system identification, estimation, and learning. Least squares estimation and its convergence properties, Kalman filter and extended Kalman filter, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.

Introduction to robotics and learning in machines. Kinematics and dynamics of rigid body systems. Adaptive control, system identification, sparse representations. Force control, adaptive visual servoing. Task planning, teleoperation, imitation learning. Underactuated systems, approximate optimization and control. Dynamics of learning and optimization in networks. Elements of biological planning and control.

Motor primitives, entrainment, active sensing, binding models. Term projects. Prereq: 6. Theory and application of probabilistic techniques for autonomous mobile robotics. Topics include probabilistic state estimation and decision making for mobile robots; stochastic representations of the environment; dynamic models and sensor models for mobile robots; algorithms for mapping and localization; planning and control in the presence of uncertainty; cooperative operation of multiple mobile robots; mobile sensor networks; application to autonomous marine underwater and floating , ground, and air vehicles.

A comprehensive introduction to digital control system design, reinforced with hands-on laboratory experiences. Major topics include discrete-time system theory and analytical tools; design of digital control systems via approximation from continuous time; direct discrete-time design; loop-shaping design for performance and robustness; state-space design; observers and state-feedback; quantization and other nonlinear effects; implementation issues.

Laboratory experiences and design projects connect theory with practice. Provides a review of biology concepts, regulation mechanisms, and models. Covers basic enabling technologies, engineering principles for designing biological functions, modular design techniques, and design limitations. Presents a quantitative description of how biomechanical and neural factors interact in human sensory-motor behavior.

Students survey recent literature on how motor behavior is controlled, comparing biological and robotic approaches to similar tasks. Topics may include a review of relevant neural, muscular and skeletal physiology, neural feedback and "equilibrium-point" theories, co-contraction strategies, impedance control, kinematic redundancy, optimization, intermittency, contact tasks and tool use. Prereq: 1. The fundamentals of fluid mechanics are developed in the context of naval architecture and ocean science and engineering.

Transport theorem and conservation principles. Navier-Stokes' equation. Ideal and potential flows. Vorticity and Kelvin's theorem. Hydrodynamic forces in potential flow, D'Alembert's paradox, added-mass, slender-body theory. Viscous-fluid flow, laminar and turbulent boundary layers. Model testing, scaling laws. Linearized theory of lifting surfaces. Experimental project in the towing tank or propeller tunnel.

Design tools for analysis of linear systems and random processes related to ocean vehicles; description of ocean environment including random waves, ocean wave spectra and their selection; short-term and long-term wave statistics; and ocean currents. Advanced hydrodynamics for design of ocean vehicles and offshore structures, including wave forces on towed and moored structures; inertia vs.

Design exercises in application of principles. Laboratory exercises in seakeeping and VIV at model scale. Reviews the theory and design of hydrofoil sections; lifting and thickness problems for sub-cavitating sections and unsteady flow problems. Covers lifting line and lifting surface theory with applications to hydrofoil craft, rudder, control surface, propeller and wind turbine rotor design.

Topics include propeller lifting line and lifting surface theory; wake adapted propellers, steady and unsteady propeller thrust and torque; waterjets; performance analysis and design of wind turbine rotors. Presents numerical principles of vortex lattice and lifting surface panel methods. Projects illustrate the development of theoretical and computational methods for lifting, propulsion and wind turbine applications. Surface wave theory, conservation laws and boundary conditions, properties of regular surface waves and random ocean waves.

Linearized theory of floating body dynamics, kinematic and dynamic free surface conditions, body boundary conditions. Simple harmonic motions. Diffraction and radiation problems, added mass and damping matrices. General reciprocity identities on diffraction and radiation. Ship wave resistance theory, Kelvin wake physics, ship seakeeping in regular and random waves.

Discusses point wave energy absorbers, beam sea and head-sea devises, oscillating water column device and Well's turbine. Discusses offshore floating energy systems and their interaction with ambient waves, current and wind, including oil and gas platforms, liquefied natural gas LNG vessels and floating wind turbines.

Homework drawn from real-world applications. Survey of principal concepts and methods of fluid dynamics. Mass conservation, momentum, and energy equations for continua. Navier-Stokes equation for viscous flows. Similarity and dimensional analysis. Lubrication theory. Boundary layers and separation. Circulation and vorticity theorems. Potential flow. Introduction to turbulence. Lift and drag. Surface tension and surface tension driven flows.

Ghoniem, A. Hosoi, G. McKinley, A. Discusses a range of topics and advanced problem-solving techniques. Sample topics include brief review of basic laws of fluid motion, scaling and approximations, creeping flows, boundary layers in high-speed flows, steady and transient, similarity method of solution, buoyancy-driven convection in porous media, dispersion in steady or oscillatory flows, physics and mathematics of linearized instability, effects of shear and stratification.

Akylas, G. McKinley, R. Fundamentals and modeling of reacting gas dynamics and combustion using analytical and numerical methods. Conservation equations of reacting flows. Multi-species transport, chemical thermodynamics and chemical kinetics. Non-equilibrium flow. Detonation and reacting boundary layers. Ignition, flammability, and extinction. Premixed and diffusion flames. Combustion instabilities. Supersonic combustion. Turbulent combustion. Liquid and solid burning. Fire, safety, and environmental impact.

Applications to power and propulsion. Direct and iterative methods for linear systems. Finite differences for elliptic, parabolic and hyperbolic equations. Fourier decomposition, error analysis and stability. High-order and compact finite-differences. Finite volume methods.

Time marching methods. Navier-Stokes solvers. Grid generation. Finite volumes on complex geometries. Finite element methods. Order your assignment today, we will be happy to assist you. Proceed to order page. All custom-written essays, research papers, speeches, book reviews, and other custom task completed by our writers are both of high quality and cheap.

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Revision Lecture 2 - Black Body radiation Sample Problems

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