This course covers the classical partial differential equations of mathematical physics: the heat equation, the Laplace equation, and the wave equation. The primary technique covered in the course is separation of variables, which leads to solutions in the form of eigenfunction expansions. The topics include Fourier series, separation of variables, Sturm-Liouville theory, unbounded domains and the Fourier transform, spherical coordinates and Legendre’s equation, cylindrical coordinates and Bessel’s equation. The software package Mathematica will be used extensively. Prior knowledge of Mathematica is helpful but not essential. In the last two weeks of the course, there will be a project on an assigned topic. The course will include applications in heat conduction, electrostatics, fluid flow, and acoustics.
Basic plasma parameters; quasi-neutrality, Debye length, plasma frequency, plasma parameter, Charged particle motion: orbit theory. Basic plasma equations; derivation of fluid equations from the Vlasov equation. Waves in plasmas. MHD theory. Energy balance.
This is an introduction to turbulence theory and modeling for graduate students in engineering and the physical sciences. This course stresses intuitive physical understanding, mathematical analysis techniques,and numerical methodologies. It will highlight applications in various disciplines, including aeronautics,fusion sciences, geophysics and astrophysics.
This course provides a thorough grounding on the theory and application of linear steady-state finite element method (FEM) applied to solid mechanics. Topics include: review of matrix algebra and solid mechanics, Principle of Minimum Potential Energy, Rayleigh Ritz Method, FEM computational procedures, isoparametric shape functions and numerical integration for 1D, 2D, and 3D elements, error estimation and convergence, and the demonstration of FEM best practices using a commercial FEM code. A semester project that involves coding FEM software in Matlab is required for graduate students.
Course Description: The mechanics of continuous media. The basic notations and concepts in applied mechanics will be covered. These concepts are the foundation for both solid and fluid mechanics and applications in both of these areas will be used as examples. The course will include 1) indicial notation and tensor analysis, 2) concepts of stress, 3) both Eulerian and Lagrangian descriptions of deformation and strain, 4) conservation of mass, momentum, energy, and 5) constitutive equations to describe material response.
This course focuses teaching the multidisciplinary aspects of designing complex, precise systems. In these systems, aspects from mechanics, optics, electronics, design for manufacturing/assembly, and metrology/qualification must all be considered to design, build, and demonstrate a successful precision system. The goal of this class is to develop a fundamental understanding of multidisciplinary design for designing the next generation of advanced instrumentation. This course is open to graduate students in engineering and physics backgrounds although it has a strong emphasis on mechanical engineering and systems engineering topics. This course is open to undergraduates who are in their senior year.
Review of basic thermodynamic quantities and laws; equations of state; statistical mechanics; heat capacity; relations between physical properties; Jacobian algebra; phase transformations, phase diagrams and chemical reactions; partial molal and excess quantities, phases of variable composition; free energy of binary and multicomponent systems; surfaces and interfaces. The emphasis is on the physical and chemical properties of micro and nano solids including stress and strain variables.
In this course, you will apply previously learned theoretical concepts to practical problems and applications. In addition, you will learn experimental techniques and enhance your technical writing skills. This course has two parts, a series of small laboratory exercises and a project. During the semester, students will work in groups of three to complete the assigned work, labs, and reports. The lab section of the course is designed to present basic applied concepts that will be useful to a broad base of engineering problems. The project portion is where you will work on a more specific idea, tailored around your desired future goals.
Description: The mechanical response of crystalline (metals, ceramics, semiconductors)and amorphous solids (glasses, polymers) and their composites in terms of the relationships between stress, strain, damage, fracture, strain-rate, temperature, and microstructure. Topics include: (1) Material structure and property overview. (2) Isotropic and anisotropic elasticity and viscoelasticity. (3) Properties of composites. (4) Plasticity. (5) Point and line defects. (6) Interfacial and volumetric defects. (7) Yield surfaces and flow rules in plasticity of polycrystals and single crystals. (8) Macro and micro aspects of fractures in metals, ceramics and polymers.(9) Creep and superplasticity. (10) Deformation and fracture mechanism maps. (11) Fatigue damage and failure; fracture and failure in composites (If time permits).
In this course, we will survey the role of mechanics in cells, tissues, organs and organisms. A particular emphasis will be placed on the mechanics of the musculoskeletal system, the circulatory system and the eye. Engineering concepts will be used to understand how physical forces contribute to biological processes, especially disease and healing. Experimental and modeling techniques for characterizing the complex mechanical response of biosolids will be discussed in detail, and the continuum mechanics approach will highlighted.
COLLINS G; RYGG R
This course will survey the field of high-energy-density science (HEDS), extending from ultra-dense matter to the radiation-dominated regime. Topics include: experimental and computational methods for the productions, manipulation, and diagnosis of HED matter, thermodynamic equations-of-state; dynamic transitions between equilibrium phases; and radiative and other transport properties. Throughout the course, we will make connections with key HEDS applications in astrophysics, laboratory fusion, and new quantum states of matter.
Introduction to probability theory, stochastic processes, and statistical continuum theory. Experimental facts of turbulent motion. Kinematics and dynamics of homogeneous turbulence. Isotropic turbulence. The closure problem. Hopf's functional formalism and its generalizations. Mixing-length and phenomenological theories. Turbulent shear flows. Transition from laminar to turbulent flow. The general concepts of stability theory.