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

Theoretical topics of fluid dynamics relevant to natural phenomena or man-made hazards in water and atmosphere. Basic law of fluid motion. Scaling and approximations. Slow flows, with applications to drag on a particle and mud flow on a slope. Boundary layers: jets and plumes in pure fluids or in porous media. Thermal and buoyancy effects, selective withdrawal and internal waves. Transient boundary layers in impulsive flows or waves. Induced streaming and mass transport. Dispersion in steady flows or in waves. Effects of earth rotation on coastal flows. Wind induced flow in shallow seas. Stratified seas and coastal upwelling.

The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.

The index of refraction in a material isn't always the same for every wavelength. This is how prisms split white light into so many colors. Created by David SantoPietro.

This course covers fundamentals of subsurface flow and transport, emphasizing the role of groundwater in the hydrologic cycle, the relation of groundwater flow to geologic structure, and the management of contaminated groundwater. The class includes laboratory and computer demonstrations.

Fundamentals of subsurface flow and transport, emphasizing the role of groundwater in the hydrologic cycle, the relation of groundwater flow to geologic structure, and the management of contaminated groundwater. Topics include: Darcy equation, flow nets, mass conservation, the aquifer flow equation, heterogeneity and anisotropy, storage properties, regional circulation, unsaturated flow, recharge, stream-aquifer interaction, well hydraulics, flow through fractured rock, numerical models, groundwater quality, contaminant transport processes, dispersion, decay, and adsorption. Includes laboratory and computer demonstrations.

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"It took scientists more than 25 years to work out the structure of silicon’s 7x7 surface reconstruction. Since reaching that milestone, experimental and theoretical studies have supported that this reconstruction produces a conductive, metallic surface. But new data gathered by an international team of researchers from Spain, the Philippines, France, and the United Kingdom say otherwise—a contradiction that could have technological implications for the integration of 2D silicon into electronic devices. The most widely accepted picture of silicon 111 ’s 7x7 surface reconstruction is the so-called dimer-adatom-stacking fault model. Here, dangling bonds produced by cleaving the bulk crystal occur on silicon adatoms, which are bonded to underlying bulk-silicon atoms, and on rest atoms in the lower layer. The rearrangement of charge associated with this structure produces an odd number of electrons, which implies that the surface should be metallic..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.

This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport.

This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport.

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