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.

This course provides a deep understanding of engineering systems at a level intended for research on complex engineering systems. It provides a review and extension of what is known about system architecture and complexity from a theoretical point of view while examining the origins of and recent developments in the field. The class considers how and where the theory has been applied, and uses key analytical methods proposed. Students examine the level of observational (qualitative and quantitative) understanding necessary for successful use of the theoretical framework for a specific engineering system. Case studies apply the theory and principles to engineering systems.

Student use scaling to obtain an idea of the immense size of Mars in relation to the Earth and the Moon, as well as the distances between them. Students calculate dimensions of the scaled versions of the planets, and then use balloons to represent their relative sizes and locations.

Many intriguing phenomena observed in the "nanoworld" can be attributed to the increase in the surface to volume ratio ( SVR ) at the nanoscale. Understanding the surface area effects to volume changes is thus crucial to the understanding of nanoscale phenomena and nanotechnology applications. As an introduction to the nanoworld, the major goals of this module are to (1) give students a feel for just how small the nanoscale is, (2) give students practice in mathematically communicating nanoscale quantities and relating them to the familiar macroscale, (3) show students that there are different ways to be small (three-, two-, and one-dimensionally), and (4) illustrate the first and foremost property that increases in importance at the nanoscale, viz., surface area. Activity 1 presents some intriguing phenomena that pique student interest in surface area effects, i.e., how physical form of a solid influences the degree to which it interacts with its environment. They find that the more spread out a solid is, the more readily it interacts. In Activity 2, two important mathematical tools are reintroduced into the student scientists' toolbox, namely, powers of 10 and scaling. Students learn to deal with powers of 10 and scale (both linear and the surprises that sometimes result when things do not scale linearly) to represent the magnitudes involved with the nanoscale. In the third activity, students then determine the relationship of the SVR changes with the shape or size of an object. They learn that this ratio changes dramatically in the nanoscale. The challenge in the culminating design project is to introduce a finely divided (high surface area) material in a carbonated beverage that will create the highest liquid geyser possible. The class also has an option to end with playing a "nano-concept" game that will help students review the foundational knowledge about the nanoscale.

This course provides an introduction to the study of environmental phenomena that exhibit both organized structure and wide variability---i.e., complexity. Through focused study of a variety of physical, biological, and chemical problems in conjunction with theoretical models, we learn a series of lessons with wide applicability to understanding the structure and organization of the natural world. Students will also learn how to construct minimal mathematical, physical, and computational models that provide informative answers to precise questions.

Some of the topics addressed in this book are: Scaling and Order-of-Magnitude Estimates; Velocity and Relative Motion; Acceleration and Free Fall; Force and Motion; Analysis of Forces; Newton's Laws in Three Dimensions; Vectors; Circular Motion; Gravity.

Introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. Forced and parametric oscillators. Phase space. Periodic, quasiperiodic, and aperiodic flows. Sensitivity to initial conditions and strange attractors. Lorenz attractor. Period doubling, intermittency, and quasiperiodicity. Scaling and universality. Analysis of experimental data: Fourier transforms, Poincar, sections, fractal dimension, and Lyapunov exponents. Applications drawn from fluid dynamics, physics, geophysics, and chemistry.

Digital filters must be properly scaled to prevent overflow in fixed-point implementations. Scaling by the sum of the absolute value of the impulse response of a filter prevents overflow. However, this is sometimes too conservative in practice, so less stringent rules are often used.

This unit provides an introduction to nanoscience, focusing on concepts related to the size and scale, unusual properties of the nanoscale, tools of the nanosciences, and example applications. Upon completing this unit, students will understand: The study of unique phenomena at the nanoscale could vastly change our understanding of matter and lead to new questions and answers in many areas, including health care, the environment, and technology: There are enormous scale differences in our universe, and at different scales, different forces dominate and different models better explain phenomena; Nanosized materials exhibit some size-dependent effects that are not observed in bulk materials; New tools for observing and manipulating matter increase our ability to investigate and innovate. Length: 5 lessons, up to ten 50-minute classroom periods if all lessons are used. Not all lessons are required. Use the lessons most appropriate for your students.

Students analyze and begin to design a pyramid. Working in engineering teams, they perform calculations to determine the area of the pyramid base, stone block volumes, and the number of blocks required for their pyramid base. They make a scaled drawing of the pyramid using graph paper.

Introduction to momentum and scalar transport in environmental flows, with emphasis given to river and lake systems. Derivation and solutions to the differential form of mass conservation equations. Topics include: molecular and turbulent diffusion, boundary layers, dissolution, phase partitioning, bed-water exchange, air-water exchange, settling and coagulation, buoyancy-driven flows, and stratification in lakes.