Courses

Earth and Planetary Sciences 131 (FQ 2023): Risk: Natural Hazards and Related Phenomena

We live in an uncertain world.  Hazards and risk are common.  The world is a complex system.  How can we understand and manage our exposure to hazards and risk?   How can we recover when the worst happens? The world wide web offers many new possibilities.  In this course, we will discuss a number of examples, drawn from the field of natural hazards -- earthquakes, tsunamis, hurricanes and the like -- as well as hazards in other fields as time permits. We will also discuss new ideas using internet technologies to anticipate, mitigate, respond, and recover from disasters of various types. Forecasting and data-driven analyses are important, along with social networking to build resilient communities.  Many of these ideas originate from discussions at the Santa Fe Institute, internationally famous for its emphasis on complex systems.  During the course, we will make use of a number of web sites and apps that will allow us to examine practical aspects of risk and risk management. Primary goal for the course is for the student to gain a deeper understanding of risk in the modern world, and how it may be anticipated and mitigated, and how we can respond to and recover from these potentially catastrophic events.

Physics-EPS 30 (WQ 2024): Fractals, Chaos and Complex Systems

This course will introduce students to the ideas of Fractals, Chaos, Complexity and Computation.  We will begin with the examples of objects, such as trees, river networks, coastlines, weather, earthquakes, the human body, the stock market, evolution, and others that display examples of fractal geometry.  We will then explore many of the fascinating ideas popularized by B. Mandelbrot and others about self-similarity across different geometric scales.  Chaos, how it arises in familiar everyday systems, and the link with fractal geometry, will be discussed.  We will talk about how processes of "self-organization" arise in systems with feedback, and the ways in which those processes lead to the emergence of coherent space-time structures for systems with no natural length or time scales.  We will discuss the idea of Cellular Automata and its relationship to computation.  We will examine how chaos and order are inextricably linked with a kind of strange duality.  Many of these ideas are having a profound effect in fields far from their point of origin.  As a result, we will explore the profound philosophical implications of these ideas, including their effects on modern art and architecture, and especially on the definition of life itself.

Physics 255 (WQ 2025): Econophysics: The Statistical Physics of the Financial Markets

Econophysics is the application of ideas from statistical mechanics to the financial markets.  Markets are complex self-adapting systems that are observed to undergo sudden transitions such as “booms” or “bubbles” and “busts” or “crashes”. Transitions in system dynamics are associated with the nucleation and growth of fluctuations, together with a threshold in the state space of the system.  Markets are also observed to obey scaling dynamics, an interesting example being the existence of the Pareto distribution of wealth among populations.  In this course, we will introduce the dynamics of markets from a physics and systems perspective.  We will discuss the statistical distributions of returns, the phase dynamics of prices, and models for the markets.  We will discuss specific markets such as the equity stock markets (NYSE/Euronext, NASDAQ), the fixed income (bond) markets (Government and Municipals), and the commodities markets (CME and Futures).   We will discuss time-dependent models for equity valuations such as the Black-Scholes equation that are used in options pricing.  Students will be expected to contribute actively to discussions, as well as complete a project using financial data and analysis.  Familiarity with some form of computer programming is mandatory.

Physics 250: Nucleation and Phase Transitions -- The Tipping Point

Complex systems are observed to undergo sudden changes in behavior when the system "tips" from one dominant dynamical pattern to another. The transition in system dynamics is associated with the nucleation and growth of fluctuations, together with a threshold in the state space of the system. The threshold can be characterized as a "tipping point". Tipping points, or first-order transitions, can be associated with stock market crashes, earthquakes, hurricanes, and epidemics. In this course we will examine the dynamics of nucleation and growth in complex systems. We develop the tools to understand the effects of tipping points, and how these lead to the appearance of fractals and scaling phenomena. We examine the role of fluctuations, and how these lead to selection of new dynamical states, and we will illuminate the role of the"spinodal" the classical limit of stability of the system. Students in this course will study the dynamics of a variety of complex systems that demonstrate tipping points through the development and use of analytical and numerical methods.

Earth and Planetary Sciences 160: Data Analysis in the Earth Sciences

Students learn to analyze geological and geophysical data from the standpoint of statistics and the theory of probability.  We will consider uncertainty in measurements, common types of probability distributions, error analysis, definition of mean and variance as well as estimation of these quantities, random numbers and how to generate these, fitting models to data, maximum likelihood methods, testing goodness-of­fit, analysis of directional data, and numerical methods.  A variety of statistical packages are available.  Examples of software packages include the MatLab statistics toolbox, standard routines in IDL from RSI, and Excel. We will teach the fundamentals of programming, using MatLab, IDL, Excel, or other programming languages. Students will also learn how to acquire, manipulate, and analyze geological and geophysical data using data bases currently available (primarily) on the World Wide Web. We also assume that students have little or no prior background in probability, the systematic analysis of data, or in matrix algebra