
A Survey of Grid Control and Optimization
07 May 2015  Presentations  Contributor(s): Laura Slivinski
This is an introductory survey of how control problems arise on different time scales in electric grid transmission problems. The set up and general form of such problems are considered, along with operational considerations.

Chaotic Dynamical Systems: the Bernoulli Shift
04 May 2016  Presentations  Contributor(s): Laura Slivinski
This is the first part of a series of lectures on chaotic dynamics, and focuses on the Bernoulli shift. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a second year...

Chaotic Dynamical Systems: the Horseshoe Map
04 May 2016  Presentations  Contributor(s): Laura Slivinski
This is the second part of a series of lectures on chaotic dynamics, and focuses on the Horseshoe Map. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a second year graduate...

Complex Energy Systems
07 May 2015  Presentations
This is the opening guest lecture for the Electric Grid Focus Group. Dr. Michael Chertkov of Los Alamos National Lab describes the statistical and mathematical problems arising in complex energy systems, including the electric grid and gas networks. Systems with high penetration of...

Complex Energy Systems
07 May 2015  Presentations  Contributor(s): Laura Slivinski
This is the opening guest lecture for the Electric Grid Focus Group. Dr. Michael Chertkov of Los Alamos National Lab describes the statistical and mathematical problems arising in complex energy systems, including the electric grid and gas networks. Systems with high penetration of...

Complex Phytoplankton Dynamics: The Mathematical Perspective
04 May 2015  Educational Materials  Contributor(s): Arjen Doelman, Antonios Zagaris
Bibliography by Arjen Doelman and Antonios Zagaris to accompany tutorial lecture on PhytoplanktonNutrient Modeling at the 2011 MBI Workshop on Ocean Ecologies and their Physical Habitats in a Changing Climate, and the followon lectures on Phytoplankton growth in oligotrophic oceans: Linear...

Complex Phytoplankton Dynamics: The Mathematical Perspective
04 May 2015  Educational Materials
Bibliography by Arjen Doelman and Antonios Zagaris to accompany tutorial lecture on PhytoplanktonNutrient Modeling at the 2011 MBI Workshop on Ocean Ecologies and their Physical Habitats in a Changing Climate, and the followon lectures on Phytoplankton growth in oligotrophic oceans: Linear...

Complex Phytoplankton Dynamics: The Mathematical Perspective
04 May 2015  Educational Materials  Contributor(s): Laura Slivinski
Bibliography by Arjen Doelman and Antonios Zagaris to accompany tutorial lecture on PhytoplanktonNutrient Modeling at the 2011 MBI Workshop on Ocean Ecologies and their Physical Habitats in a Changing Climate, and the followon lectures on Phytoplankton growth in oligotrophic oceans: Linear...

Correlated Observation Errors in Data Assimilation
30 Apr 2015  Presentations
Remote sensing observations often have correlated errors, but the correlations are typically ignored in data assimilation for numerical weather prediction. The assumption of zero correlations is often used with data thinning methods, resulting in a loss of information, and reduction in analysis...

Deriving the Shallow Water Model in Geophysical Fluid Dynamics
01 Jan 2013  Series  Contributor(s): Laura Slivinski
These collected lectures go over key concepts in the derivation shallow water model as a conceptual model for ocean dynamics. The attached PDF notes in the supporting documents expand on these lectures. This short lecture series was part of the MCRN Mathematics of Climate Modelling...

Deriving the SWM Lecture 1: Conservation of Potential Vorticity
04 May 2016  Presentations  Contributor(s): Laura Slivinski
This lecture develops the conservation equation for potential vorticity in the shallow water model.

Deriving the SWM Lecture 2: Stream Functions for Velocity Fields
04 May 2016  Presentations  Contributor(s): Laura Slivinski
This lecture develops the formulation of the stream function for the velocity field of the shallow water equation. his is the second in a series of short lectures on deriving the shallow water model, given by Chris Jones in 2013.

Deriving the SWM Lecture 3: Barotropic Vorticity Equations
04 May 2016  Presentations  Contributor(s): Laura Slivinski
This lecture develops the barotropic vorticity equations for the shallow water model. This is background lecture 2.1C in the Mathematics of Climate Modelling course.

Emulators in climate science. Uncertainty, sensitivity, calibration and more
30 Apr 2015  Presentations
An emulator or a surrogate is a statistical approximation of a complex numerical model. Emulators are fast to run and include a measure of their own uncertainty. This makes them suitable for a number of applications in climate science. Emulators were originally devised for uncertainty...

Geometric Dynamical Systems: Manifolds and Stability Part I
04 May 2016  Presentations  Contributor(s): Laura Slivinski
This is the first part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This short lecture series was part of the MCRN Mathematics of Climate Modelling Course taught at the University of North Carolina by Chris Jones in 2013. This course was a...

Geometric Dynamical Systems: Manifolds and Stability Part II
04 May 2016  Presentations  Contributor(s): Laura Slivinski
This is the second part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This is background lecture 3.1B for the Mathematics of Climate Modelling course.

Geometric Dynamical Systems: Manifolds and Stability Part III
04 May 2016  Presentations  Contributor(s): Laura Slivinski
This is the final part of a series of dynamical systems lectures on the center, stable and unstable manifold theorems. This is background lecture 3.1C for the Mathematics of Climate Modelling course.

Introduction to the Mathematics of Climate
07 May 2015  Series  Contributor(s): Arjen Doelman, Antonios Zagaris
This course will investigate the following questions from a mathematical perspective. What determines the Earth's surface temperature? Why does the carbon dioxide in the atmosphere affect the climate? How do changes in the Earth's orbital parameters change the climate? Why has the Earth...

Introduction to the Mathematics of Climate
07 May 2015  Series  Contributor(s): Laura Slivinski
This course will investigate the following questions from a mathematical perspective. What determines the Earth's surface temperature? Why does the carbon dioxide in the atmosphere affect the climate? How do changes in the Earth's orbital parameters change the climate? Why has the Earth...

Introduction to the Mathematics of Climate
07 May 2015  Series  Contributor(s): Colin James Grudzien
This course will investigate the following questions from a mathematical perspective. What determines the Earth's surface temperature? Why does the carbon dioxide in the atmosphere affect the climate? How do changes in the Earth's orbital parameters change the climate? Why has the Earth...