Welcome to CSUMS

Erik is researching the effects of noise on systems of differential equations. He is focusing on the Welander model, which is a simple model of the the oceanic heat-salt system. Shown here is a picture of the effect of noise on the Welander model.

Numerical Investigations of Various Forms of the Heston Model

Ben is working with Black-Scholes equation, studying the effects of various forms of volatility on a Black-Scholes option price, as compared to other options pricing models. Additionally, he is looking at power spectrum analysis methods, ARMA models, Kalman filters, and other techniques to develop longer-range forecasts of asset-price volatility. Any findings would be examined for ways to improve existing financial market pricing behavior with regards to financial options.

Modeling the Lagrangian Trajectories and Dynamics of Particles Released within the Terrain-Induced Wind Rotors found in Owens Valley, CA

Our group is studying the presence, figure, and characteristics of terrain-induced rotors as a follow-up to the Terrain-induced Rotor Experiment (TREX). We hope to develop a functional model of these atmospheric rotors, and if time allows, move on to modelling other extreme weather conditions.

Three-Dimensional Visualization of Terrain-Induced Rotors

Our group is studying the presence, figure, and characteristics of terrain-induced rotors as a follow-up to the Terrain-induced Rotor Experiment (TREX). We hope to develop a functional model of these atmospheric rotors, and if time allows, move on to modelling other extreme weather conditions.

Modeling Angiogenesis in Glioblastoma Multiforme

Mary and Audrey are developing a mathematical model for the early growth of glioblastoma multiforme. Their model focuses on the interactions between cancer cells, vasculature in the tumor, and angiogenic growth factors.

Mathematically Modelling the Mass-Effect of Invasive Brain Tumors

The objective of Taylor's current project is to model the mass effect and tissue deformation due to glioblastomas multiforme and surrounding edema in human brain tissue. His current model employs the finite element method to solve a boundary value problem defined through classical continuum mechanics.

Approximating Markov Noise in the Navier-Stokes Equations

Matt is exploring the effects of noise on a rotating cylinder filled with incompressible fluid. His primary goal is the determine the effectiveness of noise reduction methods to reduce computational time.

Susie is currently researching the effect of noise on a lid-driven 2d cavity. It is well known that for high Reynolds number eddies form in the bottom corners of the rectangular domain. For a fixed Reynolds number, by implementing various types of noise she hopes to characterize the transition between different flow regimes.