Dr. Julien's primary area of research is focussed in the mathematical geo- and astro-physical sciences. Specifically, the modeling of dynamical processes and instabilities occurring in geophysical and astrophysical flows. Examples include protoplanetary disks, stably and unstably stratified flows (such as penetrative convection, rotating and magneto- convection), shear flows and boundary effects in turbulent convection. Particular emphasis is placed on the identification of reduced PDE models that accurately describe coherent structures, the transport and organization of large-scale flows, mean flow generation, and wave propagation. Complementary to these interest is the development of fast numerical algorithms for the purpose of numerical simulations on state of the art high performance computing architectures. Dr Julien's also experienced in the areas of dynamical systems and physical applied mathematics.
Geophysical and Astrophysical Fluid Dynamics, Fluid Dynamics, Physical Applied Mathematics, Nonlinear Dynamics, Computational Fluid Dynamics, Hydrodynamics, Asymptotics, Dynamical Systems
APPM 2360 - Introduction to Differential Equations with Linear Algebra
Fall 2019 / Spring 2021
Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Credit not granted for this course and both MATH 2130 and MATH 3430.
APPM 5460 - Methods in Applied Mathematics: Dynamical Systems and Differential Equations
Introduces the theory and applications of dynamical systems through solutions to differential equations. Covers existence and uniqueness theory, local stability properties, qualitative analysis, global phase portraits, perturbation theory and bifurcation theory. Special topics may include Melnikov methods, averaging methods, bifurcations to chaos and Hamiltonian systems. Department enforced prerequisites: APPM 2360 and APPM 3310 and APPM 4440.
APPM 5480 - Methods of Applied Mathematics: Approximation Methods
Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods and applications to differential and integral equations. Department enforced prerequisite: APPM 5470.
APPM 7400 - Topics in Applied Mathematics
Fall 2018 / Spring 2019 / Fall 2019 / Fall 2020 / Fall 2021
Provides a vehicle for the development and presentation of new topics with the potential of being incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours.