Nonlinear Dynamics and Applied PDEs
Mathematical models of phenomena in the physical sciences or processes in the engineering and biological sciences invariably take the form of nonlinear dynamical systems and partial differential equations (PDEs). The expertise of the Nonlinear Dynamics and Applied PDEs group lies in attacking these systems with the modern techniques of applied mathematics, such as symmetry and asymptotic methods coupled with numerical explorations and dynamical systems theory.
Occasionally the goal is to understand the creation of patterns from otherwise featureless background states, or the onset of new dynamical behaviour (such as synchrony in populations of coupled oscillators). But the mathematics involved in these problem is often of equal interest, entailing novel twists and turns in the application of mathematical technology, and motivating the development of new techniques or adaptations of existing ones.
The Nonlinear Dynamics & Applied PDEs Group is composed of several core IAM faculty who are actively involved in the IAM activities and supervise IAM students or postdoctoral fellows. We are always interested to hear from potential students or fellows with background in mathematics, physics or engineering. We often supervise undergraduate thesis projects and take on summer research undergraduate students. Candidates interested in research in Nonlinear Dynamics & Applied PDEs in the IAM are encouraged to contact one or more of the core faculty as potential supervisors and let them know of their interests.
Courses given by IAM faculty provide the foundation for research in Nonlinear Dynamics & Applied PDEs, as well as outlining the essential tools which comprise the classical and modern techniques of Applied Mathematics.
Preliminary and Foundational Courses
MATH 400: Partial Differential Equations
MATH 401: Green Functions and Variational Methods
MATH 450/550: Perturbation Methods
MATH 521: Numerical Analysis of PDEs
MATH 552: Dynamical Systems Theory
MATH 607E: Numerical Methods for Differential Equations
Nonlinear Dynamics & Applied PDEs Courses
MATH 551: Asymptotic Analysis for PDEs
MATH 553: Advanced Dynamical Systems
MATH 554: Symmetries and Differential Equations
MATH 556: Industrial Mathematical Modelling
MATH 522: Numerical Analysis
MATH 557: Linear and Nonlinear Waves
|applied math: mathematical modelling, computational mathematics, stochastic analysis, statistical mechanics, soft-matter physics, materials science, biophysics, computational geometry
|Coupling bulk-surface geometric PDEs with multi-physics for cell motility and pattern formation; Data-driven modelling in Experimental Sciences and Healthcare
|Molecular simulation, Physics-inspired machine learning for coarse-graining and multi-scale methods, Materials and material defects, Numerical analysis, PDEs
|Numerical and analytic models of hydraulic fracture propagation; rock fracture processes around mining excavations, control of molecular motion; reactive flows in porous media; analysis of diffusion models with localized reactions.
|reaction-diffusion systems, asymptotic and singular perturbation theory, applied PDE, math modeling
|Nonlinear Partial Differential Equations/Semilinear Elliptic Equations/Nonlinear,Applied and Geometric Analysis/Mathematical Biology/Singular Perturbation Problems/Phase Transition