# Nonlinear Dynamics and Applied PDEs

##### Group overview

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.

##### Core Faculty

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.

##### Recommended Courses

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

##### Further Options

MATH 522: Numerical Analysis

MATH 557: Linear and Nonlinear Waves

## People

Faculty | Research Interests |
---|---|

Miranda Holmes-Cerfon | applied math: mathematical modelling, computational mathematics, stochastic analysis, statistical mechanics, soft-matter physics, materials science, biophysics, computational geometry |

Anotida Madzvamuse | Coupling bulk-surface geometric PDEs with multi-physics for cell motility and pattern formation; Data-driven modelling in Experimental Sciences and Healthcare |

Christoph Ortner | Molecular simulation, Physics-inspired machine learning for coarse-graining and multi-scale methods, Materials and material defects, Numerical analysis, PDEs |

Anthony Peirce | 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. |

Michael Ward | reaction-diffusion systems, asymptotic and singular perturbation theory, applied PDE, math modeling |

Jun-Cheng Wei | Nonlinear Partial Differential Equations/Semilinear Elliptic Equations/Nonlinear,Applied and Geometric Analysis/Mathematical Biology/Singular Perturbation Problems/Phase Transition |

Graduate Students | Research Interests |
---|---|

Sarafa Adewale Iyaniwura | Applied PDE, asymptotic analysis and perturbation methods, applied dynamical systems, reaction-diffusion systems, quorum and diffusion sensing, infectious disease modeling. |

Merlin Pelz | Nonlinear dynamics, analysis (real, complex, numerical, stochastic), probability, PDEs, SDEs, applied mathematics (especially to biology) |