The Center for Nonlinear and Complex Systems (CNCS) fosters research and teaching of nonlinear dynamics and the mechanisms governing emergent phenomena in complex systems. The CNCS at Duke is widely recognized for the breadth of its activities and the overall quality of the research which it engenders. The Center provides a research seminar series and a Graduate Certificate Program, as well as numerous opportunities for undergraduate and graduate research through its associated faculty.

Graduate Certificate in Nonlinear and Complex Systems

The purpose of the certificate is to broaden the scope of the typical disciplinary; graduate student traning program. Students are encouraged to develop interdisciplinary; and transferable sets of skills in their course work and research activities. The certificate program helps to guide students toward this broad view by requiring the completion of:

- The seminar course
- Four courses from the approved list (below)
- A Ph.D. dissertation on a topic in the domain of the CNCS

In addition, the student must have two members of the Center on their Ph.D. dissertation committee. Students are encouraged to meet together with their dissertation thesis advisor and the Associate Director of the Center (Prof. L. Virgin) early in their graduate studies to help with course planning and dissertation committee selection.

### Physics (PHYSICS)

320. Optics and Photonics

513. Introductory Nonlinear Dynamics

562. Fundamentals of Electromagnetism

563. Introduction to Statistical Mechanics

621. Advanced Optics

719. Advanced Electrodynamics

760. Mathematical Methods in Physics

761. Classical Mechanics

763. Statistical Mechanics

804. Advanced Topics in Statistical Mechanics

813. Advanced Topics in Nonlinear and Complex Systems

814. Introduction to Fluid Mechanics

### Mechanical Engineering and Materials Science (ME)

307. Transport Phenomena in Biological Systems

519. Soft Wet Materials and Interfaces

525. Nonlinear Finite Element Analysis

527. Buckling of Engineering Structures

531. Engineering Thermodynamics

532. Convective Heat Transfer

536. Compressible Fluid Flow

541. Intermediate Dynamics: Dynamics of Very High Dimensional Systems

542. Modern Control and Dynamical Systems

543. Energy Flow and Wave Propagation in Elastic Solids

544. Advanced Mechanical Vibrations

546. Intelligent Systems

571. Aerodynamics

572. Engineering Acoustics

631. Intermediate Fluid Mechanics

632. Advanced Fluid Mechanics

639. Computational Fluid Dynamics and Heat Transfer

643. Adaptive Structures

671. Advanced Aerodynamics

672. Unsteady Aerodynamics

741. Nonlinear Control Systems

742. Nonlinear Mechanical Vibration

775. Aeroelasticity

### Biomedical Engineering (BME)

301. Electrophysiology

307. Transport Phenomena in Biological Systems

506. Measurement and Control of Cardiac Electrical Events

512. Theoretical Electrocardiology

513. Nonlinear Dynamics in Electrophysiology

516. Computational Methods in Biomedical Engineering

531. Intermediate Biomechanics

566. Transport Phenomena in Cells and Organs

834. Viscoelasticity

### Civil and Environmental Engineering (CEE)

307. Transport Phenomena in Biological Systems

520. Continuum Mechanics

541. Structural Dynamics 581. Pollutant Transport Systems

621. Plasticity

625. Intermediate Dynamics

630. Nonlinear Finite Element Analysis

641. Advanced Soil Mechanics

647. Buckling of Engineering Structures

648. Multivariable Control

682. Dynamic Engineering Hydrology

690. Advanced Topics in Civil and Environmental Engineering

### Mathematics (MATH)

451S. Nonlinear Ordinary Differential Equations

541. Applied Stochastic Processes

545. Introduction to Stochastic Calculus

551. Applied Partial Differential Equations and Complex Variables

553. Asymptotic and Perturbation Methods

555. Ordinary Differential Equations

557. Introduction to Partial Differential Equations

561. Numerical Linear Algebra, Optimization and Monte Carlo Simulation

563. Applied Computational Analysis

573S. Modeling of Biological Systems

575. Mathematical Fluid Dynamics

577. Mathematical Modeling

641. Probability

651. Hyperbolic Partial Differential Equations

653. Elliptic Partial Differential Equations 660. Introduction to Numerical PDEs

661. Numerical Solution of Hyperbolic Partial Differential Equations

663. Numerical Solution of Elliptic and Parabolic Partial Differential Equations

### Biology

268. Ecological Theory and Data

291. Mathematical Biology

292. Population Ecology

293. Simulating Ecological and Evolutionary Systems

303. Principles of Ecological Modeling

304. Plant Growth Modeling

### Computer Science

240. Computational Complexity

250. Numerical Analysis

252. Numerical Methods for Partial Differential Equations

264. Nonlinear Dynamics

270. Artificial Intelligence

271. Numerical Artificial Intelligence

350. Topics in Numerical Mathematics

364. Advanced Topics in Nonlinear and Complex Systems

### Earth and Ocean Sciences

203. Physical Oceanography

207. Analysis of Coastal Engineering Models

221. Hydrogeology

222. New Perspectives and Methods in the Earth Sciences

223. Computational Methods in Hydrologic Sciences

230. Advanced Structural Geology

250. Applied Mathematics for the Environmental and Earth Sciences

252. Geophysics and Crustal Dynamics

### Electrical and Computer Engineering

241. Linear Systems: Theory and Control

243. Pattern Classification and Recognition

255. Mathematical Modeling for Systems Analysis I

258. Artificial Neural Networks

263. Multivariable Control

281. Random Signals and Noise

282. Digital Signal Processing

285. Signal Detection and Extraction Theory

288. Image and Array Signal Processing

289. Adaptive Filters

299. Nonlinear Control Systems (Advanced Topics)

### School of the Environment

216. Applied Population Ecology

290. Physical Oceanography

356. Environmental Fluid Mechanics

The only formal paperwork that must be completed to obtain the certificate occurs when the student's Ph.D. dissertation is submitted to the Graduate School. The student should check the box on the Graduate School "<a href="http://www.gradschool.duke.edu/intent/degreere.htm">Intent to Receive Degree Form</a>" indicating that they would like to receive the CNCS Graduate Certificate. The student must then send the Associate Director of the Center the following information:

- the semester(s) when CNS 201 was taken
- the name of the four courses taken (from the approved list
- the Ph.D. dissertation title
- the list of final Ph.D. dissertation committee members
- the date of the final defense
- the final Ph.D. dissertation abstract
- the student's graduate transcript

Biology

Biomedical Engineering

Civil Engineering

Computer Science

Earth and Ocean Sciences

Electrical Engineering

Mathematics

Mechanical Engineering and Materials Science

Physics

School of the Environment