# NON-LINEAR PHYSICS - 2023/4

Module code: PHYM038

## Module Overview

Non-linear physics introduces the relevant theory with examples in physics, astrophysics, chemistry, biology and engineering. The material is developed through lectures and examples classes, and applied in the coursework.

### Module provider

Mathematics & Physics

### Module Leader

IZZARD Robert (Maths & Phys)

### Number of Credits: 15

### ECTS Credits: 7.5

### Framework: FHEQ Level 7

### JACs code: F300

### Module cap (Maximum number of students): N/A

## Overall student workload

Independent Learning Hours: 97

Lecture Hours: 22

Tutorial Hours: 11

Laboratory Hours: 3

Captured Content: 17

## Module Availability

Semester 2

## Prerequisites / Co-requisites

Newtonian mechanics, vectors and vector calculus, complex analysis. Familiarity with writing computer programs to solve differential equations, e.g. in C, python or similar. Ability to make professional-level scientific data plots, e.g. with tools like gnuplot or python's matplotlib, and write short scientific reports.

## Module content

• Linear and non-linear dynamics

• Fixed points, bifurcations and limit cycles in one and two dimensions

• Phase space analysis

• Lyapunov Stability and the Poincaré-Bendixon theorem

• Fractals, and concepts of fractal dimensions

• Attractors, strange attractors and chaos

• Lorenz and Rössler attractors

• Measures of non-linearity and quantification by Lyapunov exponents

• Non-linear maps, the cascade route to chaos and the 0-1 test for chaos

• Unimodal maps, renormalization and Feigenbaum constants

• Examples of oscillators in two and three dimensions (van der Pol, Duffing, etc…)

• Other examples from physics, astrophysics, chemistry, engineering and biology

## Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Online Scheduled Summative Class Test | Online (open book) tests within 4hr window | 10 |

Coursework | Coursework assignment | 30 |

Examination | End of semester examination - 2 hours | 60 |

## Alternative Assessment

N/A

## Assessment Strategy

The __assessment strategy__ provides students with the opportunity to demonstrate their insight into non-linear physics and complex phenomena, and develop their problem solving skills with personalized feedback. The in-class tests are not just to monitor progress but also give each student detailed feedback on their work. These are an excellent way to focus understanding and technique in preparation for both the coursework and the examination, and the individual feedback is a highly efficient way to improve methodology. The coursework assigned during the semester allows the student to put into practice the concepts learned in class, therefore building a deeper understanding of non-linear phenomena and mastering the techniques used in their analysis. The final written examination, at the end of the semester, assesses the overall understanding of the fundamental concepts and theory of complex phenomena.

Thus, the __summative assessment__ for this module consists of:

Online 24hr summative tests (10%) during the semester.

One piece of coursework (30%) to be completed during the semester requiring approximately five weeks. The coursework must be completed by the end of the semester.

One two-hour examination at the end of the semester (60%), with a section A of compulsory questions and a section B of two questions chosen from three. In Part A answer all questions (20 points). In Part B answer two questions out of three (20 points each). If all three questions in Part B are attempted only the best two will be counted.

__Formative assessment and feedback__

Students receive continuous feedback through discussions during class time, online through the Surreylearn discussion board, and I am available most days by old-fashioned email or (in non-pandemic circumstances) in person. Assessment of the submitted coursework is returned to the students with feedback on their performance.

## Module aims

- To provide a sound grounding and the basic theorems, methods and applications of the theory of non-linear physics. To gain computational and mathematical skill to characterise the qualitative complex systems in physics, finance, and other disciplines.
- To then encourage the in-depth investigation of aspects of non-linearity through extended coursework problems.

## Learning outcomes

Attributes Developed | ||

001 | Upon successful completion of the module the student will be able to appreciate the implications of non-linearity in physics and identify its basic mechanisms. They will be able to analyse and classify the motion of complex non-linear systems by identifying their qualitative features and by categorizing them in terms of periodic, quasi-periodic or chaotic behaviour. They will be able to recognize effects of non-linearity in situations of everyday life. | |

002 | On successful completion of the coursework part of the module, they will be able to apply fundamental (analytical and numerical) methods of non-linear dynamics to analyse chaotic systems and will appreciate the concept and the benefits of chaos control. |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

## Methods of Teaching / Learning

The non-linear physics course builds on development during the Covid lockdown to provide a complete set of hybrid-flipped-learning classes.

The main course material is available as 11 approximately 90-minute videoed lectures, recorded in my home studio, which are split into small pieces for ease of watching in modern "YouTube style".

The in-person class time (11x2hr) is then used to answer students' questions, have discussions about the material such as the coursework, and present examples of non-linear physics by watching videos together and discussing their content, looking at specific problems in detail or, at the end of the semester in particular, looking at past examination papers and focusing on problem-solving technique.

The 11x1hr tutorial sessions are to demonstrate specific examples and applications of the material, with two summative 24h-online assessments to provide highly-efficient personalized feedback during the semester. These assessments are good for highlighting any issues during the first half of the course so that these are ironed out in time for the coursework.

The coursework focuses on specific non-linear system(s) that give the student with opportunities to gain knowledge of advanced topics and to prove independent thinking, investigation and computational skills. The assignment is handed out mid-semester and typically requires the use of computational techniques such as non-linear differential equation solving, e.g. with Python, with the results to be presented in report form at the end of the semester (usually in week 12). A 3-hour computing laboratory session prepares the student for this part of the course, introducing and building on Python skills, with associated documentation.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

## Reading list

https://readinglists.surrey.ac.uk

Upon accessing the reading list, please search for the module using the module code: **PHYM038**

## Programmes this module appears in

Programme | Semester | Classification | Qualifying conditions |
---|---|---|---|

Mathematics and Physics MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Mathematics and Physics MMath | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics with Nuclear Astrophysics MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics with Astronomy MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics with Quantum Technologies MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics MPhys | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Physics MSc | 2 | Optional | A weighted aggregate mark of 50% is required to pass the module |

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2023/4 academic year.