Introduction to Nonlinear Physics Introduction （介绍非线性物理的介绍）.pdf

Introduction to Nonlinear Physics Lecture I Introduction to Non-linear physics Lecture 1 Tobias Galla Anne Juel Nonlinear Dynamics room G.12 anne.juel@manchester.ac.uk http://www.maths.manchester.ac.uk/~ajuel/ Adapted from T. Galla’s slides Nonlinear physics Why did you choose this course ? Reasons why you should choose this course • interesting and timely topic • combination of mathematical methods, numerical studies and experimental applications. • most phenomena in physics due to nonlinear effects • applications in a variety of different fields (in physics, but also biology, epidemiology, economics ... you name it) • essential for a broad Physics education. Reasons why you should not choose this course Reasons why you should not choose this course None Nonlinear physics Why did I choose to give this course ? • Research in complexity and soft matter: focus on instabilities in fluid dynamics and solid mechanics, which are inherently nonlinear phenomena. • Manchester Centre for Nonlinear Dynamics: multi- pronged approach of quantitative experiments and mathematical analysis/numerical simulations. • Concepts of nonlinear dynamics fundamental to understanding complex systems. e.g. game theory and evolutionary dynamics, biological systems (gene regulation, epidemics, metabolic systems), models in economics, models of socio-dynamics (traffic, opinion spreading, decision making). • Lots of interest in the public Nonlinear dynamics in a nutshell 1. /wiki/Fractal 2. Bifurcation diagram of the logistic map: Universality in chaos /wiki/L