The Syllabus of AC2674 2016 Course can be dowloaded here.

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Computational Physics (AC274)

Sauro Succi

• 1 Location and Timetable 

Wed-Fri, 10-12, Pierce 100F

• 2 Course Description and Motivation 

In this Course, we shall familiarise with the main computational tools which permit to simulate and analyse the dynamic behaviour of a wide range of physical problems involving fluids, solids, soft matter and quantum systems, as well as the dynamics of (some) biological and social systems. Special attention will be paid to the modelling/programming techniques involved with the generation of massive amounts of data which result from large-scale simulations of the above systems, as well as to the techniques to analyse and extract physical knowledge from such datasets.

• 3 Learning goals 

The main goal of the course is to make the student acquainted with major computational techniques for solving a broad range of complex problems involving fluids, solids, waves, quantum systems, as well as biological and social systems with internal degrees of freedom (psycho-physics). Techniques to analyse the corresponding large sets of data will also be presented.

At the completion of the course, the student is expected to be able to:

       1. Employ and develop concepts and methods for the large scale simulations of the dynamic behaviour of complex systems, as well as the corresponding data analysis techniques. 
       2. Read the current literature and appreciate the various approaches to large-scale simulation of scientific and engineering applications 
       3. Choose and code the most appropriate computational techniques for modelling and data-analysing complex problems in physics, engineering biology and also social sciences. 
       4. Contribute to research projects involving the simulation and data anal-ysis of complex natural and social systems. 

• 4 Contents 

Grid methods for classical and quantum  fields 

        1. Finite Difference Method (Project 1a: Numerical simulation of advection-di usion-reaction transport phenomena) 
        2. Finite Volume Method 
        3. Quantum Wave Equations (Project 1b: Numerical simulation of quantum scattering and tunnelling) 

Analysing and learning from data 

       1. Signals: time-series and probability distribution functions 
       2. (Multi)fractal analysis of turbulent signals (Project 2: Statistical analysis of turbulent time-series) 
       3. Rudiments of Machine Learning 

Simulating complex states of matter 

       1. Lattice Boltzmann I: Fluids 
       2. Lattice Boltzmann II: Soft matter (Project 3: Lattice Boltzmann simulation of multiphase ow) 
       3. Agent-based Models for Active Matter 

Computational psycho-physics 

      1. Finite Differences as Social Networks
      2. Predicting X-events 
      3. Neural networks: the Hopfield model (Project 4: Simulating the Hopfield neural network) 

• 5 References 

T. Pang, Computational Physics, Cambridge Univ. Press, (https://www.amazon.com/Introduction-Computational-Physics-Tao-Pang/dp/05...) 

• 6 Pre-requisites 

None, although some foreknowledge of numerical analysis and coding practice (Fortran, C, C++, Matlab, Mathematica, Python, Julia...) will help.

• 7 Grading policy 

Weekly assignments: 30% 

Running projects (every three weeks): 30% 

Final project (second week of December): 40% 

The final project may be related to an ongoing PhD thesis, on the strict condition that it represents original work. 

• 8 Lecture plan 

Most subjects will be illustrated through a Theory lecture (2h), followed by a Practice lecture (2h) based on the use of warm-up computer programs. Starting from these practical examples, the student is expected to write up her/his own programs for further practice.

8.1 Lecture schedule 

L1: Sept 2: Introduction to AC274

Part I: Grid Methods for Classical and Quantum Fields

L2-3: Sept 7-9: Finite Difference Method

L4-5: Sept 14-16: Finite Volume Method

L6-7: Sept 21-23: Quantum Wave Equations

L8-9: Sept 28-30: Numerical Solution of Compressible Flows (P. Mocz)

Part II: Data Analysis and Learning

L10-11: Oct 5-7: Time series, correlations and probability distributions

L12: Oct 12: (Multi)-fractal analysis of turbulent time-series

L13-14: Oct 14-19: Machine Learning

Part III: Complex States of Matter

L15-16: Oct 21-26: Lattice Boltzmann for Fluids

L17-18: Oct 28-Nov 2: Lattice Boltzmann for Soft Matter (G. Falcucci)

L19-20: Nov 4-9: Agent-based Models for Active Matter

Part IV: Computational Psycho-Physics

L21: Nov 11: The Social Rules of Finite Difference Methods

L22: Nov 16: Predicting X-events

L23-24: Nov 18-25: The Hopfield Neural Network

L25: Nov 30: Wrap-up Lecture