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## PH30031: Simulation techniques

Owning Department/School: Department of Physics
Credits: 6
Level: Honours (FHEQ level 6)
Period: Semester 1
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment: Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this module you must take PH20019 AND take PH20020
Description: Aims:
The aims of this unit are to identify some of the issues involved in constructing mathematical models of physical processes, and to introduce major techniques of computational science used to find approximate solutions to such models.

Learning Outcomes:
After taking this unit the student should be able to:
* de-dimensionalise an equation representing a physical system;
* discretise a differential equation using grid and basis set methods;
* outline the essential features of each of the simulation techniques introduced and give examples of their use in contemporary science;
* use the simulation schemes to solve simple examples by hand.

Skills:
Numeracy T/F A, Problem Solving T/F A.

Content:
Construction of a mathematical model of a physical system (4 hours): De-dimensionalisation, order of magnitude estimate of relative sizes of terms. Importance of boundary conditions. The need for computed solutions.
Discretisation (2 hours): Grids and basis sets. Discretisation errors.
The finite difference method (4 hours): Review of ODE solutions. Construction of difference equations from PDEs. Boundary conditions. Applications.
The finite element method (3 hours): Illustration of global, variational approach to solution of PDEs. Segmentation. Boundary conditions. Applications.
Introduction to computational methods for matrix problems (3 hours).
Molecular Dynamics and Monte Carlo methods (6 hours): Examples of N-body problems, ensembles and averaging. The basic MD strategy. The basic MC strategy; random number generation and importance sampling. Applications in statistical mechanics. Simulated annealing. Computer experiments.
Programme availability:

#### PH30031 is Compulsory on the following programmes:

Department of Physics
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 3)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 4)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 4)
• USPH-AFB05 : BSc(Hons) Physics with Computing (Year 3)
• USPH-AAB06 : BSc(Hons) Physics with Computing with Study year abroad (Year 4)
• USPH-AKB06 : BSc(Hons) Physics with Computing with Year long work placement (Year 4)

#### PH30031 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences with Year long work placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Year 3)
• UXXX-AKM02 : MSci(Hons) Natural Sciences with Professional Placement (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences with Study year abroad (Year 4)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
• TSMA-AFM08 : MSc Modern Applications of Mathematics
• TSMA-AWM14 : MSc Modern Applications of Mathematics
Department of Physics
• USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 3)
• USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 4)
• USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 4)
• USPH-AFB01 : BSc(Hons) Physics (Year 3)
• USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 4)
• USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 4)
• USPH-AFB09 : BSc Physics (Year 3)
• USPH-AFM02 : MPhys(Hons) Physics (Year 3)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 3)

Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.