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## PH30031: Simulation techniques

Owning Department/School: Department of Physics
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period: Semester 1
Assessment: EX 100%
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must ( take PH20019 OR take PH20107 OR take MA20219 ) AND ( take PH20020 OR take PH20107 OR take MA20223 )
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)

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

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)
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-AFB10 : BSc(Hons) Physics with Astrophysics (Year 3)
• USPH-AAB10 : BSc(Hons) Physics with Astrophysics with Study year abroad (Year 4)
• USPH-AKB10 : BSc(Hons) Physics with Astrophysics with Year long work placement (Year 4)
• USPH-AAB02 : BSc(Hons) Physics with Study year abroad (Year 4)
• USPH-AKB02 : BSc(Hons) Physics with Year long work placement (Year 4)
• USPH-AFM02 : MPhys(Hons) Physics (Year 3)
• USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
• USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 4)
• USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 4)
• USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (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)
• USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 4)
Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Year long work placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Professional Placement (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)

 Notes: This unit catalogue is applicable for the 2020/21 academic year only. Students continuing their studies into 2021/22 and beyond should not assume that this unit will be available in future years in the format displayed here. Programmes and units are subject to change 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. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.