## PH30031: Simulation techniques

[Page last updated: 23 October 2023]

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 Summary: EX 100%
Assessment Detail:
• Examination (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 )
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.

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.

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

Content: Construction of a mathematical model of a physical system (3 hours): De-dimensionalisation, order of magnitude estimate of relative sizes of terms. Importance of boundary conditions. The need for computed solutions.
Discretisation (3 hours): Grids and basis sets. Discretisation errors.
ODE Initial value problems (3 hours): Euler, Leapfrog, Runge-Kutta, and implicit methods. Stability of different methods. Applications.
Computational tools (4 hours): Linear algebra matrix and eigenvalue problems, iterative methods for systems of nonlinear algebraic equations, Fast Fourier Transforms
Numerical methods for PDE problems (5 hours): The finite difference method, construction of difference equations from PDEs, boundary conditions. The finite element method, Illustration of variational approach to solution of PDEs, segmentation and boundary conditions. Initial Value problem PDE methods, forward-time centred-space (FTCS), Crank-Nicolson, spectral, and pseudo-spectral methods. Discrete vs continuous dispersion. Stability.
Many-Body problems (4 hours): Examples of N-body problems, ensembles and averaging. Molecular Dynamics simulations. Monte Carlo methods. The basic MC strategy, MC quadrature method, random number generation and importance sampling, Metropolis algorithm. Applications in statistical mechanics.

Course availability:

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

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 courses:

Department of Chemistry
• USSC-AFB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Biology with Physics stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Chemistry with Physics stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Physics with Biology stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Physics with Chemistry stream) with Year long work placement (Year 4)
• USSC-AFM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) (Year 3)
• USSC-AAM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Study year abroad (Year 4)
• USSC-AKM01 : MSci(Hons) Natural Sciences (Biology with Physics stream) with Professional Placement (Year 4)
• USSC-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) (Year 3)
• USSC-AAM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)
• USSC-AKM01 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Professional Placement (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)
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-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-AFM02 : MPhys(Hons) Physics (Year 3)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 3)
• USPH-AAM12 : MPhys(Hons) Physics with Study year abroad (Year 4)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 4)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 4)
• USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 3)
• USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 3)
• USPH-AAM14 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 4)
• USPH-AKM10 : MPhys(Hons) Physics with Astrophysics with Professional Placement (Year 4)
• USPH-AKM11 : MPhys(Hons) Physics with Astrophysics with Professional and Research Placements (Year 4)
• USPH-AAM15 : MPhys(Hons) Physics with Astrophysics with Study year abroad and Research Placement (Year 4)
• USPH-AAM13 : MPhys(Hons) Physics with Study year abroad and Research Placement (Year 4)

 Notes: This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24. Courses 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. Find out more about these and other important University terms and conditions here.