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## PH30031: Simulation techniques

Credits: 6
Level: Honours (FHEQ level 6)
Period: Semester 1
Assessment: EX 100%
Supplementary Assessment: Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this unit 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
• USPH-AFB05 : BSc (hons) Physics with Computing (Full-time) - Year 3
• USPH-AKB06 : BSc (hons) Physics with Computing (with Placement) (Full-time with Thick Sandwich Placement) - Year 4
• USPH-AAB06 : BSc (hons) Physics with Computing with Year Abroad (Full-time with Study Year Abroad) - Year 4
• USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 3

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

Programmes in Natural Sciences
• UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 3
• UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
• UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• UXXX-AFM01 : MSci (hons) Natural Sciences (Full-time) - Year 3
• UXXX-AKM02 : MSci (hons) Natural Sciences with Professional Placement (Full-time with Thick Sandwich Placement) - Year 4
• UXXX-AAM02 : MSci (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time) - Year 1
• TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time) - Year 1
Department of Physics
• USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 3
• USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 4
• USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USPH-AFB01 : BSc (hons) Physics (Full-time) - Year 3
• USPH-AKB02 : BSc (hons) Physics (with Placement) (Full-time with Thick Sandwich Placement) - Year 4
• USPH-AAB02 : BSc (hons) Physics with Year Abroad (Full-time with Study Year Abroad) - Year 4
• USPH-AFB09 : BSc Physics (Full-time) - Year 3
• USPH-AKB09 : BSc Physics (with Placement) (Full-time with Thick Sandwich Placement) - Year 4
• USPH-AFM02 : MPhys Physics (Full-time) - Year 3
• USPH-AFM04 : MPhys Physics with Research Placement (Full-time) - Year 3

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.