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Characteristic time scales for heterogeneous transport processes

Study level

Master of Philosophy


Vacation research experience scheme

Faculty/Lead unit

Science and Engineering Faculty

School of Mathematical Sciences

Topic status

We're looking for students to study this topic.


Dr Elliot Carr
Senior Lecturer
Division / Faculty
Science and Engineering Faculty


Diffusion is the process by which particles are transported from a region of high concentration to a region of low concentration as a result of random motions. Processes exhibiting diffusive behaviour occur in a wide variety of fields including hydrology, drug delivery, thermal engineering and cell biology. In a one-dimensional homogeneous medium, diffusion processes are often characterised by a time scale proportional to L2/D, where D is the diffusivity and L is the length of the medium. This simple formula explains, in a straightforward manner, that diffusion processes take longer for smaller values of D and larger values of L. This project will focus on deriving similar formulas for more sophisticated transport processes in heterogeneous media.

Relevant Literature: EJ Carr (2018) Characteristic time scales for diffusion processes through layers and across interfaces, Physical Review E, 97, 042115.

More information can be found on Dr Carr's personal research website.

Research activities

You will meet regularly with Dr Carr to acquire new knowledge, brainstorm ideas, discuss your progress and receive direction on future work. This project will involve deriving new mathematical results, developing code in Maple and MATLAB and communicating your work in written and oral forms.


You will develop new skills in differential equations, symbolic calculation (Maple), numerical computation (MATLAB) and mathematical typesetting (LaTeX). There is also potential for you to contribute new results to the scientific/mathematical literature and publish your work in the form of a journal article

Skills and experience

This project can be tailored to either an undergraduate (VRES), Honours or Masters student and can be personalised to suit your individual interests and skills. Proficiency in MATLAB and differential equations at the level of a first or second year student is assumed.


You may be able to apply for a research scholarship in our annual scholarship round.

Annual scholarship round



Contact the supervisor for more information.