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Collisions with evolving surfaces

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 Pascal Buenzli
Division / Faculty
Science and Engineering Faculty


The density of impacts of particles colliding with an evolving surface is of particular interest for several industrial and biological applications. These include etching and deposition processes [1], the incorporation of molecules in a tissue during its growth, budding cell membranes, and biological tissue growth [2]. Impacts on an evolving surface are generated unevenly depending on the relative velocity between the particles and the surface. The distribution of impacts further evolves in a curvature-dependent manner due to the local distortions of the surface [3].


  1. Sethian JA (1999) Level set methods and fast marching methods. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science; 2nd Ed. (Cambridge University Press)
  2. Simpson MJ, Sharp JA, Baker RE (2015) Survival probability for a diffusive process on a growing domain, Phys Rev E 91:042701
  3. Alias A, Buenzli PR (2017) Modeling the effect of curvature on the collective behavior of cells growing new tissue, Biophys J 112:193–204

Research activities

In many applications, the density of impacts influences directly the evolution of the interface. This project will derive general equations for the co-evolution of impact density and interface movement using explicit parameterisations of the interface, or implicit representations of the interface such as a level-set description [1]. You will investigate conditions leading to quasi-steady states (travelling waves) and simulate these equations numerically. The model will be applied to biologically relevant situations such as bone remodelling, wound closure, scratch assays, or bioscaffold tissue growth to understand the specific influence of interface geometry.


There is the possibility in this project to work in close collaboration with an experimental bone biology group in Denmark collecting novel data on bone resorbing surfaces. Results from the mathematical models will be compared with experimental data available through collaboration or from the literature, and with previous mathematical models of bioscaffold tissue growth [3].

Skills and experience

This project can be tailored to suit research students at Honours, Masters, and PhD level. Some proficiency in differential equations and computer modelling is expected.


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

Annual scholarship round



Contact the supervisor for more information.