University of East Anglia Featured PhD Programmes
Coventry University Featured PhD Programmes
University of Reading Featured PhD Programmes

Mathematical methods for scale-bridging: From interacting particle systems to differential equations

  • Full or part time
  • Application Deadline
    Applications accepted all year round
  • Self-Funded PhD Students Only
    Self-Funded PhD Students Only

Project Description

Many phenomena in the natural and social sciences can be modeled on a small (or microscopic) scale by many ’particles’ that change their state according to a random input (noise) and the state of the others, think of molecules in solution or agents in a market.

Due to the high dimensionality, these models are difficult to analyse computationally. On a larger scale, however, the behaviour of such systems can often be described by differential equations which are numerically much more tractable. This leads to the problem of scale bridging, ie how to connect rigorously these different descriptions at different scales by proving limit theorems.

The topic of scale-bridging is a long-standing challenge for mathematics. In the explanation of his sixth problem, Hilbert set the task ’of developing mathematically the limiting process… which lead from the atomistic view to the laws of motion of continua’. Scale-bridging lies at the intersection of several mathematical disciplines.

The focus of the project is on applying two new mathematical developments for the purpose of scale bridging. First, the theory of gradient flows and Wasserstein metrics developed by Otto and co-authors and for the first time applied to the analysis of interacting particle systems by the first supervisor and co-authors (ADPZ 2013), and second the recent progress in the theory of stochastic homogenisation by Armstrong, Cardaliaguet, Souganidis and others. Typical examples will include interacting diffusions, zero-range processes and variants of the Ising model.

Applicants should submit an application for postgraduate study via the online application service

In the funding section, please select the ’self -funding’ option and specify the project title

Funding Notes

We are interested in pursuing this project and welcome applications if you are self-funded or have funding from other sources, including government sponsorships or your employer.

Related Subjects

How good is research at Cardiff University in Mathematical Sciences?

FTE Category A staff submitted: 24.05

Research output data provided by the Research Excellence Framework (REF)

Click here to see the results for all UK universities

Email Now

Insert previous message below for editing? 
You haven’t included a message. Providing a specific message means universities will take your enquiry more seriously and helps them provide the information you need.
Why not add a message here
* required field
Send a copy to me for my own records.

Your enquiry has been emailed successfully

FindAPhD. Copyright 2005-2020
All rights reserved.