| EPSRC Reference: |
EP/Z533580/1 |
| Title: |
SNSCHEs: Mathematical analysis of binary fluid mixtures |
| Principal Investigator: |
Brzezniak, Professor Z |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
University of York |
| Scheme: |
UKRI Postdoc Guarantee TFS |
| Starts: |
01 September 2024 |
Ends: |
31 August 2026 |
Value (£): |
192,297
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Summary on Grant Application Form |
A good understanding of fluid mechanics models is essential in many applied fields, ranging from aerodynamics to meteorology. In this project, we will concentrate on two mathematical models arising from the diffuse interface theory, and we will study their long-time behavior in a setting that should correspond better to physical reality than the results available in contemporary literature.
The first model, called the Navier-Stokes-Cahn-Hilliard equations (NSCHEs), describes more accurately the flow of two viscous incompressible Newtonian fluids with different densities and viscosities. The second model pertains to two-phase complex fluids with quadratic anchoring in Soft Matter Physics. It can be viewed as a generalization of the NSCHEs for an immiscible mixture of nematic liquid crystal fluid immersed in a viscous fluid matrix.
Regarding the research proposed in this project, our focus is on the well-posedness and the existence of invariant measures and the large deviations principle for stochastic NSCHEs. These equations involve gradient-dependent noise and white noise affecting the NSEs and the CHEs separately. Particularly, we plan to study two concepts in the theory of randomly perturbed dynamical systems: the quasipotential and the action functional. These concepts play an important role in the theory of small perturbations of dynamical systems and in the analysis of transitions between equilibria.
Moreover, this project primarily involves mathematical analysis for a model of two-phase complex fluids with quadratic anchoring proposed in this proposal, not in the numerical sense as in the literature. Therefore, our starting point for studying this model of two-phase complex fluids is to establish good solution theories both in the deterministic and the stochastic cases. Such theories will then enable us to explore various qualitative features of the solutions and will pave the way for studying other related equations that are currently beyond our grasp.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.york.ac.uk |