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Critical and extreme phenomena in Complex Systems (Advert Reference: RDF22/EE/MPEE/BENASSI)

   Faculty of Engineering and Environment

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  Dr Costanza Benassi, Dr Daniel Ratliff, Dr Antonio Moro  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

Phase transitions are ubiquitous. They manifest themselves in Nature as catastrophic events, and their mathematical understanding underpins the description of a plethora of phenomena across a wide range of physical scales, from quantum field theory to biological chemistry, from magnetism to neural networks. In general, phase transitions are characterised by sudden and dramatic changes in the phenomenology of the system in response to the fine tuning of the relevant parameters. These extreme phenomena are pervasive and their investigation is thus at the forefront of our understanding of complex systems.

Within this project you will study and investigate a variety of statistical mechanical and complex systems, as their critical features are underpinned by a unifying mathematical framework. Many different mathematical tools and techniques are available, depending on the physical and mathematical scenario and on the specific system under investigation. In particular, you will explore a blend of approaches and investigate different mathematical frameworks, ranging from statistical mechanics to the theory of integrable systems, from random matrix theory to the theory of nonlinear waves, with the aim of understanding the general mechanisms underlying the occurrence of extreme phenomena in complex systems.

Some examples of models you will investigate are lattice spin systems emerging from statistical mechanics, and probabilistic models of random matrices. These complex systems show a rich critical behaviour, with strikingly diverse and varied phenomenologies, and regard very different mathematical and physical scenarios. Nonetheless their investigation shows that they share a common ground – indeed, their critical features can be analysed through similar mathematical lenses, as a testimony of a universal extreme phenomenon.

Hence, within this project you will develop skills and knowledge in various fields of mathematics and mathematical physics. Specifically, you will investigate some relevant models for complex systems with the goal of appraising their critical properties and possible regimes, to uncover the unifying features of extreme and critical phenomena. This will give you the opportunity to delve into a variety of topics from statistical mechanics, the theory of nonlinear waves and integrable systems.

The Principal Supervisor for this project is Dr Costanza Benassi.

Eligibility and How to Apply:

Please note eligibility requirement:

  • Academic excellence of the proposed student i.e. 2:1 (or equivalent GPA from non-UK universities [preference for 1st class honours]); or a Masters (preference for Merit or above); or APEL evidence of substantial practitioner achievement.
  • Appropriate IELTS score, if required.
  • Applicants cannot apply for this funding if currently engaged in Doctoral study at Northumbria or elsewhere or if they have previously been awarded a PhD.

For further details of how to apply, entry requirements and the application form, see

Please note: Applications that do not include a research proposal of approximately 1,000 words (not a copy of the advert), or that do not include the advert reference (e.g. RDF22/…) will not be considered.

Deadline for applications: 18 February 2022

Start Date: 1 October 2022

Northumbria University takes pride in, and values, the quality and diversity of our staff and students. We welcome applications from all members of the community.

Funding Notes

Each studentship supports a full stipend, paid for three years at RCUK rates (for 2021/22 full-time study this is £15,609 per year) and full tuition fees. UK and international (including EU) candidates may apply.
Studentships are available for applicants who wish to study on a part-time basis over 5 years (0.6 FTE, stipend £9,365 per year and full tuition fees) in combination with work or personal responsibilities.
Please also read the full funding notes which include advice for international and part-time applicants.


Symmetric matrix ensemble and integrable hydrodynamic chains. Benassi, C., Dell’Atti, M., &
Moro, A., 2021, In: Letters in Mathematical Physics, 111, 78.
Thermodynamic limit and dispersive regularization in matrix models. Benassi, C. & Moro, A., 2020, In : Physical Review E (PRE). 101, 5, 052118.
Loop Correlations in Random Wire Models. Benassi, C. & Ueltschi, D., 2020, In :
Communications in Mathematical Physics. 374, 2, p. 525-547.
Decay of Correlations in 2D Quantum Systems with Continuous Symmetry. Benassi, C.,
Fröhlich, J. & Ueltschi, D., 2017, In : Annales Henri Poincare. 18, 9, p. 2831–2847.
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