Whether the 3D incompressible Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this talk, I will present some new numerical evidence that the 3D Navier-Stokes equations develop nearly self-similar singular scaling properties with maximum vorticity increased by a factor of $10^7$. This potentially singular behavior is induced by a potential finite time singularity of the 3D Euler equations. Unlike the Hou-Luo blowup scenario, the potential singularity of the 3D Euler and Navier-Stokes equations occurs at the origin. We have applied several blowup criteria to study the potentially singular behavior of the Navier-Stokes equations. The Beale-Kato-Majda blow-up criterion, the blowup criteria based on the growth of enstrophy and negative pressure, the Ladyzhenskaya-Prodi-Serrin regularity criteria all seem to imply that the Navier-Stokes equations develop nearly singular behavior. Finally, we present some new numerical evidence that a class of generalized axisymmetric Navier-Stokes equations with time dependent fractional dimension and nonlinear rotation force seem to develop asymptotically self-similar blowup.

According to the UN, 4.2 billion people, that is, more than 50% of the world’s population, lack access to safely managed sanitation. As part of SDG6, we should aim to achieve safely managed sanitation for all by 2030. But how are we going to do that? And how do we even define safely managed sanitation? We’ll be talking about this and other aspects of sanitation with Jillian Maxcy-Brown (University of Alabama), Michael Templeton (Imperial College London) and Sonia Grego (Duke University).

Life is full of hydrated interfaces that all must obey physical principles. Neglecting conservation laws (unintentionally or not) is no misdemeanor but a serious violation of nature’s principles and can lead to an absurd picture of nature. I here present, what (biological) interfaces naturally “produce” once “fed” with momentum conservation and the 2nd law of thermodynamics. Data show the existence of linear and nonlinear pulses, which are capable to trigger and suppress enzymatic activity. Together with the 2nd law, momentum conservation allows to control biological processes from remote. Specificity of this control also arises from physics and is found in the phase diagrams of this interfaces near transitions (state-function relation). Together this leads to a physical perspective for the origin of biological communication and a concept for the integration of physical principles and biochemical reactions.

This paper examines the efforts of the National Health Service (England) (NHSE) to address employee-based racial inequalities via the Workforce Race Equality Standard (WRES). The WRES mandates NHS-affiliated organisations including healthcare trusts to prepare annual reports detailing their performance against nine pre-established race-oriented indicators and planned actions to remedy identified inequities. Drawing on critical race theory (CRT), the study uses qualitative content analysis to analyse the WRES reports from 40 NHSE trusts between the period 2019 to 2021. Results indicate trust tendencies to present incomplete data or factual presentations with limited reflection of their race positions, and there is also evidence of practices of impression management. Regarding action plans, whilst there is evidence of some good practice, organisations do not seek to meaningfully capture and/or act on the lived experiences of colleagues, or disrupt institutional structures and systems that underlie discriminatory practices. Instead, actions often resort to generic NHSE or equality, diversity and inclusion initiatives or are grounded in the racial deficit model, and ignore intersectionality. Planned actions also sometimes show little progression over time or connection to the trust data. Overall, action plans may highlight practices of interest convergence: they espouse good intentions whilst, simultaneously, maintaining the status quo. Whilst the WRES is a laudable voluntary achievement, genuine change calls for a commitment to the cause – that is a felt accountability.

The stratified inclined duct (SID) is a relatively new experimental paradigm that produces a sustained shear flow between two counterflowing layers of fluid supplied by reservoirs at each end of the duct containing fluids of different density. The duct can be tilted at a small angle θ to the horizontal and, for a given fluid, the flow is determined by two nondimensional parameters θ and the Reynolds number. We have observed four different flow regimes in SID: Laminar when the interface between the layers remains undisturbed, Holmboe characterised by sharp cusped waves on the interface, Intermittent when the flow has bursts of turbulence followed by relatively calm periods and Turbulent when the turbulence occurs throughout the duct and is sustained in time. The laminar regime occurs at low Re and θ, and transitions to the other regimes occur successively as Re and θ increase, so SID allows a systematic study of the different regimes. One of the most important questions in stratified turbulence is the efficiency with which the fluid is mixed. When the stratification is stable, with density decreasing with height, work needs to be done against gravity to move light fluid downwards and dense fluid upwards so that irreversible mixing can occur. The ‘tax’ that this irreversible mixing imposes on the kinetic energy of the flow, the so-called ‘mixing efficiency’ is important to parameterise mixing in ocean and climate models. In this talk I will discuss the philosophy behind SID and explain why the experiment is relevant to this issue, particularly in the context of the energetics of the flow. We focus first on the self-organisation properties of the flows, wherein more strongly turbulent flows tend to an asymptotic state characterised by a uniform gradient Richardson number of order 0.1-0.2 across the shear layer. We then summarise our results on turbulent energetics and mixing statistics. We derive the kinetic and scalar energy budgets and explain the specificity and scalings of SID turbulence. We assess the relevance of standard mixing parameterisations models, and we compare representative values with the literature. The dependence of these measures of mixing on controllable flow parameters provides asymptotic estimates that may be extrapolated to more strongly turbulent flows. Complementing the experiments we introduce the first accurate 3D DNS for SID. Implementing a suitable forcing method and boundary conditions allow us to maintain steady exchange flow for an arbitrarily long time at a minimal computational cost. With the newly developed numerical model, we explore the diverse transitions in SID from a numerical perspective.

Active flutter suppression is a promising technology for advanced flight vehicles, but greatly relies on accurate and simple models of fluid-structure interaction. For example, it is a great challenge to establish such a model for the flutter controller of an aircraft subject to a transonic flow, which is nonlinear by nature. The lecture addresses how to construct a surrogate model from CFD data to predict the transonic flutter of an aircraft wing and to actively suppress it in a wide range of flow regime. The lecture presents how to use simple physical knowledge to improve both interpretability and generalizability of the surrogate model, which are two essential issues in data-driven modeling. The lecture also shows the design of a flutter controller via machine learning.

In logical geometry, Aristotelian diagrams are studied in a precise and systematic way. Although there has recently been a good amount of progress in logical geometry, it is still unknown which underlying mathematical framework is best suited for formalizing the study of these diagrams. Hence, in this paper, the main aim is to formulate such a framework, using the powerful language of category theory. We build multiple categories, which all have Aristotelian diagrams as their objects, while having different kinds of morphisms between these diagrams. The categories developed here are assessed according to their ability to generalize previous work from logical geometry as well as their interesting category-theoretical properties. According to these evaluations, the most promising category has as its morphisms those functions on fragments that increase in informativity on both the opposition and implication relations. Focusing on this category can significantly increase the effectiveness of further research in logical geometry.

Describing exactly how waves multiply scatter between a complex arrangement of particles is challenging. There exist accurate numerical methods, but they lack intuition, and can be slow for a large quantity of particles. To resolve this, we use theoretical methods to deduce dispersion equations, usually for an infinite media, which leads to a basis for the solution. The solution can then be completely determined with some boundary conditions or matching. This is true for periodic materials, homogeneous, and also holds true for waves in material with a random arrangement of particles (averaged over all configurations) for any frequency. In this talk, I will give an overview of results for waves in a random particulate, while making some light comparisons with periodic materials. There are many opportunities and applications of this theory in both developing new sensors and designing materials, which I will mention.

All beauty, richness and harmony in the emergent dynamics of a complex system largely depend on the specific way in which its elementary components interact. The last twenty-five years have seen the birth and development of the multidisciplinary field of Network Science, wherein a variety of distributed systems in physics, biology, social sciences and engineering have been modeled as networks of coupled units, in the attempt to unveil the mechanisms underneath their observed functionality. There is, however, a fundamental limit to such a representation: networks capture only pairwise interactions, whereas the functioning of many real-world systems not only involves dyadic connections, but rather is the outcome of collective actions at the level of groups of nodes. For instance, in ecological systems, three or more species may compete for food or territory, and similar multi-component interactions appear in functional and structural brain networks, protein interaction networks, semantic networks, multi-authors scientific collaborations, offline and online social networks, gene regulatory networks and spreading of consensus or contagious diseases due to multiple, simultaneous, contacts. Such multi-component interactions can only be grasped through either hypergraphs or simplicial complexes, which indeed have recently found a huge number of applications. In this report, we cover the extensive literature of the past years on this subject, and we focus on the structure and dynamics of hypergraphs and simplicial complexes. These are indeed becoming increasingly relevant, thanks to the enhanced resolution of data sets and the recent advances in data analysis techniques, which (concurrently and definitely) have shown that such structures play a pivotal role in the complex organization and functioning of real-world distributed systems.

Wastewater contains a wide suite of microbial and chemical contaminants. However, not all microorganisms in wastewater are bad. They can be a source of inoculum which we can then tap into to assemble microbial barriers within biotechnologies. These microbial barriers can aid in efficient wastewater treatment. In this seminar, we discuss the role of microbial barriers in removing antibiotic resistance genes and organic micropollutants from wastewater. With the help of microbial barriers in bioreactors, wastewater can be converted into high-quality reclaimed water to meet the UN’s Sustainable Development Goal 6 (SDG6) of providing clean water and sanitation for all and to allow sustainable cities and communities to develop (SDG11). The reclaimed water can also be used for food (SDG2) and energy production (SDG7).