We investigate theoretically the breakup dynamics of an elasto-visco-plastic filament surrounded by an inert gas. The filament is initially placed between two coaxial disks, and the upper disk is suddenly pulled away, inducing deformation due to both constant stretching and capillary forces. We model the rheological response of the material with the Saramito–Herschel–Bulkley (SHB) model. Assuming axial symmetry, the mass and momentum balance equations, along with the constitutive equation, are solved using the finite element framework PEGAFEM-V, enhanced with adaptive mesh refinement with an underlying elliptic mesh generation algorithm. As the minimum radius decreases, the breakup dynamics accelerates significantly. We demonstrate that the evolution of the minimum radius, velocity and axial stress follow a power-law scaling, with the corresponding exponent depending on the SHB shear-thinning parameter, $n$. The scaling exponents obtained from our axisymmetric simulations under creeping flow are verified through asymptotic analysis of the slender filament equations. Our findings reveal three distinct breakup regimes: (a) elasto-plastic, (b) elasto-plasto-capillary, both with finite-time breakup for $n\lt 1$, and (c) elasto-plasto-capillary with no finite-time breakup for $n=1$. We show that self-similar solutions close to filament breakup can be achieved by appropriate rescaling of length, velocity and stress. Notably, the effect of the yield stress becomes negligible in the late stages of breakup due to the local dominance of high elastic stresses. Moreover, the scaling exponents are independent of elasticity, resembling the breakup behaviour of finite extensible viscoelastic materials.

Researchers across disciplines increasingly use Generative Artificial Intelligence (GenAI) to label text and images or as pseudo-respondents in surveys. But of which populations are GenAI models most representative? We use an image classification task—assessing crowd-sourced street view images of urban neighborhoods in an American city—to compare assessments generated by GenAI models with those from a nationally representative survey and a locally representative survey of city residents. While GenAI responses, on average, correlate strongly with the perceptions of a nationally representative survey sample, the models poorly approximate the perceptions of those actually living in the city. Examining perceptions of neighborhood safety, wealth, and disorder reveals a clear bias in GenAI toward national averages over local perspectives. GenAI is also better at recovering relative distributions of ratings, rather than mimicking absolute human assessments. Our results provide evidence that GenAI performs particularly poorly in reflecting the opinions of hard-to-reach populations. Tailoring prompts to encourage alignment with subgroup perceptions generally does not improve accuracy and can lead to greater divergence from actual subgroup views. These results underscore the limitations of using GenAI to study or inform decisions in local communities but also highlight its potential for approximating “average” responses to certain types of questions. Finally, our study emphasizes the importance of carefully considering the identity and representativeness of human raters or labelers—a principle that applies broadly, whether GenAI tools are used or not.

The early stage of a gravity-driven flow resulting from the sudden removal of a floating body is investigated. Initially, the fluid is at rest, with a rigid, symmetric wedge floating on its surface. The study focuses on the initial evolution of the wedge-shaped depression formed on the water’s free surface. The fluid has finite depth, and the resulting flow is assumed to be governed by potential theory. The initial flow is described by a linear boundary-value problem, which is solved using conformal mapping and the theory of complex analytic functions. The behaviour of the flow velocity near the corner points of the fluid domain is analysed in detail. It is shown that the linear theory predicts a power-law singularity in the flow velocity at the vertex of the wedge-shaped depression, with the exponent depending on the wedge angle. As the cavity extends toward the bottom, the flow singularity at the vertex becomes stronger. The local flow near the vertex is shown to be self-similar at leading order in the short-time limit. At the other two corner points – where the initial free surface intersects the surface of the wedge – the linear theory predicts continuous velocities with singular velocity gradients. Theoretical predictions are compared with numerical results obtained using OpenFOAM. Good agreement is observed at short times, except in small vicinities of the corner points, where inner solutions are required. In practical applications, understanding the short-time behaviour of the depressions is important for predicting jet formation in regions of high surface curvature.

Codebooks—documents that operationalize concepts and outline annotation procedures—are used almost universally by social scientists when coding political texts. To code these texts automatically, researchers are increasingly turning to generative large language models (LLMs). However, there is limited empirical evidence on whether “off-the-shelf” LLMs faithfully follow real-world codebook operationalizations and measure complex political constructs with sufficient accuracy. To address this, we gather and curate three real-world political science codebooks—covering protest events, political violence, and manifestos—along with their unstructured texts and human-coded labels. We also propose a five-stage framework for codebook-LLM measurement: Preparing a codebook for both humans and LLMs, testing LLMs’ basic capabilities on a codebook, evaluating zero-shot measurement accuracy (i.e., off-the-shelf performance), analyzing errors, and further (parameter-efficient) supervised training of LLMs. We provide an empirical demonstration of this framework using our three codebook datasets and several pre-trained 7–12 billion open-weight LLMs. We find current open-weight LLMs have limitations in following codebooks zero-shot, but that supervised instruction-tuning can substantially improve performance. Rather than suggesting the “best” LLM, our contribution lies in our codebook datasets, evaluation framework, and guidance for applied researchers who wish to implement their own codebook-LLM measurement projects.

Rotor–stator interactions in turbomachines are characterised by a complex interplay of hydrodynamic instabilities, acoustic pressure waves and receptivity mechanisms, as well as the collision of coherent structures with the blade geometry. An unsteady dual analysis of self-excited instabilities and flow interactions, exemplified by a simple model compressor stage under subsonic conditions, is proposed and presented. Using a low-dissipation sliding-plane implementation, instability-resolving nonlinear-adjoint looping simulations provide detailed sensitivity information that allows for the dissection of the full flow into sub-components linked to distinct flow phenomena. This sensitivity information further links observed flow behaviour to its hydrodynamic or acoustic origin, thereby laying the foundation for a cause-and-effect analysis and for flow control.

The study of the shape of droplets on surfaces is an important problem in the physics of fluids and has applications in multiple industries, from agrichemical spraying to microfluidic devices. Motivated by these real-world applications, computational predictions for droplet shapes on complex substrates – rough and chemically heterogeneous surfaces – are desired. Grid-based discretisations in axisymmetric coordinates form the basis of well-established numerical solution methods in this area, but when the problem is not axisymmetric, the shape of the contact line and the distribution of the contact angle around it are unknown. Recently, particle methods, such as pairwise-force smoothed particle hydrodynamics (PF-SPH), have been used to conveniently forego explicit enforcement of the contact angle. The pairwise-force model, however, is far from mature, and there is no consensus in the literature on the choice of pairwise-force profile. We propose a new pair of polynomial force profiles with a simple motivation and validate the PF-SPH model in both static and dynamic tests. We demonstrate its capabilities by computing droplet shapes on a physically structured surface, a surface with a hydrophilic stripe and a virtual wheat leaf with both micro-scale roughness and variable wettability. We anticipate that this model can be extended to dynamic scenarios, such as droplet spreading or impaction, in the future.

Invariant maps are a useful tool for turbulence modelling, and the rapid growth of machine learning-based turbulence modelling research has led to renewed interest in them. They allow different turbulent states to be visualised in an interpretable manner and provide a mathematical framework to analyse or enforce realisability. Current invariant maps, however, are limited in machine learning models by the need for costly coordinate transformations and eigendecomposition at each point in the flow field. This paper introduces a new polar invariant map based on an angle that parametrises the relationship of the principal anisotropic stresses, and a scalar that describes the anisotropy magnitude relative to a maximum value. The polar invariant map reframes realisability in terms of a limiting anisotropy magnitude, allowing for new and simplified approaches to enforcing realisability that do not require coordinate transformations or explicit eigendecomposition. Potential applications to machine learning-based turbulence modelling include post-processing corrections for realisability, realisability-informed training, turbulence models with adaptive coefficients and general tensor basis models. The relationships to other invariant maps are illustrated through examples of plane channel flow and square duct flow. Sample calculations are provided for a comparison with a typical barycentric map-based method for enforcing realisability, showing an average 62 % reduction in calculation time using the equivalent polar formulation. The results provide a foundation for new approaches to enforcing realisability constraints in Reynolds-averaged turbulence modelling.

In recent years, integrating physical constraints within deep neural networks has emerged as an effective approach for expediting direct numerical simulations in two-phase flow. This paper introduces physics-informed neural networks (PINNs) that utilise the phase-field method to model three-dimensional two-phase flows. We present a fully connected neural network architecture with residual blocks and spatial parallel training using the overlapping domain decomposition method across multiple graphics processing units to enhance the accuracy and computational efficiency of PINNs for the phase-field method (PF-PINNs). The proposed PINNs framework is applied to a bubble rising scenario in a three-dimensional infinite water tank to quantitatively assess the performance of PF-PINNs. Furthermore, the computational cost and parallel efficiency of the proposed method was evaluated, demonstrating its potential for widespread application in complex training environments.

The pressure effects on the mixing fields of non-reacting and reacting jets in cross-flow are studied using large eddy simulation (LES). A hydrogen jet diluted with 30 % helium is injected perpendicularly into a cross-stream of air at four different pressures: 1, 4, 7 and 15 bar. The resulting interaction and the mixing fields under non-reacting and reacting conditions are simulated using LES. The subgrid scale combustion is modelled using a revised flamelet model for the partially premixed combustion. Good agreement of computed and measured velocity fields for reacting and non-reacting conditions is observed. Under non-reacting conditions, the mixing field shows no sensitivity to the pressure, whereas notable changes are observed for reacting conditions. The lifted flame at 1 bar moves upstream and attaches to the nozzle as the pressure is increased to 4 bar and remains so for the other elevated pressures because of the increasing burning mass flux with pressure. This attached flame suppresses the fuel–air mixing in the near-nozzle region. The premixed and non-premixed contributions to the overall heat release in the partially premixed combustion are analysed. The non-premixed contribution is generally low and occurs in the near-field region of the fuel jet through fuel-rich mixtures in the shear layer regions, and decreases substantially further with the increase in pressure. Hence, the predominant contributions are observed to come from premixed modes and these contributions increase with pressure.

Several million years of natural evolution have endowed marine animals with high flexibility and mobility. A key factor in this achievement is their ability to modulate stiffness during swimming. However, an unresolved puzzle remains regarding how muscles modulate stiffness, and the implications of this capability for achieving high swimming efficiency. Inspired by this, we proposed a self-propulsor model that employs a parabolic stiffness-tuning strategy, emulating the muscle tensioning observed in biological counterparts. Furthermore, efforts have been directed towards developing the nonlinear vortex sheet method, specifically designed to address nonlinear fluid–structure coupling problems. This work aims to analyse how and why nonlinear tunable stiffness influences swimming performance. Numerical results demonstrate that swimmers with nonlinear tunable stiffness can double their speed and efficiency across nearly the entire frequency range. Additionally, our findings reveal that high-efficiency biomimetic propulsion originates from snap-through instability, which facilitates the emergence of quasi-quadrilateral swimming patterns and enhances vortex strength. Moreover, this study examines the influence of nonlinear stiffness on swimming performance, providing valuable insights into the optimisation of next-generation, high-performance, fish-inspired robotic systems.

We investigate the energy transfer from the mean profile to velocity fluctuations in channel flow by calculating nonlinear optimal disturbances, i.e. the initial condition of a given finite energy that achieves the highest possible energy growth during a given fixed time horizon. It is found that for a large range of time horizons and initial disturbance energies, the nonlinear optimal exhibits streak spacing and amplitude consistent with direct numerical simulation (DNS) at least at ${Re}_\tau = 180$, which suggests that they isolate the relevant physical mechanisms that sustain turbulence. Moreover, the time horizon necessary for a nonlinear disturbance to outperform a linear optimal is consistent with previous DNS-based estimates using eddy turnover time, which offers a new perspective on how some turbulent time scales are determined.

The transient dynamics of a wake vortex, modelled as a strong swirling $q$-vortex, is investigated with a focus on optimal transient growth driven by continuous eigenmodes associated with continuous spectra. The pivotal contribution of viscous critical-layer eigenmodes (Lee and Marcus, J. Fluid Mech. vol. 967, 2023, p. A2) amongst the entire eigenmode families to optimal perturbations is numerically confirmed, using a spectral collocation method for a radially unbounded domain that ensures correct analyticity and far-field behaviour. The consistency of the numerical method across different sensitivity tests supports the reliability of the results and provides flexibility for tuning. Both axisymmetric and helical perturbations with axial wavenumbers of order unity or less are examined through linearised theory and nonlinear simulations, yielding results that align with existing literature on energy growth curves and optimal perturbation structures. The initiation process of transient growth is also explored, highlighting its practical relevance. Inspired by ice crystals in contrails, the backward influence of inertial particles on the vortex flow, particularly through particle drag, is emphasised. In the pursuit of optimal transient growth, particles are initially distributed at the periphery of the vortex core to disturb the flow. Two-way coupled vortex–particle simulations reveal clear evidence of optimal transient growth during ongoing vortex–particle interactions, reinforcing the robustness and significance of transient growth in the original nonlinear vortex system over finite time periods.

In the dynamical systems approach to turbulence, unstable periodic orbits (UPOs) provide valuable insights into system dynamics. Such UPOs are usually found by shooting-based Newton searches, where constructing sufficiently accurate initial guesses is difficult. A common technique for constructing initial guesses involves detecting recurrence events by comparing past and future flow states using their $L_2$-distance. An alternative method uses dynamic mode decomposition (DMD) to generate initial guesses based on dominant frequencies identified from a short time series, which are signatures of a nearby UPO. However, DMD struggles with continuous symmetries. To address this drawback, we combine symmetry-reduced DMD (SRDMD) introduced by Marensi et al. (2023, J. Fluid Mech., vol. 954, A10), with sparsity promotion. This combination provides optimal low-dimensional representations of the given time series as a time-periodic function, allowing any time instant along this function to serve as an initial guess for a Newton solver. We also discuss how multi-shooting methods operate on the reconstructed trajectories, and we extend the method to generate initial guesses for travelling waves. We demonstrate SRDMD as a method complementary to recurrent flow analysis by applying it to data obtained by direct numerical simulations of three-dimensional plane Poiseuille flow at the friction Reynolds number $\textit{Re}_\tau \approx51$ ($\textit{Re}=802$), explicitly taking a continuous shift symmetry in the streamwise direction into account. The resulting unstable relative periodic orbits cover relevant regions of the state space, highlighting their potential for describing the flow.

We present a numerical scheme that solves for the self-similar viscous fingers that emerge from the Saffman–Taylor instability in a divergent wedge. This is based on the formulation by Ben Amar (1991, Phys. Rev. A, vol. 44, pp. 3673–3685). It is demonstrated that there exists a countably infinite set of selected solutions, each with an associated relative finger angle, and furthermore, solutions can be characterised by the number of ripples located at the tip of their finger profiles. Our numerical scheme allows us to observe these ripples and measure them, demonstrating that the amplitudes are exponentially small in terms of the surface tension; the selection mechanism is driven by these exponentially small contributions. A recently published paper derived the selection mechanism for this problem using exponential asymptotic analytical techniques, and obtained bifurcation diagrams that we compare with our numerical results.

This paper presents a peridynamics-based computational approach for modelling coupled fluid flow and heat transfer problems. A new thermo-hydrodynamic peridynamics model is formulated with the semi-Lagrangian scheme and non-local operators. To enhance accuracy and numerical stability, a multi-horizon scheme is developed to introduce distinct horizons for the flow field and thermal field. The multi-horizon scheme helps to capture the convective zone and complex thermal flow pattern while effectively mitigating possible oscillations in temperature. We validate the computational approach using benchmarks and numerical examples including heat conduction, natural convection in a closed cavity, and Rayleigh–Bénard convection cells. The results demonstrate that the proposed method can accurately capture typical thermal flow behaviours and complex convective patterns. This work offers a new foundation for future development of a unified peridynamics framework for robust, comprehensive multi-physics analysis of thermal fluid–solid interaction problems with complex evolving discontinuities in solids.

Geophysical and astrophysical fluid flows are typically driven by buoyancy and strongly constrained at large scales by planetary rotation. Rapidly rotating Rayleigh–Bénard convection (RRRBC) provides a paradigm for experiments and direct numerical simulations (DNS) of such flows, but the accessible parameter space remains restricted to moderately fast rotation rates (Ekman numbers ${ {Ek}} \gtrsim 10^{-8}$), while realistic ${Ek}$ for geo- and astrophysical applications are orders of magnitude smaller. On the other hand, previously derived reduced equations of motion describing the leading-order behaviour in the limit of very rapid rotation ($ {Ek}\to 0$) cannot capture finite rotation effects, and the physically most relevant part of parameter space with small but finite ${Ek}$ has remained elusive. Here, we employ the rescaled rapidly rotating incompressible Navier–Stokes equations (RRRiNSE) – a reformulation of the Navier–Stokes–Boussinesq equations informed by the scalings valid for ${Ek}\to 0$, recently introduced by Julien et al. (2024) – to provide full DNS of RRRBC at unprecedented rotation strengths down to $ {Ek}=10^{-15}$ and below, revealing the disappearance of cyclone–anticyclone asymmetry at previously unattainable Ekman numbers (${Ek}\approx 10^{-9}$). We also identify an overshoot in the heat transport as ${Ek}$ is varied at fixed $\widetilde { {Ra}} \equiv {Ra}{Ek}^{4/3}$, where $Ra$ is the Rayleigh number, associated with dissipation due to ageostrophic motions in the boundary layers. The simulations validate theoretical predictions based on thermal boundary layer theory for RRRBC and show that the solutions of RRRiNSE agree with the reduced equations at very small ${Ek}$. These results represent a first foray into the vast, largely unexplored parameter space of very rapidly rotating convection rendered accessible by RRRiNSE.

We perform the first mapping of the ideological positions of European parties using generative Artificial Intelligence (AI) as a “zero-shot” learner. We ask OpenAI’s Generative Pre-trained Transformer 3.5 (GPT-3.5) to identify the more “right-wing” option across all possible duplets of European parties at a given point in time, solely based on their names and country of origin, and combine this information via a Bradley–Terry model to create an ideological ranking. A cross-validation employing widely-used expert-, manifesto- and poll-based estimates reveals that the ideological scores produced by Large Language Models (LLMs) closely map those obtained through the expert-based evaluation, i.e., CHES. Given the high cost of scaling parties via trained coders, and the scarcity of expert data before the 1990s, our finding that generative AI produces estimates of comparable quality to CHES supports its usage in political science on the grounds of replicability, agility, and affordability.

Rogue waves (RWs) can form on the ocean surface due to the well-known quasi-four-wave resonant interaction or superposition principle. The first is known as the nonlinear focusing mechanism and leads to an increased probability of RWs when unidirectionality and narrowband energy of the wave field are satisfied. This work delves into the dynamics of extreme wave focusing in crossing seas, revealing a distinct type of nonlinear RWs, characterised by a decisive longevity compared with those generated by the dispersive focusing (superposition) mechanism. In fact, through fully nonlinear hydrodynamic numerical simulations, we show that the interactions between two crossing unidirectional wave beams can trigger fully localised and robust development of RWs. These coherent structures, characterised by a typical spectral broadening then spreading in the form of dual bimodality and recurrent wave group focusing, not only defy the weakening expectation of quasi-four-wave resonant interaction in directionally spreading wave fields, but also differ from classical focusing mechanisms already mentioned. This has been determined following a rigorous lifespan-based statistical analysis of extreme wave events in our fully nonlinear simulations. Utilising the coupled nonlinear Schrödinger framework, we also show that such intrinsic focusing dynamics can be captured by weakly nonlinear wave evolution equations. This opens new research avenues for further explorations of these complex and intriguing wave phenomena in hydrodynamics as well as other nonlinear and dispersive multi-wave systems.