Papers

Magnetars are young, isolated neutron stars that possess an exceptionally strong magnetic field, with surface dipolar strengths on the order of $10^{15}$ G. One of the plausible scenarios for generating such a strong field is an exponential amplification by a turbulent convective dynamo during the protoneutron star phase. However, the short expected duration of the convection ($\sim 10$ s) imposes a stringent constraint on the dynamo growth rate. We perform an extensive set of 82 three-dimensional convective dynamo simulations in the anelastic approximation and investigate the kinematic phase to quantify the dynamo growth rate $\gamma$. We find that $\gamma$ increases with both the magnetic Prandtl number ${\rm Pm}$ and the Rayleigh number ${\rm Ra}$, with the most unstable mode becoming highly non-axisymmetric and multipolar. We further observe a gradual transition from large-scale to small-scale dynamo as the magnetic Reynolds number ${\rm Rm}$ increases, resulting in a magnetic field that is predominantly concentrated at small scales. The trend remains unchanged when the outer magnetic boundary condition is varied. Since resolving the increasingly small scales becomes numerically impractical, we employ the theoretical small-scale Kazantsev dynamo model to explore the large ${\rm Pm}$ regime characteristic of protoneutron stars. The model qualitatively captures the growth rate behaviour observed in simulations and, upon extrapolation to the large ${\rm Pm}$ limit, indicates that $\gamma$ is only weakly dependent on the resistivity in a PNS. Under conditions relevant to the PNS, this model predicts a magnetic energy growth rate of the order of $\sim 1$ ms$^{-1}$.

The derivative-free loss method (DFLM) is a mesh-free neural network approach for solving partial differential equations by simulating stochastic walkers rather than computing derivatives directly. Although DFLM has previously been applied to the Navier–Stokes equations, extending it to turbulent flows reveals two limitations of its simplest implementation. The walkers do not account for the swirling, directionally stretching motion of the flow, and randomly sampling the walkers used to evaluate the target introduces noise into the learned solution. We address both limitations with an analytic approximation of the walkers' local motion that captures directional stretching and eliminates this sampling noise, while remaining computationally efficient. We study the resulting method as a non-intrusive multiscale solver capable of learning macroscopic flow behavior without resolving every scale on a fine grid or explicitly coupling coarse- and fine-scale models. For two turbulent two-dimensional flows, the proposed method reproduces the macroscopic energy spectrum of fully resolved reference simulations more accurately than the standard method, particularly where directional stretching is strongest, confirming DFLM's efficacy as a multiscale solver for turbulent fluid systems.

Wall shear stress (WSS) is implicated in carotid atherosclerosis, and 4D flow MRI offers a non-invasive route to its estimation, but the agreement of MRI-derived plaque-surface WSS with computational fluid dynamics (CFD) has not been quantified in a large cohort. We compared peak-systolic velocity and WSS from 4D flow MRI and patient-specific CFD in 240 carotid arteries of 120 patients, with CFD geometries and boundary conditions derived from MRI. Velocity and circumferential WSS were compared at three standardized cross-sections, and plaque-surface WSS in 63 of 149 stenosed arteries with a reliably segmented plaque. Agreement was assessed with Bland-Altman analysis, Spearman correlation with stenosis degree, and exploratory multivariable regression of the plaque-surface discrepancy on hemodynamic and geometric variables. MRI reproduced the broad flow features but underestimated peak velocity, increasingly toward the distal internal carotid artery. WSS disagreement was location dependent: mean circumferential WSS showed little average bias in the common carotid artery, whereas MRI missed the high WSS at the bifurcation apex and underestimated plaque-surface mean and maximum WSS by $40.9 \pm 28.8\%$ and $44.5 \pm 26.8\%$; the difference in Pa increased with stenosis degree ($\rho = 0.47$ and $0.50$). In exploratory regression, the CFD-derived pressure drop across the plaque was the only significant correlate of the mean WSS discrepancy, whereas stenosis degree and geometric variables were associated with the maximum WSS discrepancy. Under the present protocol, MRI-derived plaque-surface WSS showed magnitude- and location-dependent disagreement with CFD, greater in more severely stenosed arteries and, in exploratory analyses, associated with factors beyond stenosis degree.

We present a palm-scale (65 mm, 34 g) swim-and-breach robot platform. Two vertically stacked propellers provide both propulsion and differential-thrust pitch control under a proportional-integral-derivative (PID) loop, and a tail rudder adds yaw control. The hull, evaluated by flow simulation, reduces the drag five-fold relative to an equivalent cuboid, and the propellers are optimized using B-series modeling validated by dynamometer measurements. The current robot swims at 13.9 body lengths per second and turns at 209 deg per second, corresponding to the upper limits reported for underwater robots. In free swimming, the pitch loop turns the body to any commanded nose-up pitch angle, and, with the rudder stabilizing the exit, the current robot leaps 1.6 body lengths high and 3.7 long in a seamless cruise-leap-cruise sequence. The platform can be used to build small-scale robots that cross barriers and dry gaps between pools for inspection in streams, flooded structures, and industrial systems.

Machine-learning surrogate models offer a promising alternative to high-fidelity Computational Fluid Dynamics (CFD) simulations for aerodynamic analysis and design. However, constructing accurate surrogates for realistic aircraft configurations remain challenging due to complex geometries, multiple flow regimes, and limited training data. This work presents the methodology that achieved first place in the ONERA CRM Wall Distribution Regression Challenge, which focuses on predicting pressure and skin-friction coefficient distributions over the NASA Common Research Model wing-body-pylon-nacelle configuration under different operating conditions. The proposed approach formulates the problem as a conditional neural field mapping spatial coordinates, surface normals, and operating conditions to aerodynamic wall quantities. Fourier feature encoding, a relative squared error objective aligned with the challenge metric, ensemble learning, and $k$-fold cross-validation are progressively introduced to improve prediction accuracy and exploit the limited training data. Beyond presenting the final methodology, the paper documents the successive model design choices that led to the winning solution through a comprehensive ablation study and discusses several alternative approaches that were investigated but ultimately discarded. On the hidden competition test set, the proposed methodology achieves an overall score of 8.81, outperforming the strongest organizer-provided baseline, which achieved a score of 8.64, while requiring approximately three orders of magnitude fewer trainable parameters. These results illustrate that carefully designed coordinate-based neural fields constitute an efficient and robust framework for aerodynamic surrogate modeling on complex geometries under limited-data conditions.

Odd slip at solid-liquid interfaces, characterized by a velocity component perpendicular to the applied shear stress, introduces a novel class of odd transport phenomena with transverse momentum transfer at boundaries, distinct from odd viscosity, odd elasticity, or odd diffusivity. This effect arises on chiral active surfaces with persistent energy input and defined handedness, such as carpets of rotating biological or synthetic cilia with flexible anchoring. Although odd slip itself is dissipationless, its maintenance comes at an energetic cost, which we estimate from the microscopic model. With respect to its orientation dependence, odd slip can be classified as pseudo-scalar or pseudo-vectorial. We use a perturbative expansion to determine the resistance tensors of problems with different levels of broken symmetries. They reveal how the surface chirality and body asymmetry together violate the Onsager symmetry, but uphold the Onsager-Casimir reciprocity. Strikingly, suspensions of particles with odd slip embedded in a conventional Newtonian bulk fluid exhibit odd viscosity, providing a new minimal mechanism for its emergence beyond current microscopic models.

X-ray tomographic particle tracking velocimetry is a promising tool to provide pore-scale insight into fluid flow inside opaque porous media. This is critical for applications ranging from geo-energy to electrochemistry. Current approaches to implement this three-dimensional, three-component (3D-3C) velocimetry technique use conventional micro-computed tomography (CT) workflows to recover tracer particle trajectories. These workflows first reconstruct a sequence of 3D CT images from radiographs which are sequentially acquired at time intervals that span multiple viewing angles. The tracer particles are then detected in each of these CT images and finally linked into trajectories. However, motion-blurring induced by the static CT volume reconstruction impairs the detectability of fast-moving tracer particles, severely limiting the temporal resolution and dynamic range of the velocimetry outcome. In this work, we show that this limitation can be overcome by explicitly recovering particle trajectories directly from the acquired radiographs, bypassing the intermediate tomographic reconstruction step and the static-scene assumptions of traditional 3D CT reconstructions. We implement this approach in a new open-source algorithm, CTracks, and validate it using experimental data on pipe flow and on flow through a complex porous medium, demonstrating a five-fold increase in the maximum detectable velocity compared with state-of-the-art methods. Numerical simulations further confirm improved detection rates and bounded trajectory errors at these increased velocities. Our work thus demonstrates that 3D-3C velocimetry in opaque microscopic geometries can be extended to substantially faster flows by replacing X-ray tomographic image reconstruction with direct particle trajectory reconstruction.

In the existing quantum algorithms for the lattice Boltzmann method, resolving the unitarity problem of the BGK collision operator from first principles remains a fundamental challenge, and a systematically constructed unitary alternative that reproduces the BGK relaxation structure to leading order has not yet been established in the literature. In this work, we propose a novel quantum lattice Boltzmann method (QLBM) based on the rotation collision operator, in which the non-unitary BGK relaxation is replaced by a unitary rotation in the amplitude space of the distribution function, and the corresponding gate-level quantum circuits are also constructed. Specifically, the rotation collision operator is developed for both the D2Q5 model of the convection-diffusion equation and the D2Q9 model of the incompressible Navier–Stokes equations. It is worth noting that, for the D2Q5 model, the equilibrium-state preparation circuit can be precompiled and reused, and the resulting unitary blocks can be sequentially composed once the state-dependent collision parameters are specified. Finally, some numerical experiments are performed to validate the developed QLBM, demonstrating its accuracy and effectiveness.

Turbulence approaching an aerofoil leading edge is strained and blocked in the final few nose radii. Rapid-distortion theory assumes that the pre-impact field is a linear image of the upstream turbulence; we test that assumption directly. Grid turbulence is computed over a NACA~0012 aerofoil and sampled on three congruent surfaces around the nose, giving the cross-spectral tensor between upstream and pre-impact stations. Relative to a no-aerofoil control, the linearity spectrum falls by a factor of three already at the energy-containing scales ($\kappa = k\,r_{\mathrm{LE}} \approx 0.3$), showing that a substantial part of the pre-impact turbulence is generated locally rather than inherited. The same location appears in physical space: the anisotropy invariant $III_b$ changes sign from prolate to oblate within the last few per cent of chord, departing the plane-strain rapid-distortion prediction. The change is produced by pressure–strain redistribution, which drains the strain-amplified wall-normal stress into the other components; the term is absent in the control and becomes active once the accumulated strain is rapid. Across a fourteen-fold range of nose radius the sign change occurs at $x \approx -1.5\,r_{\mathrm{LE}}$ and the generated turbulence is spanwise-dominated. At second order the mapping remains usable: when inserted into a standard Amiet prediction it improves agreement with measured leading-edge noise, and the same coefficients transfer to independent published cases when only nose radius and free-stream speed are supplied.

It is generally believed that statistically stationary states of Rayleigh-Bénard convection (RBC) can be described by statistically stationary solutions to the Boussinesq approximation. Based on an analysis of the mechanical energy equation, we argue that this belief is not justified, because the expression for mean conversion of internal energy into kinetic energy by compressions and expansions, which is implicitly given by the approximation, does not qualify as an approximation. In consequence, it is questionable whether the exact Boussinesq expression relating the mean kinetic energy dissipation in a stationary state to the Rayleigh and Nusselt numbers is valid. Using assumptions that partly lie outside the Boussinesq approximation, we derive scaling relations for the mean kinetic energy dissipation in a stationary state in three and two dimensions. The relation for the three-dimensional system is similar to the Boussinesq expression, but includes an unknown prefactor, while the relation for the two-dimensional system is completely different. Our arguments suggest that statistically stationary solutions to the Boussinesq approximation in three dimensions, reproduce scaling relations between various statistical quantities quite well, although they should not be regarded as approximations in a strict sense, while solutions in two dimensions completely fail. We suggest that this should be investigated by performing DNS of weakly compressible RBC and compare with DNS of Boussinesq RBC.

Phase separation in network-forming materials couples mass transport to mechanical relaxation, yet how adsorbing boundaries reshape this coupling remains unclear. We compare fluid-particle-dynamics simulations resolving solvent hydrodynamics with free-draining Brownian dynamics for attractive colloids confined between parallel walls. Adsorbing boundaries do not slow coarsening uniformly but stratify the network into spatially distinct kinetic regimes. With hydrodynamics, the self-similar central network exhibits growth consistent with poroelastic relaxation, Lb~t^(1/2), whereas the adsorbed region follows an effective Lw~t^(1/3) law. In free-draining dynamics, central coarsening approaches t^(1/3), while the boundary exponent remains time dependent over the accessible times. Direction-resolved displacements reveal suppressed wall-normal motion and reduced lateral mobility near the walls. Increasing wall attraction connects adsorbed islands into an extended layer while leaving local dense-phase packing nearly unchanged. For island-like domains, we propose a testable encounter-controlled scaling framework linking boundary growth to domain geometry, size-dependent mobility, and evolving adsorbed mass. Locally self-similar central coarsening thus coexists with distinct or nonstationary boundary kinetics, precluding a common dynamic-scaling length for the central and adsorbed regions over the accessible times; in both regions, the growth law depends on whether solvent hydrodynamics is resolved.

Turbulence is synonymous with inertia dominated fluid motion, entailing high velocities and large spatial scales. Conversely, in complex fluids, elastic material properties can promote and sustain turbulent-like motions even at arbitrarily small inertia. The common route to this purely elastic state of turbulence, however, strictly occurs only in specific flows with curved streamlines, thus excluding canonical cases such as pipe flow. Investigating dilute polymer solutions in pipe experiments across an unprecedented elasticity and viscosity range, we trace an instability, previously assumed to require finite inertia, to Reynolds numbers four orders of magnitude below the theoretically predicted minimum level. At sufficiently high polymer concentrations and large shear rates, an abrupt drop in the transition threshold confirms that the vanishing inertia limit has been reached, and consequently that the fluctuating motions observed are of purely elastic origin.

We develop a two-dimensional inviscid model for extensible membranes with continuous vortex shedding from both edges, coupled to a weak spectral Galerkin discretization of the membrane equation that permits direct computation at zero bending rigidity. Viewing the pressure jump as a flux for bound vorticity explains how membranes respond to concentrated fluid loading. For fixed-fixed membranes, compliance draws the body toward the leading-edge vortex, delaying its detachment and enhancing lift primarily during start-up; after periodic shedding develops, compliance mainly amplifies the force oscillations rather than mean lift. Vortex detachment can unload heavy membranes into compression, producing bending-regularized wrinkles. For $R_2>0$, the membrane equation remains well-posed independently of the sign of the tension, provided the membrane remains an immersion. Releasing the trailing edge creates an intrinsic degeneracy: the tension vanishes at the free endpoint, making the $R_2=0$ problem formally underdetermined, while the weak formulation selects its bounded-energy branch. This vanishing-tension endpoint traps pressure disturbances and drives rapid tip-snapping; the dominant frequency and effective wave number approach their zero-rigidity limits with an inverse-logarithmic correction arising from a singular Bessel branch. Finally, decreasing the stretching modulus destabilizes periodic flutter, and the repeated fluid-driven departure and elastic return suggest a homoclinic tangle underlying the transition from periodic to chaotic flutter.

Jets in stratified flows are ubiquitous in geophysics. A fundamental question is whether the instabilities and coherent structures generated by the flow interact with the physical boundaries and, if so, how. To this end, a simple canonical model flow is employed: a parallel Bickley jet confined between walls in a uniformly stratified fluid. We first show that short wavelength Kelvin-Helmholtz instability can generate asymmetry in the mean flow. Although the fluctuations decay rapidly away from the jet, the asymmetric mean flow does not. We then examine long-wavelength coherent structures that can emit internal gravity waves, which decay slowly towards the walls or, in some cases, radiate away from the jet. These waves transport momentum and distort the mean flow, reducing the jet centreline velocity significantly. When radiation occurs, whether the instability persists at high Reynolds numbers depends strongly on the boundary conditions imposed at the walls. Moreover, we found an instability and associated nonlinear coherent structures that persist at Richardson numbers above the Miles-Howard criterion. The existence of this viscous mode does not rely on the presence of the walls.

Precise manipulation of liquid droplets underpins lab-on-a-chip platforms for diagnostics, chemical synthesis, and biological assays. Yet autonomous droplet transport through confined geometries of varying complexity remains an open challenge. Droplets exhibit contact-angle hysteresis, deformability, and capillary pinning, which make their response to actuation nonlinear and history dependent, that classical controllers and pre-programmed trajectories cannot cope in multi-turn environments. Here we demonstrate autonomous navigation of a liquid droplet through geometries of increasing complexity on a gravity driven (Labyrinth) platform using model-based reinforcement learning. A thin silicone oil film reduces contact-line pinning while two-axis tilt supplies the gravitational driving force, and an overhead camera tracks the droplet in real time. An offline-trained policy discovers effective tilt strategies from limited physical interaction data, without simulation or analytical droplet models. The system operates under partial observability, as oil-film thickness, instantaneous contact angle, and droplet deformation state remain hidden from the controller. Despite these challenges, the learned policy achieves reliable navigation across straight, right-angle, and curved-arc paths, including outside-corner geometries. We further demonstrate that a policy trained on a simpler geometry transfers to complex ones, succeeding zero-shot on right-angle and staircase paths and reaching full success on a curved arc with a fifth of the training data. The findings suggest promising avenues for enabling droplet based microfluidic systems to serve as intelligent chemical laboratories.

Rotating detonation engines (RDEs) exhibit strongly nonlinear, multiscale wave dynamics that set the observed thermal field. High-fidelity simulations (DNS/LES) resolve these structures but remain computationally prohibitive, while low-order models such as the one-dimensional Koch-Kutz model capture circumferential wave motion yet lack the expressivity for high-frequency content. We use continuous data assimilation (nudging) to synchronize the Koch-Kutz solver with processed high-fidelity temperature data, introducing the prediction-observation mismatch as a relaxation source in the conserved energy equation; where observations are temporally sparse, interpolation supplies a target at every source update. As the nudging strength increases, the reduced model is progressively drawn onto the high-fidelity trajectory, and the forcing recorded along it provides an explicit, state-dependent estimate of the correction the model requires. We then train a Jacobian-regularized closure a priori on this recorded source. With the observation term removed, the corrected model advances autonomously, remains bounded, and recovers the temperature spectrum and the marginal statistics of the conserved variables relative to the baseline.

Numerical simulations reveal how vortices stretch and transfer energy, but establishing smooth evolution requires bounds that remain valid beyond the simulated resolution. Here I develop a computer-assisted framework that establishes global regularity for continuous families of three-dimensional periodic Navier-Stokes flows. Its central construction combines finite reference trajectories with a common error bound that covers an interval of centre fields and infinitely many smooth perturbation modes. The method retains the complete nonlinear residual before spectral truncation and controls the evolution until viscous decay guarantees regularity for all subsequent times. Applications to cyclic-shear, Arnold-Beltrami-Childress and three-component Taylor-Green fields yield explicit perturbation radii and include initial conditions outside the direct Fourier-Wiener smallness criterion. A parameter-uniform extension covers a connected family of non-Beltrami Taylor-Green centres without repeating the proof for individual parameter values. An ensemble of 4,096 configurations, supplemented by 1,600 refinement trajectories and public turbulence data, connects the mathematical observables to spectral transfer and vortex geometry. Matched neural-operator experiments show that physics-informed training improves physical prediction, while also revealing that these gains do not necessarily improve the discovery of proof-limiting initial conditions. Together, these results provide a reusable method for establishing regularity across prescribed flow families and a quantitative setting for evaluating how learned predictions can assist rigorous computation.

A decade ago, a landmark study on flow control via subsurface phonons transformed our understanding of fluid-structural interactions, compelling us to reimagine ways by which to suppress boundary layer instabilities. While subsequent investigations have steadily enriched this landscape, several questions remain largely unanswered. The notion of Tollmien-Schlicting (TS) wave stabilization relies on phase-engineered surface interactions, which destructively engage with the wave and impede its growth. Although the fundamental drivers of the phenomenon are established, its granular physics remain insufficiently resolved, particularly as it pertains to directional effects, competing energy production mechanisms, and the precise streamwise locations governing the process. Revisiting this initial vision, we confront these open questions, revealing fresh insights, and establishing broad foundational strokes to guide the next era of investigations. We begin by defining the amplitude and phase criteria of an elastic wall admittance driving perturbation energy changes relative to a rigid wall. The established framework isolates the roles of the work-rate, viscous energy, production, and dissipation in shaping the fluid's response and clarifies how each contributes to the collective outcome. Crucially, we demonstrate how streamwise translation of the interaction surface significantly alters these parameters, revealing critical thresholds at which the control result is fully reversed. Our model identifies specific pathways to sustained TS wave attenuation, and defines the limits of what can be accomplished passively. Finally, we conceptualize a two-dimensional phononic subsurface, whose tailored and disproportional response to the flow in the wall-normal and streamwise directions, brings about the elusive combination of local and downstream stabilization.

We present a three-dimensional visco-magnetoacoustic framework for analog gravity in magnetohydrodynamic (MHD) flows. While standard fluid dissipation typically breaks the Lorentzian signature of acoustic metrics, we demonstrate that evaluating wave perturbations in the eikonal limit alongside the Shakura-Sunyaev $\alpha$-viscosity prescription preserves a well-defined effective spacetime geometry for the fast magnetoacoustic mode. The slow-magnetoacoustic mode and Alfvén mode do not admit a non-degenerate metric. To investigate analog horizon thermodynamics, we utilize astrophysical accretion disks as background media, specifically modeling numerical magnetized advective accretion flows around rotating black holes and analytical advection-dominated inflow-outflow solutions (ADIOS). Standard self-similar ADIOS models strictly enforce a constant Mach number, precluding horizon formation. We therefore introduce a magnetic field perturbation that breaks self-similarity, generates a dynamic Mach number, and enables the formation of a visco-magnetoacoustic horizon. By evaluating the spontaneous phonon emission at these horizons, we reveal that the analog Hawking temperature is highly sensitive to the magnetic field topology; the spatial orientation of the background magnetic gradients dictates whether the Hawking radiation is amplified or suppressed. Furthermore, we find that increasing the viscosity parameter leads to a monotonic increase in the analog Hawking temperature.

Upstream swimming drives bacterial spreading and surface colonization. Many pathogens encounter fluid flows as they infect the intestines, lungs, and urinary tract, so how bacteria use their flagella to counter these flows matters for disease and treatment. Yet how morphology and flagellar arrangement govern motility against flow remains unknown. Here, we investigate the biophysical determinants of rheotaxis by combining microfluidics, directed evolution, genetics, holography, and hydrodynamics simulations. Using upstream swimming competitions, we find that peritrichous E. coli and S. enterica rapidly outcompete monotrichous P. aeruginosa and V. cholerae, accumulating upstream at densities up to five orders of magnitude higher, even though Vibrio swims three times as fast. Motility selection experiments show that rheotaxis increases with flagellar number and length, confirmed by overexpressing the master regulator flhD/C. Three-dimensional holography and single-cell tracking reveal that multiflagellarity stabilizes surface residence and promotes the weathervane effect that reorients cells upstream, a mechanism further supported by simulations that fully resolve flagellar arrangement and fluid-structure interactions. These results establish multiflagellarity as a key facilitator of upstream navigation, governed by near-wall residence and shear-driven reorientation rather than by swimming speed.

Building-integrated wind turbines (BIWT) remain under-deployed in dense European urban contexts despite their potential contribution to net-zero energy targets. This paper presents a measurement-validated computational fluid dynamics (CFD) framework to identify optimal locations for micro-wind turbines on the envelopes of dense Parisian Haussmannian blocks. The methodology couples a multi-month on-site anemometry campaign on two case-study buildings, a calibrated steady RANS digital twin using the realisable k-$\epsilon$ turbulence model, and the introduction of an architecturally integrated accelerator wing -termed aerofoil -placed at the envelope edge to amplify and stabilise the local flow. Quantitative validation against year-long anemometer records yields a mean absolute percentage error (MAPE) of approximately 18 % and a hit-rate FAC2 above 0.85, meeting the COST 732 acceptance criteria for urban CFD models. On the École Nationale Supérieure d'Architecture Paris-Val-de-Seine (ENSAPVS) case study, the inter-tower configuration produces a directional speed-up factor of 3.4 (95 % CI 3.18-3.62) for the prevailing north-westerly sector at +70 m above ground; the addition of the aerofoil yields a further +13 % local speed-up, equivalent to +44 % in extractable power. A capacity-factor analysis based on the measured Weibull distribution and the Savonius rotor power curve estimates an annual yield of approximately 69 MWh, offsetting around 6 % of the building's annual electricity consumption -a substantially lower but more realistic figure than the cube-of-mean estimate. The findings are synthesised in a decision dendrogram that maps wind-rose typology, building plan, height and implantation onto recommended device families, providing architects and engineers with a transferable design-stage tool.

Real-time reconstruction of fluid flows from sparse sensor measurements is important for both physical understanding and flow control. When first-principles models are too expensive for online data assimilation (DA), learned reduced-order models provide an efficient alternative, but are commonly optimized for forward prediction rather than state estimation. We propose Deep Koopman Sensing, a data-driven reduced-order DA framework that combines a nonlinear autoencoder with parameter-conditioned linear latent dynamics approximating the Koopman operator. We compare the proposed model with parametric dynamic mode decomposition (pDMD), a multilayer perceptron (MLP), and xLSTM across four benchmarks: 1D viscous Burgers, 2D flow past a cylinder, 2D dambreak, and 3D flow past a sphere. Our results reveal a marked distinction between forecasting and sensing: open-loop accuracy does not reliably predict assimilation performance, while Deep Koopman Sensing achieves the lowest assimilation error across all four benchmarks. More importantly, with an extended Kalman filter, incorporating sensor measurements improves the estimates of both linear latent models across all four benchmarks, whereas it degrades the nonlinear models, despite their strong open-loop performance. With ensemble filtering, the nonlinear models are no longer degraded by assimilation, while the Koopman model still attains the lowest assimilation error. These results show that latent dynamics should be designed for the downstream estimation task rather than selected solely for forecast accuracy, and demonstrate Koopman-based reduced-order modeling as an effective approach for real-time flow reconstruction from sparse, streaming measurements.

Kraichnan's Direct Interaction Approximation (DIA) provides a classical closure framework for homogeneous turbulence, yet its quantitative predictions across all scales remain incompletely understood. We present a fully resolved numerical solution of the forced DIA equations without additional modelling assumptions, enabling a consistent analysis of stationary spectral properties and temporal dynamics across all wavenumbers. The main focus is on the fluctuation-dissipation relation between the normalised velocity correlation function and the Green function of linear response. This relation holds only at large scales and is systematically violated in the inertial and dissipation ranges. The non-Gaussian nature of this violation is encoded in the DIA through its non-Markovian equations, even though the DIA can be derived using a Gaussian mean-field approximation in the stochastic field functional. In the inertial range, characteristic decay times agree quantitatively with those obtained from direct numerical simulations, while deviations arise in the dissipation range. These results highlight the ability of the DIA to capture temporal dynamics despite its limitations in predicting spectral scaling.

Ultrashort laser pulses can induce order out of chaos. A femtosecond pulse melts a metal surface for about a hundred picoseconds; under photoexcitation with no net polarization axis, the resolidifying film nonetheless organizes into regular nanoscale patterns. Here we derive from first principles the nonlinear hydrodynamics responsible for it and show it accounts for the full phase diagram of morphologies from measurable laser and material parameters. Starting from the Navier-Stokes equations in the lubrication limit, the molten film obeys a damped Kuramoto-Sivashinsky equation that reduces to a Swift-Hohenberg formalism near threshold, with every coefficient fixed by the laser fluence, melt thickness, optical skin depth, and thermocapillary response. The ratio of melt depth to optical skin depth sets the pattern wavelength, while the inter-pulse delay, via post-pulse damping, gates the route from flat surface to ordered pattern to chaos. We validate the phase diagram (hexagonal cavity arrays, bistable mixed states, labyrinths) numerically and confront it with pulse-resolved experiments on two metals, Ni and Fe3Cr. The agreement between theory and experiment quantitatively links the microscopic laser-material response to the macroscopic pattern selected after many pulses. This order is self-limiting: the same corrugation the instability builds scatters the modes that build it, and simulations, with every scale fixed by material parameters, place the coherence breakdown near a roughness of 30 nm after a few tens of pulses, a finite window confirmed by pulse-by-pulse measurements of orientational order on the experimental surfaces; at stronger coupling, disorder does not destroy the pattern but saturates and pins it instead. This yields a closed, predictive description of laser-driven self-organization, from single-pulse melt dynamics to the arrest of nanoscale order.

Dense suspensions can undergo a dramatic increase in viscosity at a critical value of the shear stress. This phenomenon, termed discontinuous shear thickening (DST), has been attributed to an increase in the fraction of particle interactions becoming frictional with increasing shear stress, and a successful mean-field theory has been developed to explain various accompanying rheological properties. On a microscopic scale, however, conventional structural analysis measures such as the grain-position pair correlation function show no significant changes with the onset of DST, though recent work has shown that similar analysis in the dual space of contact forces does lead to marked changes at this transition. Furthermore, experimental results have suggested the existence of higher-order microscopic correlations and the importance of incorporating fluctuations away from a mean-field description. To this end, we use a higher-order cluster analysis tool to study the force networks obtained from simulations of dense suspensions to construct an effective interaction potential in force space. We show that there are significant changes occurring in this potential as a function of density and stress close to DST. We discuss the implications of these observations on an emergent field theory of the DST transition.

We present the development and application of a three-dimensional Physics-Informed Neural Network (PINN) framework for the investigation of haemodynamic behaviour in the human aorta. The model incorporates a time-resolved simulation of pulsatile blood flow over a two-minute interval, enabling the extraction of pressure and velocity fields with high temporal fidelity. The mechanical stress exerted on the aortic wall was quantified through Laplace's law, with temporal averaging applied to derive representative stress distributions. This approach circumvents the computational overhead associated with conventional computational fluid dynamics (CFD) methods by eliminating mesh generation and exploiting the automatic differentiation capabilities inherent to neural networks. The proposed methodology demonstrates that PINNs can serve as an efficient and accurate alternative for modelling complex vascular flow phenomena, offering significant advantages in scalability and computational cost reduction while maintaining physical consistency.

Accurately resolving the near-field flow generated by many swimming bacteria while retaining computational efficiency remains challenging. Stokeslet-based models with many force points can capture detailed near-field hydrodynamics but are computationally expensive. Other approaches include far-field and low-order models that use fewer points but sacrifice near-field accuracy. We introduce a reduced-order framework based on the method of regularized Stokeslets that preserves important near-field flow features while using substantially fewer force points. The method replaces the force distribution of a high-fidelity model with forces on a sparse set of points whose strengths are determined by constrained least-squares calibration to the high-fidelity velocity field of a single bacterium. The calibrated forces yield an approximation that preserves the dominant reference-flow structure while satisfying the force-free and torque-free conditions of self-propelled swimming. Principal component analysis is then used to represent the phase-dependent variation of the calibrated forces using only a few dominant modes. By fitting the corresponding modal coefficients as continuous functions of flagellar phase, the reduced-order forces can be approximated at any phase of the flagellar cycle. The framework is applied in both free space and near a no-slip planar boundary, where it preserves the dominant flow structures and captures the wall-induced redirection of the surrounding fluid. The optimized cell-body regularization parameter depends weakly on wall distance, and the remaining velocity discrepancy is concentrated primarily near the cell body. By substantially reducing the number of force points, the reduced-order model lowers both the computational cost and memory requirements of velocity-field evaluation, making large-domain simulations of multi-swimmer flow fields more practical.

Burning neat hydrogen in aircraft turbines eliminates carbon emissions, yet rapid reaction rates trigger nozzle flashback hazards and high nitrogen oxide emissions across flight throttles. This study investigates aerothermal holding mechanisms, flashback safety margins, and emission pathways in a dual-swirl combustor across equivalence ratios from 0.55 to 1.00. Three-dimensional simulations combine curvature-corrected shear-stress transport turbulence closure, dual-rate finite-rate and eddy-dissipation chemical kinetics, and discrete ordinates radiation, validated against experimental laser benchmarks using ASME grid standards. Advancing engine throttle triggers a topological flame transition from a faceplate-attached M-flame at lean idle to a lifted V-flame above equivalence ratio 0.895, while wall flashback safety indices consistently exceed 3.42. Nitric oxide emissions transition from water-chaperoned nitrous oxide intermediate reactions at lean idle (28.01 ppm, EINOx = 1.85 g/kg), scaling to 319.21 ppm (EINOx = 35.40 g/kg) at takeoff under thermal Zeldovich dominance, governed by a power-law exponent of 4.92. These findings deliver validated operability limits and establish an accessible workstation-based screening methodology for practical zero-carbon aero-engine combustor development.

To enable flexible and rapid aerodynamic performance evaluation in turbomachinery design, this paper proposes a panoramic performance prediction framework. Unlike most previous prediction models that directly predict the objective functions of interest, our approach first predicts the basic parameters of the Navier-Stokes equations, such as temperature, pressure, and density. Utilizing these basic physical quantities, it subsequently predicts key performance parameters of the turbine stage meridian plane. By adopting this methodology, our proposed panoramic performance prediction framework functions similarly to a CFD simulator, capable of predicting various objective of interest to the designers. To enhance prediction accuracy, a transformer-enhanced neural operator (TNO) is introduced within this framework. Using the Rotor 37 blades as a reference, the proposed TNO is trained to predict the performance of a transonic compressor blade in the meridian plane. The TNO can accurately predict total quantities such as isentropic efficiency, mass flow, and distributions of total pressure ratio. Remarkably, the prediction error of TNO is observed to be smaller than that of state-of-the-art deep learning operators such as the FNO and DeepONet. Furthermore, the TNO is applied to downstream tasks, including sensitivity analysis and optimization of various objective functions. The results confirm that the TNO can operate almost like a CFD simulator, while reducing the computational cost of downstream tasks by four orders of magnitude. The effectiveness and reliability of the proposed TNO for solving different kinds of downstream tasks have been well demonstrated.

This paper introduces an online evolve–filter–relax (EFR) strategy for long-term stability of Operator Inference (OpInf) reduced-order models (ROMs) of complex fluid flow simulations. The main novelty of the new EFR-OpInf strategy is the use of online (i.e., at the learned ROM online evaluation level) spatial filtering inspired from large eddy simulation to significantly improve long-term stability and predictive performance of standard OpInf. Furthermore, the EFR-OpInf strategy reduces, and in some cases even eliminates, the need for standard $L^2$ regularization, while providing physical interpretability for the OpInf hyperparameters. The EFR-OpInf framework is modular, readily integrated into existing OpInf workflows, and accommodates a user-selected ROM filtering strategy. We demonstrate the EFR-OpInf's effectiveness using a fully non-intrusive projection-based ROM filter, a ROM differential filter, and a hybrid projection-differential ROM filter. The new EFR-OpInf models are evaluated on a high-Péclet-number convection–diffusion–reaction problem that embeds the variation in one parameter and two unsteady Navier–Stokes problems that focus on predictions beyond a training horizon: a transitional two-dimensional flow past a cylinder and a three-dimensional turbulent minimal channel flow. Across these three scenarios, EFR-OpInf can reduce prediction errors by up to an order of magnitude relative to standard OpInf. Moreover, EFR-OpInf remains stable over long prediction horizons in cases where standard OpInf diverges. Depending on the ROM filter used, EFR-OpInf's computational cost is comparable to that of standard OpInf.