Papers

Reconstructing the stress field of a planar viscoelastic flow from optical measurements loses its direct evidence wherever optical coverage is interrupted, and no improvement in optical precision restores an observation that was never made. We characterize what a second, velocity channel adds, and what neither channel can supply. Two calibrated optical components determine the local deviatoric stress pointwise, while velocity constrains spatial stress variation through momentum balance, so the two channels are complementary rather than redundant. The isotropic part of the stress is unobservable to both: the divergence of an isotropic field is a pure gradient, which the Leray projection annihilates, so every representable isotropic mode lies in the joint null space. That accounts for the null space exactly when the optical field is complete, and bounds it from below otherwise, since finite incomplete sampling and aperture zeros can remove further directions. We verify the count directly on three discretizations. In paired synthetic tests with finite measurement apertures, spatially correlated noise and optical stripe dropout, adding velocity reduces the mean whole-domain deviatoric error from 50.40% to 27.82% at 3% reference noise, and the improvement survives shared gaps, inverse-grid refinement at fixed physical sampling, and a constitutively generated stress field. The improvement does not rest on how the regularization parameter is chosen: it holds under both the expected-norm discrepancy rule and generalized cross-validation, and we report each selection with its position in the search interval, which is where the two rules differ.

In this paper, we study the analogue of the Kolmogorov scale in surface gravity wave turbulence, characterized by the cutoff wavenumber $k_c$ at which the power-law inertial range transitions into the dissipation range. We perform numerical simulations of the primitive dynamical equations with a broad-scale dissipation of magnitude $\gamma_0 k^2$ in spectral space to establish the relation between $k_c$ and $\gamma_0$. Our results show a scaling $k_c\sim\gamma_0^{\beta}$, where $\beta$ depends on the slope $\alpha$ of the power-law spectrum. We find that $\beta(\alpha)$ agrees more closely with the prediction obtained by balancing the nonlinear and dissipation terms in the dynamical equations than with that based on the kinetic equation. This observation reveals that non-resonant triad interactions play a more significant role than resonant quartet interactions in the formation of $k_c$.

The topological classes of coherent structures in magnetohydrodynamic turbulence are studied using the irreducible representations of the SO(3) and SO(2) rotation groups. We probe the coherent structures around axisymmetric magnetic fields in the universe. Such axisymmetric fields can be found around filamentary structures as well as cosmic strings. We have considered a Gaussian and a non Gaussian magnetic field. We find that the field distribution leads to different coherent structures for the two cases. Our results show that the scattering of particles from the Gaussian structure depends predominantly on two lengthscales. In the case of the non Gaussian distribution, we can define a third intermediate lengthscale, similar to the Taylor lengthscale. In both the cases, we find that there is a dominance of the polarization anisotropy which indicates that the field gradients are forced into rigid spatial configurations. In the early universe, this will change the mean free path of the baryons and leptons in the coherent structures. Trapping of charged particle as well as their acceleration will be more frequent in the case of a magnetic field with a heavy tailed distribution. The lengthscale of density inhomogeneities close to these structures will thus be determined by the magnetic field distribution of the fields.

Near flutter, modal frequency can be well resolved from accumulated phase while the sign of a small modal growth rate remains uncertain because the response envelope changes only weakly over a finite record. This work tests whether a validated physical relation between frequency and damping can exploit the better-resolved phase information to improve near-flutter stability identification. A coupling-audited SU2 Euler campaign for a modified Isogai-parameterized NACA 64A010 section at Mach 0.85 is subjected to systematic grid and temporal verification, multichannel critical-pole tracking, bootstrap trajectory closure, finite-record information analysis, and nonlinear Monte Carlo validation. The temporal study shows that 50 steps per structural period predict the wrong damping sign although frequency is already close to the finer solutions. The verified critical trajectory gives a flutter-speed index of 0.537665 and a local frequency-to-damping slope of 3.754. Restricting a free pole estimate to this trajectory gives an approximately 3.89-fold damping-precision gain, reproduced by Monte Carlo with a median RMSE gain of 3.915. At a representative operating offset and 30 dB amplitude SNR, the minimum tested record exceeding 95% correct-sign probability decreases from 15 to 5 cycles. Physically validated pole trajectories can therefore substantially reduce the observation time required for reliable near-boundary aeroelastic stability identification.

Sheet-like structures are ubiquitous in magnetohydrodynamic systems and are known to play a crucial role in astrophysical plasma transport. Here, by applying a theoretical framework to data from numerical simulations, we demonstrate that current-sheet formation is a direct consequence of energy conversion between kinetic and magnetic fields. The strain-magnetic field organisation associated with this conversion favours the emergence of sheet-like structures, and analytical calculations show that sheet-like geometry constitutes the dominant flow configuration. We further show that the same conversion-driven reorganisation of the strain motion is responsible for the depletion of the mean Inertial energy transfer, a previously observed phenomenon whose physical origin has remained unclear. Finally, we identify experimentally accessible diagnostics through which these predictions can be tested in multi-spacecraft observations of turbulent plasmas.

Transforming textile fibres into sensors can facilitate continuous physiological monitoring for improving human healthcare. Coating fibres with electronic conductors can help detect physiological stimuli but their sensitivity scales with thickness and often lowers the fibre mechanical flexibility. Proton conductors are potential alternatives; however, they suffer from fragile physical interfaces, and sluggish kinetics. Here, we report a bio-templated, scalable strategy to create superprotonic interfaces using natural silk fibres. We exploit ordered nanofibrils on silk fibres to selectively grow continuous metal-organic framework (MOF) nanostrips. This patterned, ca. $10\,\mu\mathrm{m}$-diameter fibre-structure provides low-defect interfacial pathways for ultrafast proton transport, yielding conductivities up to 40 $S\,cm^{-1}$ - two orders of magnitude above the state of the art - with millisecond response and high mechanical robustness. The individual micro-thread sensors facilitate respiratory monitoring with a mean bias of 0.01 breaths $min^{-1}$ in volunteer testing, unaffected by human movement and readily capture breathing signature in high-flow oxygen therapy devices. We integrate arrays of micro-thread sensors in textiles and exploit deep learning to demonstrate high-resolution spatiotemporal humidity mapping in dynamic flow-fields and resolve asymmetric respiratory patterns that elude conventional single-point detectors. Our results should have broad-ranging implications, e.g. in wearable health monitoring, bioelectronics, and human-machine interfaces.

A simple, accurate asymptotic formula is derived for the spatially resolved evaporative flux from multiple spherical-cap droplets of arbitrary contact angle. Kelvin transforms are used to determine the exact response of a spherical-cap droplet to a point source, with extensions to higher multipoles. This yields explicit formulae for evaporative shielding and reveals a universal spatial structure in the point-source problem. Resolving the spatial variation enables the determination of the associated liquid flow and particle transport. The resulting flux is used to derive an explicit measure of shielding-induced liquid transport.

A ghost-point immersed boundary method is coupled with auxiliary differential equations to impose a locally-reacting impedance condition on a wall that does not conform to a Cartesian grid, in the framework of the linearized Euler equations. The ghost-point reconstruction follows the normal-stencil approach: an elliptical least squares cloud of fluid nodes is used to build a high-order polynomial along the local wall normal, which is then extrapolated onto the ghost points by one-dimensional La grange interpolation. The impedance, modeled as a massspringdamper oscillator, is advanced in time through two auxiliary state variables per ghost point, coupled to the reconstruction at every RungeKutta stage. The method is validated against exact and semi-analytical references on a flat immersed wall, a cylindrical wall reflecting an acoustic pulse, and a cylinder scattering a harmonic monopole. Convergence orders ranging from about three on the curved wall to about four and a half on the flat wall are measured, and a cross-check against an exact harmonic reference shows that a persistent offset observed against a semi-analytical reference is a property of that ref erence rather than of the coupled solver. A spectral stability analysis of the linearized semi-discrete operator further shows that the normal-stencil reconstruction reduces, without eliminating, a known instability that occurs when the immersed wall becomes tangent to the grid.

In computational fluid dynamics, the immersed boundary method is a classical technique to account for complex geometries when Cartesian grids are used, as is the case in finite difference methods. The present paper presents a new discrete ghost point method, which is one of the different immersed boundary methods available, for solving problems in acoustics and aeroacoustics with the linearized Euler equations or the compressible Navier-Stokes equations. This method is based on high-order schemes and a ghost point method. The flow field values at the ghost points are determined in two steps. A least-squares interpolation is first used to reconstruct the flow on a stencil of points located on the normal to the immersed boundary. Then, a 4th order Lagrangian extrapolation based on the normal stencil points adjacent to the boundary point is used to impose the boundary conditions at the immersed boundary by reconstructing the field values at the ghost points. This approach is verified and validated for the acoustical problem of a pressure pulse impinging on a cylinder. The approach is also validated for compressible flow past a circular cylinder at several Reynolds numbers.

Droplets in complex environments often encounter compositional gradients that drive their propulsion. For example, surfactant gradients induce surface-tension-driven propulsion via the Marangoni effect. Here, we show that such propulsion emerges generically, even in the absence of surfactants. Employing a thin-interface approximation, we derive a compact expression for the droplet velocity in terms of droplet size, viscosity, the sensitivity of surface tension to a regulating component, and the chemical potential gradient of that component. Our theory reveals that droplets move toward regions of lower stability, as encoded in the morphology of the phase diagram, particularly near critical points. Numerical simulations confirm these results, which establish a general route to predicting and designing droplet motility from the phase behavior of complex fluids.

In this paper we discuss the dynamics of a lubricating film separating two flat surfaces. It may be possible for the gap between the surfaces to reduce to zero at one point on the boundary in a finite time. Typically, the maximum pressure diverges as the gap between the surfaces approaches zero. We discuss the form of the pressure field in the vicinity of its maximum. We also introduce a numerical method for accurate determination of the pressure across the lubrication surface, enabling us to determine the hydrodynamic forces. We determine the phase diagram describing the evolution of the gap, as a function of the initial configuration and of the line of action of the external forces. When contact does occur, we consider whether the subsequent motion involves sliding of the point of contact. We argue that, when sliding does occur, the motion does not depend upon the microscopic properties of the surface roughness.

Streaming from a deforming cavity wall serves micromixing, pumping and particle handling. We solve it in closed form in a two-dimensional circular cavity, for any azimuthal wall mode $m$, as $\mathrm{Wo}^2 \to 0$. A biharmonic inversion against the Reynolds stress, corrected by the second-order slip a moving wall imposes, gives the Lagrangian mean a tracer follows for a deforming no-slip wall, $\psi_L = -[m(5m+4)a_m^2/(128(m+2)(2m+1))]\,r^{2m}(r^2-1)^2\sin 2m\theta$, with a companion form for a shear-free interface. For a single mode the factor $(5m+4)/(m+2)$ relating it to the auxiliary solution $\psi_2$ is the same for every member of the co-phased prescribed-velocity family; at $m=2$ the physical Eulerian mean peaks an order of magnitude above $\psi_2$, with opposite sign. The no-slip cell centers lie at $r^2 = m/(m+2)$, and at large $m$ the peak streamfunction falls as $m^{-2}$, the peak speed as $m^{-1}$. At fixed radial wall-velocity amplitude the ranking over $m$ follows the wall kinematics: an externally driven wall peaks at $m=1$, a wall with zero first-order surface strain at $m=3$. Mode superpositions invert without degenerating, each harmonic carrying its own correction. At finite $\mathrm{Wo}$ the first-order field stays closed form in Bessel functions and the mean flow reduces to quadrature; the construction approaches the $m=2$ Rayleigh limit on a separate tangentially driven boundary problem. An independent finite-element solver, with the closed form withheld, reproduces $\psi_2$ with quadratic mesh convergence.

We determine the maximum stable volume of bubbles attached to flat surfaces as a function of contact radius, contact angle, and capillary length. By solving the Young-Laplace equation using a shooting method, we calculate equilibrium bubble shapes and determine when bubbles detach through three distinct modes: necking at the cavity, sideways instability, and spreading followed by necking on the surrounding surface. Our predicted detachment volumes agree well with experimental measurements of electrolytic, boiling, and carbonated bubbles, as well as pendant drops. These results bring together and extend previous analytical estimates and, by symmetry, also apply directly to pendant drops.

Autoencoders (AEs) have become a dominant approach to nonlinear latent-space construction in data-driven reduced-order modelling (ROM), with their decoders lifting latent representations back to the ambient state space. Their prominence, however, has overshadowed an established alternative: manifold-learning methods grounded in classical numerical analysis. We revisit this alternative using Parsimonious Diffusion Maps (PDMs), benchmarking them against Proper Orthogonal Decomposition (POD)-based ROMs and several convolutional AE architectures for the two-dimensional incompressible flow past a rotating cylinder —a bifurcating Navier-Stokes (NS) system organized by a codimension-2 Bogdanov-Takens point and its associated Hopf, saddle-node, and homoclinic bifurcations. Our approach uses PDMs to identify a parsimonious and interpretable set of intrinsic latent coordinates and to estimate their dimension directly from data. Gaussian process regression then learns the latent dynamics, while convex K-nearest-neighbor (K-NN) interpolation in PDMs space constructs the pre-image map, for which we establish pointwise consistency. The resulting nonlinear ROM substantially outperforms POD-based ROMs and achieves reconstruction and prediction accuracy comparable to —and, in some bifurcating regimes, better than— that of AE-based ROMs. At the same time, latent-variable learning with PDMs requires orders of magnitude less computational time than AE training.

The aeroelastic instability known as vortex induced vibrations (VIV) has its origin in the coupling of bluff body shedding and the structure dynamics, and can have adverse effects on several industrial fields. In this work the use of locally resonant metamaterials (LRM) is explored as a wind turbine blade VIV mitigation strategy. The problem is cast into a classical airfoil in transverse oscillation, elastically mounted. A fluid structure interaction model is then generated and validated for the main system. This is achieved using an open source finite volume code with arbitrary Lagrangian Eulerian capabilities and a built-in rigid body motion solver. Subsequently, the capabilities of the code are extended by coupling the dynamics of a single resonator into the main system through a tailored development. The performance of the resonator was evaluated for different designs, which were parameterized mainly by the resonator frequency and its relative mass with respect to the airfoil. Analysis of the results identified a frequency band where the resonator effectively influenced vibration amplitudes. However, the amplitude attenuation was very low when considering realistic relative resonator masses. In particular, achieving a 50% amplitude reduction required a mass ratio larger than 0.25. Studying the mechanisms uncovered the cause of these beneficial effects, which relied on the aeroelastic frequency bifurcation introduced by the resonator. These fundamental findings open the door to future applications of alternative technologies for VIV suppression.

How spatial structures manifest in multi-time correlations is a fundamental question in turbulence. We develop a non-Hermitian bosonic framework that unifies equal-time anomalous statistics and their temporal propagation within a common operator representation. A continuous Wegner flow reorganizes stochastic mode couplings in an extended wave-frequency space. Applied to the Taylor-Kraichnan model, the framework recovers the established equal-time hierarchy and constructs multi-time contributions through propagators acting on successively smaller sets of active fields. This construction separates uniform transport from intrinsic relative dynamics and shows how a higher-order equal-time state evolves under a generator acting only on the fields that remain dynamically active. Within an isotropic radial closure, we derive an explicit fourth-order two-time zero mode scaling function that describe how relative dispersion progressively weakens sensitivity to the initial separation. The framework thus connects spatial intermittency to temporal evolution by identifying how the sequence of observation times determines the propagation of equal-time anomalous structures.

Nonequilibrium flow and transport problems are inherently multiscale. Kinetic theory provides a fundamental physical basis for describing such phenomena, since it connects microscopic transport and interaction processes with emergent macroscopic behavior across regimes. In many situations, however, continuum descriptions lose validity in parts of the domain, whereas fully resolved kinetic descriptions become prohibitively expensive when numerical resolution remains tied to the smallest collision scales. Over the past two decades, a broad class of multiscale kinetic methods has therefore been developed to bridge rarefied, transitional, and continuum regimes in gas dynamics and other carrier-based transport systems. Existing reviews have clarified important parts of this field, including general numerical methods for kinetic equations, asymptotic-preserving methodology, and specific method families. This review adopts a different perspective by examining the subject through four interacting layers: numerical methods, computational strategies, asymptotic properties, and framework-level formulations. It surveys the main developments along these lines and emphasizes the common principles that connect them, including transport-interaction coupling, asymptotic consistency, scale-adaptive representation, and scale-dependent physical description. From this perspective, multiscale kinetic computation has evolved into a broader transport methodology for nonequilibrium systems across scales.

Next-generation aircraft, rotorcraft, and wind turbines demand improved aerodynamic efficiency, making drag reduction a central design objective; in transition-sensitive configurations, the extent of laminar flow strongly affects viscous drag and performance. Accurate prediction of laminar-turbulent transition is therefore essential. Transport-equation-based transition models, however, increase computational cost and implementation complexity. Neural-network-based closures can be difficult to interpret and integrate into independent flow solvers, while a single compact correction trained on heterogeneous transition data may fail to preserve mechanism-specific behavior. This study develops a mechanism-separated transition model using field inversion and symbolic regression. The framework treats natural, crossflow, and separation-induced transition with separate correction branches and yields explicit, closed-form corrections to the Spalart-Allmaras production term, without additional transport equations or runtime neural-network inference. The closed-form model is implemented in an independent flow solver to assess implementation portability and is evaluated on canonical cases and complex three-dimensional configurations, including a natural-laminar-flow transport wing and a hovering rotor. Across the tested cases, the model captures the principal transition-front trends and associated aerodynamic-performance changes. For the hovering-rotor case, it requires about 55% of the wall-clock time of the comparable transport-equation transition model.

Point cloud-based CFD enables flow analysis directly on discrete points obtained from 3D scanning and medical imaging, bypassing surface reconstruction, geometry cleanup, and boundary-fitted mesh generation. Derived from immersogeometric analysis, the method immerses the point cloud in a background mesh and enforces no-slip conditions on discrete points through a Nitsche-based weak boundary condition (BC). The framework delivers accurate velocity fields, pressure distribution, and integrated loads; however, accurate prediction of the local wall shear stress (WSS) has remained a critical challenge. The geometry intersects the background mesh arbitrarily, producing cut elements that lack the regularity required for consistent gradient evaluation. The issue is compounded by the stabilization term of the weak BC, whose parameter estimation in the symmetric Nitsche formulation is dependent on the cut configuration and affects the variationally consistent definition of traction from which the WSS is computed. In this work, we propose a new method to obtain accurate wall shear stress in immersed flow analysis with application to point cloud-based CFD, using a non-symmetric Nitsche's formulation with near-wall modeling and a patch-based stress recovery approach with traction compatibility. The method is validated on canonical benchmarks and applied to turbulent flow past a sphere and to a patient-specific aorta, showcasing excellent agreement with reference results.

Interbasin exchange through the Indo-Pacific gateway supplies salt to the Atlantic and is widely invoked as a control on the stability of the Atlantic overturning circulation. We ask whether that control can act on the equilibrium structure of a conceptual thermohaline model. A closed five-box model with an exact salt invariant is constructed, comprising North Atlantic, upper-limb, Indian, Pacific, and deep reservoirs, with the return flow split between a warm route through the Indian reservoir and a cold route, together with an Indonesian Throughflow branch and an Agulhas retroflection. Adding the steady-state budgets of the gateway reservoirs shows that every internal exchange cancels, so the salt they export to the Atlantic is fixed by the net Atlantic freshwater export alone. This holds independently of the warm-route fraction, the throughflow, the retroflection, and how the export is apportioned among gateway reservoirs; across a parameter sweep the largest departure is of order ten to the minus eleven. The gateway therefore enters as a purely additive forcing and cannot renormalize the salt-advection feedback. Replacing the discrete transit lag by a gamma memory kernel leaves the equilibria unchanged but yields a closed-form threshold for oscillatory instability depending only on kernel shape. Broad memory is strongly stabilizing, and a discrete lag is the least stable member of the family. Because the instantaneous feedback vanishes at the fold, oscillatory instability always precedes the saddle-node, over an interval widening more than tenfold as memory sharpens. Gateways therefore appear to act on transient rather than equilibrium dynamics

We study a two-dimensional Gaussian Rouse chain divided into two contiguous blocks with different local friction coefficients but identical Hookean elasticity. In quiescent conditions, friction heterogeneity leaves the continuous-time equilibrium Gaussian conformation unchanged while producing distinct block mobilities and a modified generalized relaxation spectrum. The exact friction-weighted translational diffusion coefficient retains the scaling $D_\gamma\propto N^{-1}$, with a friction-dependent prefactor; the corresponding diffusion law and generalized-mode formulation extend beyond the diblock to more general local friction profiles. We then place the chain in an incompressible Batchelor-Kraichnan random flow. Under a common external flow, the high-friction block becomes more extended than the low-friction block. The deformation asymmetry strengthens with friction contrast and develops across the weak- to moderate-flow regime, remaining clearly visible at the strongest finite-time conditions. It also persists when the chain-specific longest-mode Weissenberg number is matched across friction ratios, showing that, within the same finite-time protocol, the effect is not accounted for solely by a shift of the global relaxation timescale. In generalized-mode coordinates, the smooth random strain does not directly mix mode indices and preferentially amplifies the slowest mode. At larger flow strengths, extension distributions broaden markedly and exhibit pronounced temporal drift over the simulated time window. Since all simulated chain-specific longest-mode Weissenberg numbers remain below unity, this drift is interpreted as slow convergence toward the broad, power-law-tailed stationary Hookean regime near the coil-stretch threshold. Overall, friction heterogeneity alone is sufficient to redistribute deformation along an otherwise mechanically uniform polymer.

On 7 and 8 September 2026 programmatic search produced singularities: a forced Navier-Stokes singularity at every fixed viscosity, statements (C) and (D) of the Clay problem, and two Euler singularities. The unforced problem, statements (A) and (B), stands open, and a search for it needs a target. This paper fixes one: the positive defect problem, that a Leray-Hopf solution from smooth data on the periodic cube loses energy on a finite window, at fixed viscosity, beyond what viscosity removes. A positive defect implies blowup and so a negative answer to statement (B); the converse is not known. The paper proves the target equivalent to a floor on the energy flux through the Littlewood-Paley shells, the Fourier-side form of the coarse-grained flux of the Onsager theory of turbulence, averaged over the window; states necessary conditions on a candidate: a singular time of Type II in velocity, energy concentrating on a set of zero length, a pressure outside L^2, a velocity outside the Onsager-critical class L^3_t B^{1/3}_{3,c_0}, an obstruction to collapse onto a fixed steady Euler profile; and states what cannot certify one: no finite computation witnesses a Galerkin-uniform ceiling, and selection and forcing return the question to a positive defect. A pseudo-spectral search at 128^3 and 256^3 shows which condition of the reduction binds: the fine-shell flux floor holds to within 1 to 6 percent of the ceiling for a third of a turnover time, and fails in scale at the Kolmogorov wavenumber, so a candidate must differ from generic turbulence in the depth of its cascade, not in its timing. Every implication not marked otherwise is a theorem in Lean 4 over Mathlib; the library contains no Navier-Stokes object, and the equation enters only through hypotheses.

The continuity equation serves as a fundamental principle for mass transport in continuous media. While its mathematical structure mirrors that of probability transport and the Liouville equation, an informational interpretation of macroscopic fluid flow is less commonly explored in engineering contexts. This paper treats fluid density as a spatial probability density function, modeling macroscopic motion as the continuous transport of uncertainty. I derive the temporal evolution of Shannon entropy under general flow conditions, establishing how entropy generation depends on macroscopic compressibility and microscopic diffusion. Microscopic diffusion is shown to act as a strictly positive entropy source governed exactly by local Fisher Information. Furthermore, the framework yields an explicit algebraic scaling law characterizing the equilibrium thickness of compressive mixing layers at a local Peclet number of unity. The theoretical model is computationally validated through finite-difference simulations of one-dimensional canonical flows and advection-diffusion within a three-dimensional, spatially varying Arnold-Beltrami-Childress (ABC) flow, yielding a mean relative error of $0.001$. The framework provides an analytical perspective on thermodynamic irreversibility, with potential applications to turbulence modeling, thermal entropy generation in heat exchangers, in-cylinder mixing in internal combustion engines, and aerodynamic flows.

A physics-informed latent neural operator framework is proposed for three-dimensional compressor cascade flow prediction. The proposed method combines a Transolver-based latent encoder, which extracts compact global latent representations of flow conditions from point-cloud CFD data, with a coordinate-based PINNs decoder to reconstruct continuous flow fields while incorporating physics-informed residual constraints during training. The results show that the proposed framework can accurately reconstruct pressure and velocity distributions of complex three-dimensional cascade flows and maintains good prediction capability under previously unseen operating conditions. The present method demonstrates promising potential for efficient CFD surrogate modelling and aerodynamic prediction in turbomachinery applications.

A signed pairwise graphlet encoding of the velocity gradient tensor $\bm{A}$ is introduced as a minimal discrete representation of its off-diagonal structure, and its statistical relationship with the PQR topology of homogeneous isotropic turbulence is investigated using direct numerical simulation data at $Re_\lambda \approx 433$. Each off-diagonal component is assigned a ternary label based on a local threshold, mapping the thresholded off-diagonal sign pattern to one of $3^6=729$ discrete states. The imbalance $\Delta n=n_W-n_S$ between rotation-promoting and strain-promoting pairs is shown to act as a robust proxy for the sign of $Q$: $P(Q>0\mid\Delta n)$ increases monotonically from $0\%$ at $\Delta n\leq-2$ to $100\%$ at $\Delta n=+3$, and graphlets with a single rotation-promoting pair $(\Delta n=+1)$ predict the stable-focus-stretching region with probability approximately $65\%$ -nearly double the global base rate of $36.5\%$- despite discarding all magnitude information. This predictive power can be largely attributed to the off-diagonal contribution of $\bm{A}$, which dominates the sign of $Q$ in a majority of flow states. The graphlet–PQR association remains statistically correlated over several Kolmogorov time scales and exhibits spatial coherence comparable to that of the $Q$ field at dissipative scales, providing a consistency check that the discrete thresholding preserves the short-range organisation inherited from the velocity-gradient field. An out-of-sample predictive log-loss test further shows that $\Delta n$ captures most, but not all, of the predictive content of the complete $729$-state graphlet code: the full code retains a small, reproducible gain of order $10^{-3}$ bits per observation in predicting future PQR topology beyond $\Delta n$ and the continuous invariants, present at finite lag and absent at zero lag.

A polarimeter does not report stress. It reports a retardance and an azimuth, and converting those to a stress pair fixes both the calibration that is required and the covariance that the subsequent inference must carry. We set out that observation chain for planar viscoelastic flow, combine it with velocimetry, and ask what the combined measurement can resolve. The calibration constant is fixed by three separately measurable quantities (path length, stress-optic coefficient and wavelength) rather than being fitted. Propagating the polarimetric errors to first order gives a stress covariance that is anisotropic and site dependent even for independent homoscedastic inputs, and whose conditioning degrades as the retardance approaches zero, where the linearization itself stops describing the measurement. Wrapping imposes a separate design bound. Two numerical studies follow, both in ideal calibrated stress coordinates under a prescribed covariance rather than the propagated polarimetric one. Holding the total scalar count fixed and varying the split between velocimetric and optical sites, an unequal allocation favoring optical sites outperforms either pure configuration. We then ask what the measurement resolves between constitutive models compatible with the same velocity data. In self-consistent pressure-driven flow of the finitely extensible nonlinear elastic Peterlin model, at extensibility L^2=50 and 3% noise, the optical channel rejects the velocity-compatible Oldroyd-B family in 78.1% of realizations at the Deborah number De=2, the ratio of the relaxation time to the flow timescale, and in 100% at De=4, while rejecting only about 5% below De=0.3. The resolving power of a design is therefore a strong function of Deborah number and must be quoted with it.

We present a physics–informed neural solver for the generalized Falkner–Skan boundary-value problem that combines an exact boundary–admissible trial representation with adaptive regional residual balancing (ARRB). The three prescribed boundary conditions are embedded analytically, eliminating boundary-condition penalty terms while allowing the finite–domain streamfunction value and wall shear to be determined by the governing equation. The residual is divided into wall, middle, and tail regions, and a physical global residual is reconstructed from regional mean-squared errors using region-length fractions. Safeguarded exponential–moving–average inverse–gradient coefficients adaptively balance the regional contributions during Adam optimization. A deterministic 800-point residual monitor is used for checkpoint selection, followed by two deterministic L–BFGS stages minimizing the physical global residual. The method is tested on the Blasius, favourable-pressure–gradient Falkner–Skan, and Pohlhausen cases. For \((\beta_0,\beta_1)=(0.75,0.50)\), the predicted wall shear is \(f''(0)=0.8997161394\), compared with the finite-domain reference \(0.8997168085\), giving an absolute error of \(6.691\times10^{-7}\). The residual MSE is \(6.357\times10^{-9}\), while the relative \(L_2\) errors in \(f'\) and \(f''\) are \(2.848\times10^{-6}\) and \(4.188\times10^{-5}\). A matched single–seed ablation shows that ARRB reduces residual MSE by 52.81% relative to global–residual training and by 50.24% relative to equal-regional weighting. Wall–shear errors are reduced by 77.30% and 72.37%, respectively. These results support ARRB as an accuracy-oriented residual-conditioning strategy, while multi–seed experiments remain necessary to quantify optimization variability.

Computational Fluid Dynamics (CFD) is widely used to evaluate ventilation and contaminant transport in occupied buildings, but deployment at scale is limited by three bottlenecks: acquiring room geometry without costly scanning hardware or manual CAD modeling, decomposing the scene into individually manipulable objects, and reconfiguring those objects for alternative layouts without re-capturing the room. We present a semi-automated workflow that converts a single 360-degree video of a room into individually editable, simulation-ready geometry assets. A dense point cloud is reconstructed using Neural Radiance Fields (NeRF), and 2D instance masks from text-prompted SAM 3 segmentation are lifted to 3D using multi-view consensus and depth-band filtering. Points are separated into object instances with an octree, and occlusion gaps are healed with a connectivity graph. Chair templates are fitted by Iterative Closest Point (ICP) alignment, and table geometry is generated procedurally. A browser-based editor supports quality assurance and rapid construction of alternative layout configurations. A steady Reynolds-averaged OpenFOAM solution then drives transient passive-scalar transport; the setup is verified using a mesh-sensitivity study and validated against an IEA Annex 20 benchmark. We apply the workflow to two university classrooms and a tiered lecture-hall auditorium. The capture-to-geometry pass takes two to five hours per room on a consumer workstation. In a controlled obstruction sequence in one classroom, the modeled half-clearance time varies non-monotonically as furniture is added, and a cross-room comparison indicates that clearance behavior cannot be reliably extrapolated between rooms, motivating per-room geometry acquisition. By making that acquisition low-cost, the workflow makes geometry-resolved comparative ventilation studies practical for spaces such as classrooms.

Unstable thermal stratification modifies near-wall momentum and heat transport, causing the mean velocity profile to depart from the classical logarithmic law and complicating wall modelling for turbulent mixed convection. We develop a buoyancy-modified logarithmic-quadratic wall model for incompressible Poiseuille–Rayleigh–Bénard flow. The model combines an approximately linear relation between the near-wall mean temperature and mean streamwise velocity with a thermally modified mean-gradient representation inspired by mixing-length scaling. A priori assessments using wall quantities from the direct numerical simulation (DNS) database show that the calibrated wall law reconstructs near-wall velocity and wall-function-equivalent eddy-viscosity profiles. We implement the wall model in wall-modelled large-eddy simulations (WMLES) at friction Reynolds numbers up to $Re_\tau\approx6000$ and Rayleigh numbers up to $Ra=10^{10}$. For cases with DNS reference profiles at $Ra=10^8$ and $10^9$, the maximum pointwise absolute relative errors are $3.6\%$ for the mean velocity and $1.9\%$ for the mean temperature. For cases with available DNS global-transport data, the maximum relative deviations in the Nusselt number $Nu$ and skin-friction coefficient $C_f$ are $11.7\%$ and $15.9\%$, respectively. The WMLES reduces the mesh count by factors of approximately $195$–$542$ relative to the corresponding DNS meshes. For the $Ra=10^{10}$ and $Ri_b=0.1$ case, extrapolation of reference DNS resolution strategies gives a mesh count of order $10^{11}$, approximately three orders of magnitude larger than the present WMLES mesh count. We also examine how the balance between shear and buoyancy reorganises flow structure, and we identify signatures consistent with the coexistence of streamwise-elongated motions resembling very-large-scale motions and buoyancy-associated streamwise rolls.

In decaying turbulence, the turbulent cascade is not merely a passive background for breakup but an evolving stability boundary that dynamically selects the fragmentation-aggregation pathway. As turbulence decays, the Hinze scale sweeps through the bubble-size distribution, progressively eliminating the breakable population and driving a transition from a mixed breakup-coalescence regime to a self-sustaining pure-coalescence state. Our model predicts a critical turbulence decay exponent $m=5/3$, a transient mixed breakup-coalescence regime, and a late-stage pure-coalescence state with a universal coalescence hazard. Interestingly, the transient breakup acts as a catalyst that amplifies mixed-regime bubble growth relative to pure coalescence. Results from our direct numerical simulations of decaying homogeneous isotropic turbulence as well as high-Reynolds-number duct-flow experiments collapse onto the model predictions when expressed in terms of the measured decay rate. These results replace the conventional instantaneous Hinze criterion with a non-equilibrium, cascade-controlled framework for turbulent fragmentation and aggregation.