Papers

Stably stratified wall-bounded turbulence governs the dynamics of many environmental and engineering flows. A key challenge is characterizing how stratification modifies mean and turbulent profiles. Monin–Obukhov similarity theory (MOST) is the dominant modelling framework, although it has rarely been rigorously validated against well-controlled direct numerical simulation (DNS) data over a wide range of stratification levels. In this study, we exploit the temporally developing turbulent boundary layer (TTBL) framework to investigate stratified turbulent boundary layers from the weakly stable to the very stable regime, spanning a range of Reynolds and Richardson numbers, and isolating the effects due to buoyancy from other mechanisms such as flow rotation. We demonstrate that the TTBL set-up faithfully reproduces classical similarity theory results and that surface-based scaling of the mean velocity gradient holds over a wider range of $z/L$ ($L$ being the Obukhov length) than previously reported. This result is attributed to the similar decay rate of turbulent shear stress and heat flux in this canonical flow. Next, we show that, as stratification intensifies, the intercept of the mean velocity profile increases, until the separation of scales required for a logarithmic region to exist can no longer be sustained. We propose an empirical closure for this intercept shift in terms of the Reynolds number based on the Obukhov length. Finally, a simple damping of the MOST contribution to the mean velocity profile is proposed and validated, enabling accurate prediction of the wall friction coefficient ($C_f$) across the investigated regimes.

Transverse modes beyond the fundamental mode are increasingly being explored to increase information capacity in both mode-division multiplexing and high-dimensional quantum information processing. The ability to combine and separate these modes at arbitrary ratios over a broad bandwidth is central to these applications. Motivated by the lower bending loss and intermodal crosstalk of partial Euler bends in multimode waveguides, we develop a geometric framework based on partial Euler bends for broadband power coupling between the first two transverse electric modes on a silicon-on-insulator platform. Our methodology uses a hybrid of eigenmode expansion and finite-difference time-domain methods. Our designs feature a mode (de)multiplexer, as well as unbalanced couplers (2/3 and 1/3 splitters). The simulated 1-dB bandwidths of our directional couplers range from $101$ nm to $134$ nm. The best-performing fabricated mode (de)multiplexer has a measured 1-dB bandwidth of $90$ nm, a conversion efficiency of $94.0\%$ and crosstalk below $-18$ dB at $1550$ nm. Our results validate the use of partial Euler bends for broadband transverse mode directional couplers and provide a general framework for their design.

Recent advances in quantum computing hardware toward fault-tolerance have increased interest in evaluating near-term quantum platforms on application-relevant quantum algorithms. In this work, we introduce Quantum WalkScore (QWS), a scalable application-oriented benchmark designed to assess the performance of NISQ and future fault-tolerant quantum computers in executing essential quantum routines –discrete-time quantum walks and quantum amplitude amplification– to solve the graph nodefinding problem (marked-vertex search). QWS quantifies performance by scoring the largest problem size for which a designated target node can be found with success probability above a defined threshold. In addition to the complete protocol description, we provide example parameter-selection scenarios designed from noiseless simulation results and demonstrate QWS evaluation through experimental runs on multiple generations of IBM real quantum processors.

We report the results of the first numerical lattice study using domain-wall fermions in the Sp(4) gauge theory coupled to two flavours of (Dirac) fermions, transforming in the fundamental representation of the gauge group. This theory plays a prominent role in the literature on extensions of the Standard Model with composite dynamics. It provides a short-distance completion for a class of composite Higgs models, or, alternatively, of dark matter models based on the strongly interacting massive particle paradigm. We adopt the Möbius formulation of domain-wall fermions (MDWF), implemented within the Grid software environment. We report the results of extensive tests of the algorithm implementation, and of the optimisation of the choices of algorithmic parameters appearing in the MDWF action. We then measure masses and decay constants of the lightest flavoured mesons in ensembles with moderately large fermion masses and several choices of lattice coupling, and perform an extrapolation to the continuum. We compare our results for the physical observables to published measurements obtained in the same field theory, but derived on the lattice by employing Wilson fermions. We demonstrate that, with the deployment of moderate computational resources, the MDWF formulation can yield order-of-magnitude gains in the approach to the continuum limit, in regions of physical parameter space relevant to phenomenological applications of this theory.

Present models of the zodiacal light (scattered sunlight from interplanetary dust in the visible) and zodiacal emission (thermal emission in the mid-infrared) are primarily constrained by surface-brightness measurements obtained at relatively large solar elongations (e >~ 60 deg). As a result, their predictive accuracy at smaller elongations remains uncertain. This is particularly relevant for solar elongations of e ~ 30-60 deg, where next-generation near-Earth-object discovery missions such as NEO Surveyor and NEOMIR are designed to operate. To evaluate the reliability of these models at small solar elongations, we compile and reanalyze the available small-elongation zodiacal-light and zodiacal-emission measurements and provide the first systematic validation of modern zodiacal-light models in a regime where they have never been independently tested. We compare two models derived from the COBE/DIRBE survey: one constrained primarily by the spatial and temporal variation of the monochromatic sky brightness, and another that additionally uses interband color information and fixes the absolute normalization by requiring the minimum high-latitude residual at 25um to vanish. We find that the former reproduces the observations significantly better. At wavelengths most relevant to infrared near-Earth-object surveys (8-10 um), it typically agrees with measurements to within ~10% at e ~ 40-60 deg. Although it also performs better at e ~ 30 deg, significant discrepancies remain. These results show that zodiacal emission at small solar elongations is still only weakly constrained and that its absolute brightness remains uncertain. New mid-infrared observations are required to improve background estimates for future infrared survey missions.

Weak interactions are fundamental in the merger of binary neutron stars (BNS). They provide cooling, change the composition of matter outflows, and can lead to significant secular outflows through neutrino-driven winds. Hence, the inclusion of neutrino transport has become standard in numerical-relativity simulations of mergers involving neutron stars. In more detail, the interactions of neutrinos with matter in a truncated two-moments scheme (M1) are described through interaction rates, calculated from a set of standard interactions. Among those are charged-current reactions, for which the elastic approximation is commonly assumed. More sophisticated alternatives are provided by, e.g., the publicly available NuLib library, or rates computed within a full kinematics approach. In this work, we compare merger simulations of a BNS systems employing each of these three prescriptions for the computation of charged-current weak rates, included in the M1 equations with an implicit-explicit time integrator. We find that the elastic approximation slightly overestimates the dynamical ejecta mass, while underestimating the amount of high electron fraction material therein. Additionally, it overestimates the neutrino luminosities at early times. The effects of full kinematics in comparison to the NuLib rates appear negligible within the uncertainties of the simulation data. Similarly, the post-merger gravitational-wave spectra for the three prescriptions were found to be indistinguishable within the numerical uncertainties. Nucleosynthetic yields, computed with a nuclear network, are broadly consistent, except in the atomic mass range $A\in[90,125]$ where the elastic approximation shows larger abundances. Finally, the different interaction rates seem to affect the remnant disk properties, hinting at the importance of more accurate interaction rates for simulations spanning secular timescales.

We investigate composite Higgs models arising from a gauge-fermionic UV completion with partial compositeness, where the Higgs boson emerges as a pseudo-Nambu-Goldstone boson (pNGB), and top-partners appear as bound states of three hyperfermions, with $\mathrm{SU}(2)_L \times \mathrm{SU}(2)_R$ as the unbroken global subgroup. A bunch of new bound states is predicted by composite Higgs models: spin-0, spin-1/2 and spin-1 resonances. In this work we focus on the phenomenology of the spin-1 resonances. We demonstrate that a generic prediction of these models is the existence of two neutral and one charged spin-1 resonances, which mix significantly with the SM gauge bosons. This mixing allows their single production in Drell-Yan processes at the LHC. We study the LHC phenomenology of these states and identify scenarios where their masses could be as low as $1.5~\mathrm{TeV}$, consistent with the existing LHC data.

Composite Higgs models with underlying fermionic descriptions predict a rich spectrum beyond the Standard Model. Besides the colour triplet fermionic resonances that act as top partners, also exotically coloured baryons can appear. In this contribution we summarise the phenomenology of colour sextet baryons. The dominant decay channel proceeds via a colour octet scalar, resulting in pair production signatures with four or six top quarks. In an alternative mass hierarchy, the sextets produce bottom quarks and a collider-stable colour singlet. We derive recasting bounds on the sextet mass, which reach up to $2.64$ TeV.

The Chiral anomaly cancellation is perturbatively well understood but its nonperturbative validity in presence of a lattice has remained unproven. We provide a rigorous nonperturbative proof of anomaly cancellation and its universality in a variation of the lattice Kogut-Susskind regularization for the multiflavor Sommerfield model, describing Dirac fermions interacting with a non-compact $\mathrm{U}(1)$ quantum vector field. We identify a novel and general mechanism based on the convergence properties of the renormalized expansion and related to the one leading to universality in topological insulators. Irrelevant lattice operators, despite being suppressed along the RG flow, provide essential contributions to the anomaly cancellation.

Outflows of ionised material, often dubbed warm absorbers (WAs), are common in nearby Seyferts but sparse in distant and more energetic quasars (QSOs). We present multi-epoch X-ray and optical observations of the serendipitously identified type-I QSO 2MASS J14302580+4159572 at a redshift of $z=0.35$, revealing the rare rise and decline of a transient ionised absorber over a 22-year timescale. The discovery observations were obtained with XMM-Newton between 2002 and 2005. The first two observations show unremarkable X-ray spectra typical of unobscured type-I QSOs, whereas the 2005 observation reveals a pronounced suppression of the spectrum below $\sim3\,\mathrm{keV}$. Spectral analysis shows that this event is produced by a moderately ionised absorber with column density $N_{\rm H}\simeq5\times10^{22}\,\mathrm{cm^{-2}}$ and ionisation parameter $\log\xi\simeq1.4$. Joint analysis of XMM-Newton, NuSTAR, and Swift/XRT observations spanning 22 years indicates that the absorber remained stable for nearly 18 years before weakening in the 2023–2024 Swift/XRT data. Throughout this period, the intrinsic 3–10 keV continuum remained remarkably stable, indicating that the observed variability is driven by changes in line-of-sight ionised absorption rather than intrinsic luminosity fluctuations. We interpret the event as a thermally driven ionised outflow located outside the broad-line region (BLR), at sub-parsec to parsec scales, with a density of order $10^{6}\,\mathrm{cm^{-3}}$. Supporting this scenario, the high-ionisation [O\,III] $\lambda4363$ emission line varies in tandem with the X-ray absorption, suggesting that the outflow progressively modifies the ionisation state of the inner narrow-line region (NLR) on decadal timescales. These observations provide a rare view of the long-term evolution of a quasar warm absorber and its impact on the circumnuclear environment.

We develop a systematic method for computing the braiding matrices of four-point functions in RCFTs. This is implemented for the case of Virasoro minimal models. The first few terms of the conformal block series are directly computed through the Shapovalov form. The Fuchsian (BPZ) ODEs for order three and higher have accessory parameters that are fixed by this direct computation. We thus bypass the derivation from the null-state condition which gets tedious for higher-level null states. The braiding F-matrices are connection matrices between the Frobenius solutions at two singular points of the ODE. The F-matrices are computed numerically at first, agreeing with the results of Dotsenko–Fateev, which uses the Coulomb-gas formalism. We find that after a change of basis, the F-matrix is rendered unitary, which determines (products of) the three-point structure constants. We conjecture that the squares of the entries of the unitary F-matrix lie in a cyclotomic extension of the rational numbers. This enables us to convert our numerical estimates for the F-matrix into exact ones. The formalism is illustrated through numerous examples in Virasoro minimal models. We also discuss how these methods can be extended to cases involving symmetries that extend the Virasoro symmetry as well as for tenable examples that arise from the holomorphic modular bootstrap program.

Measured evaporation branching ratios of partially deuterated isotopologues of protonated ammonia clusters (NH$_3$)$_N$ H$^+$ ($N \geq 8$) show ratios that depend only on the clusters' deuterium mole fraction. This demonstrates randomly distributed protium and deuterium in the molecules and can be used to determine free energy differences in the product cluster. The entropy thus determined is exclusively the deuterium-protium mixing entropy. The relative dissociation energies of the four isotopologues are determined and with the support of quantum chemistry calculations, their absolute values are estimated.

In this paper, we study the asymmetric phases of the quartic type (0, 1) and (1, 0) Dirac en- sembles via three approaches: the Riemann-Hilbert approach, bootstrapping with positivity, and Hamiltonian Monte Carlo (HMC) simulations. The focus of this work is on asymmetric solutions to the Schwinger-Dyson and saddle point equations of these models, whose solution spaces prove deeply intricate. Via the Riemann-Hilbert approach, we are able to give explicit formulae for the eigenvalue distributions and free energy of various solutions. Using Hamiltonian Monte Carlo simulations, we are able to reconstruct the phase structure. Lastly, using bootstrapping with positivity, we are able to reconstruct the eigenvalue distribution of these models from their bootstrapped moments. All three methods show excellent agreement for a large matrix size.

The area law relates the bipartite entanglement entropy of a quantum many-body ground state to the size of the boundary between the subsystems, but the geometry of this boundary is rarely discussed. We inspect this in the 1D Bose-Hubbard model at fixed density by comparing four spatial bipartitions of the periodic lattice: first half, second half, even sites, and odd sites; sharing the same number of sites but differing in how the boundary is arranged. We find analytical limits with perturbation theory: in the Mott insulator the contiguous cut obeys the area lay while the alternating cut obeys a volume law $S\propto N_s$, in this sense an anomaly, and for the superfluid both cuts colapse to the binomial saturation due to delocalization of the state. We formulate these limits as a statement about the many-body problem using a generalized slave-boson approach based on mean-field with quantum fluctuations while verifying with Exact Diagonalization (ED) for small lattice sizes and Densitiy Matrix Renormalization Group (DMRG) simulations for $N_s\gg 1$. The slave-boson Gaussian ground state allows to compute the entanglement entropy from a reduced correlation matrix for any desired bipartition consistent with ED and DMRG results. Using slave bosons the computational cost is set by the local cutoff $n_{\max}$ rather than the Hilbert space dimension, so we can reach lattice sizes far beyond ED. Our method is capable of establishing the partition-dependent scaling laws as a many-body feature, not only a finite-size effect, in great agreement with the ED for $N_s\in[4,10]$ and DMRG for larger lattice sizes.

We present a multi-wavelength analysis of the highly bipolar object Hen 2-57 based on new optical spectroscopy from the Southern African Large Telescope (SALT), complemented by archival imaging, and long-term time-series photometry from OGLE and NEOWISE. The nebula exhibits a pronounced hourglass morphology with a symmetry axis at a position angle of $110\pm5^{\circ}$ and an average lobe opening angle of $\sim$$53^{\circ}$. We also identify pronounced north–south brightness asymmetry, with the southern parts of lobes consistently brighter. The spectral energy distribution shows a strong mid-infrared excess that cannot be reproduced by a single-temperature blackbody, indicating the presence of a dense circumstellar dust structure, likely in the form of a disk or torus, analogous to that observed in M 2-9. Optical spectroscopy reveals a complex kinematic structure in which the central core is redshifted relative to both the eastern ($55\pm4\ \mathrm{km\,s^{-1}}$) and western ($46\pm3\ \mathrm{km\,s^{-1}}$) lobes. While standard diagnostic diagrams place the extended lobes in the planetary nebula regime, emission-line diagnostics of the central core are consistent with those of symbiotic stars. The same region also exhibits a steep Balmer decrement, indicative of significant internal dust extinction. Long-term OGLE photometry shows no evidence for coherent stellar pulsations, whereas NEOWISE photometry reveals a gradual mid-infrared fading of $\sim$0.25 mag between 2010 and 2024. Together, these properties support a scenario in which Hen 2-57 hosts a dust-enshrouded D-type symbiotic central engine actively shaping the surrounding bipolar nebula, making it a close analogue of M 2-9.

Observable-based Kochen-Specker proofs are configurations of multi-qubit Pauli observables grouped into contexts whose products are plus or minus the indentity. Their robustness as state-independent contextuality tests can be measured by the tolerated error per context $\varepsilon = 2d/|H|$, where $d$ is the contextuality degree and $|H|$ the number of contexts. Since the degree depends only on an underlying abstract structure called the hypergram i.e. the pair formed by the context hypergraph and the anticommutation graph, the search for highly contextual proofs can be carried out on them instead, with no reference to qubits or to any particular Pauli labeling. We further exploit this by enumerating anticommutation graphs first, and then by associating to each graph $G$ the single hypergram carrying its entire hypergraph support $HS(G)$, so that exactly one candidate is examined per graph. Applied to the House of Graphs database and to censuses of vertex-transitive graphs on at most 24 vertices, this pipeline recovers the Peres-Mermin square, the doily and the Mermin pentagram, and yields configurations reaching $\varepsilon = 0.707$, against $0.424$ for the previous published record. The best configurations are predominantly those stemming from line graphs and unions of graphs; we explain the former by showing that every perfect matching of a graph is a context of its line graph, which exhibits the Peres-Mermin square and the doily as the first members of two infinite families. We close with finite geometric descriptions of the most striking configurations inside symplectic polar spaces, in terms of ovoids, hyperbolic quadrics and Fano planes.

We investigate the structure of the $K^+$ meson through calculating its valence-quark (anti quark) generalized parton distribution functions (GPDs) and form factors (FFs). For this purpose, we use a theoretical framework which is based on the exponential representation scheme (ERS). In this scheme the valence-quark GPDs of the light mesons, including the kaon, are considered as the valence quark distribution function crossed by the exponential of a profile function, at zero skewness. We apply the modified chiral quark model ($\chi QM$ ) to obtain the input valence distribution functions of the kaon in above scheme and calculate its valence GPDs. The kaon's electromagnetic and gravitational form factors are also determined and compared with existing experimental data and the results of some theoretical and phenomenological models.

A central goal in the exploration of kagome-based materials is the realization of a flat band that has meV bandwidth and lies close to the Fermi energy. The prevailing assumption is that band flattening originates from destructive hopping processes on the kagome lattice. We perform scanning tunneling microscopy (STM) on the layered kagome ferromagnet Fe$_3$Sn$_2$ and show that it indeed hosts a flat band near the Fermi energy, which is manifested as a sharp peak in the differential tunneling conductance. First-principles slab calculations reveal, however, that this band is flattened not by the destructive interference of intralayer hopping, but by interlayer hopping between rhombohedral-stacked kagome planes in Fe$_3$Sn$_2$, and is confined to the surface layer. This surface band, forming in the vicinity of the Brillouin zone corners $\bar{K}$ and $\bar{K'}$, exhibits rich magnetic-field dependence, including fine structure due to valley-symmetry breaking by rotated Fe moments, as well as a persistent diamagnetic shift associated with orbital magnetic moments, all reproduced by our calculations. Our results, highlighting the crucial role of layer stacking on the band structure of kagome magnets, demonstrate experimentally an alternative mechanism of generating magnetically tunable flat bands in atomically thin volumes of topological magnets.

A cumulative variational framework for solid deformation is proposed. Its central organizing principle is the recursive combination of three structural components of one material body: a compatible Cosserat component, a distributed-incompatibility component, and a defect-source component. At any prescribed external condition these components constitute a combined material state. They are governed under common physical boundary and initial conditions and are coupled through one cumulative energy and the associated field equations. They are not separate boundary-value problems and need not appear in a prescribed temporal sequence. The cumulative character of the framework concerns the response of the combined state to variation of externally prescribed conditions. For the special case of an initially perfect body, loss of stability may produce successive branches with defect and then source participation. Such a sequence is a bifurcation property of the selected initial state and constitutive energy, rather than a defining hierarchy of the framework. A one-dimensional specialization illustrates structural bifurcation, residual deformation and residual stress produced by retained structure, dependence on the initial combined state, directional memory under reverse loading, parametric cumulative hysteresis, and changes of observable tangent stiffness associated with structural stabilization. A spatial extension introduces defect and source gradient terms and yields a size-dependent structural stability operator. For the stable quartic energy considered, the gradient terms regularize nonuniform perturbations but do not by themselves generate a finite-wavelength localization instability on an already stable three-component branch. The examples thereby distinguish consequences of the cumulative structure and energy from phenomena requiring additional constitutive evolution laws.

MXenes have attracted considerable interest for integrated nonlinear photonics owing to their broadband optical response and chemical tunability, yet investigations have focused predominantly on Ti-based compositions, leaving the nonlinear potential of double-transition-metal MXenes largely unexplored. Here we quantify the nonlinear optical response of the double-transition-metal MXene \ce{Mo2TiC2T_x} and demonstrate its functionality as a waveguide-integrated nonlinear activation element for neuromorphic photonics. Z-scan measurements at \SI{800}{\nano\metre} reveal strong saturable absorption in films of two different thicknesses, yielding effective nonlinear absorption coefficients ($\beta_\mathrm{eff}$) between approximately $-2.69\times10^{3}$ and $-0.88\times10^{3}$ \si{\centi\metre\per\giga\watt}, with the nonlinear response decreasing at higher excitation intensities. The extracted nonlinear absorption is approximately one order of magnitude larger than that reported for \ce{Ti3C2T_x} MXene under comparable conditions. We integrate an ultrathin \ce{Mo2TiC2T_x} MXene layer onto a silicon rib waveguide to realize a compact nonlinear optical activation function, which, when implemented in a neural-network emulator, achieves $98.39\%$ classification accuracy on the MNIST benchmark. This work expands the MXene material platform beyond Ti-based compositions and establishes double-transition-metal MXenes as promising candidates for high-performance integrated nonlinear photonic and neuromorphic computing technologies.

We investigate the unresolved binary-star fraction in a complete sample of 376 open clusters located within 1 kpc of the Sun using Gaia DR3 and ASteCA based synthetic colour magnitude diagram modelling. The binary fraction is a global photometric quantity, sensitive primarily to unresolved binaries that produce measurable broadening above the single-star main sequence. We find that the median binary fraction of the sample is nearly constant, $0.29\pm 0.03$, with no clear dependence on cluster age, core radius, limiting radius or median mass. This apparent constancy suggests that the global binary content of nearby open clusters is regulated by competing dynamical processes, including disruption of soft binaries, survival and hardening of close binaries, mass segregation, evaporation of single stars, and long-term cluster dissolution. The result is consistent with theoretical expectations and previous observational studies indicating that cluster binary populations can evolve internally while maintaining a relatively stable global binary fraction. Our findings provide an observational constraint for models of open-cluster formation and dynamical evolution and highlight the need for future work combining photometric, astrometric, spectroscopic, and N-body approaches to distinguish between primordial and dynamically formed binary populations.

High-entropy alloys (HEAs) exhibit exceptional catalytic performance in various reactions due to their high configurational entropy, synergistic elemental effects, tunable electronic structures, and excellent structural stability. However, the vast compositional space of HEA catalysts makes traditional experimental and theoretical design costly and inefficient. In recent years, data-driven machine learning (ML) methods have emerged as powerful tools for studying HEAs in catalysis. Through predictive models and ML surrogates, researchers can decipher the intricate composition-structure-performance relationships of these materials. In addition, by leveraging large language models (LLMs) for knowledge extraction, hypothesis generation and validation, and as a foundation to build integrated design workflows, ML approaches can significantly accelerate the design of novel HEA catalysts. This review systematically summarizes the latest methodological advances and applications of ML methods for HEAs in catalysis, discusses the challenges, and offers insights into future research directions to support the rational design and efficient development of catalysts.

In Mn–Ni–Ga Heusler alloys, the competing magnetic states are separated by differences of a few meV per atom, so the ground state has to be resolved from the electronic structure and cannot be read off the composition. Moving away from the stoichiometric compounds, where the established rules for Heusler magnetism fall short, increases this difficulty. To overcome it, we introduce orbital fingerprints taken from the projected density of states, and use them as the input to machine-learning models for classification of the magnetic ordering, for the magnetic moment amplitude, for the spin polarization at the Fermi level and for interpolation of the phase diagram. The models are trained on a dataset of 370 spin-polarized first-principles calculations of quasirandom structures covering the ternary, which show good agreement with the magnetic ground states and lattice parameters available in the literature. For magnetic ordering, the top-ranked descriptor is the same quantity found by first-principles calculations to distinguish the phases, suggesting that the fingerprints capture the underlying physics.

Motivated by recent experimental findings on UTe$_2$ via NMR and specific heat experiments, we theoretically explore the thermodynamic signatures of condensates with small superfluid density and characterize their physical properties. We identify the hidden superconducting phase $A_2$ composed of spin-up Cooper pairs at lower temperature ($T$) and field ($H$) under ambient pressure of UTe$_2$ and show that $A_2$ reappears at higher $H$ for all three principal field directions, $a$, $b$, and $c$-axis. The phase transition lines from the $A_1$ phase with spin down pairs to the $A_2$ phase in the $H$-$T$ plane are all horizontal in common, implying a universal physical origin due to the originating from the magnetic-energy gain of the spin-up pairing state with increasing magnetic field. This multiple-phase diagram is extended to these under pressure ($P$), resulting in a simple picture based on non-unitary spin-triplet pairing symmetry $^3B_{3u}$, which enables us to consistently capture the evolution of the superconducting phases throughout the entire $H$-$T$-$P$ phase space.

Computational materials databases have become central infrastructure for data-driven discovery of inorganic materials, yet their growth remains strikingly uneven across property families. This perspective synthesizes a systematic survey of mainstream density functional theory (DFT) software, the computational cost and credibility of nineteen material-property families, and the coverage of existing computational databases, into a coherent picture of where the field stands and where it should go. We show that the ecosystem of first-principles codes is methodologically mature: for nearly every property of technological interest, at least one production-grade code can compute it.The binding constraint is no longer methodological capability but the economics of trust - which properties can be computed cheaply enough, and accurately enough, to be harvested at database scale. Mapping database coverage onto a Gartner-style readiness cycle reveals a sharp divide: ground-state structure, energetics, elasticity, and topology have reached routine production, while nine property families - including NMR/EPR parameters, core-level spectra, electron-phonon properties, thermal conductivity, and quantum transport - remain without any systematic computational database. We argue that these blank zones define the scientific opportunity of the next decade, and we propose a three-horizon roadmap: consolidating coverage and interoperability in the near term, industrializing mid-cost properties through surrogate-accelerated workflows in the medium term, and conquering the high-cost frontier through machine-learned interatomic potentials, autonomous computing infrastructure, and community governance in the long term.

We propose GPU algorithms for high-fidelity simulation of incompressible turbulent flows. Discretization in space is performed with H(div)-conforming high-order Raviart-Thomas finite elements for the velocity and an $L^2$-conforming discontinuous Galerkin approximation for the pressure. In time, a consistent splitting scheme based on higher-order BDF time stepping is used, with convection treated explicitly. In this scheme, a pressure Poisson equation and a symmetric reaction-diffusion-type equation for the velocity need to be solved in each time step. We develop a solution framework with fast matrix-free operator evaluation for all ingredients, combined with multigrid solvers for the Poisson problem, and propose a robust mixed-precision algorithmic framework. A key to mixed-precision efficiency is a least-squares projection to generate accurate initial guesses for the iterative linear solvers, enabling us to work with relative residual tolerances of $10^{-3}$. In this regime, running the solvers entirely in single precision leads to almost no change in overall iteration counts and maintains the crucial turbulence statistics, while showing up to $1.7\times$ speedup over pure double-precision simulations.

The performance synthesis calculation of aircraft engines relies on tabulated datasets for the simulation of the complex turbomachinery components at acceptable runtimes. Typically, these so-called performance maps express the change of the fluid's energetic state over the component in terms of the total pressure ratio and the isentropic efficiency of the process. However, the definitions of both parameters are different for compressors and turbines and the isentropic efficiency is in both cases not defined for a unity pressure ratio. Moreover, this parameter combination is not directly applicable when modelling the engine at the aircraft level, which is required for modern highly integrated aircraft design. As exergy analysis is an established tool for aircraft design asessment, novel performance maps are proposed that describe the change in exergy and anergy over a given turbomachine component. Both changes are expressed as non-dimensional parameters whose definition is consistent for compressors and turbines, and is compatible with a unity pressure ratio. It is shown that the presented exergy-anergy maps are obtainable on a standard turbomachine test bed or through transformation of existing maps. It is highlighted using examples, that the conversion between existing maps and exergy-anergy maps is completely lossless. The different operating regimes of the turbomachines are clearly distinguishable in the novel map representation, which allows an assessment of the map's physical consistency. It is therefore concluded, that the exergy-anergy maps are an important alternative to the performance map variants established today.

Landmark mathematical formalizations have taken specialist teams years to complete. We present FormalFlow, a system that coordinates AI proving agents under human supervision to address statement drift and proof composition in long-horizon formalization. Drawing on software-engineering principles and practices, it uses a shared blueprint to guide nested planning, proving, and review loops. Using FormalFlow, we completed a machine-checked Lean 4 proof of the quantum soundness of the classical low individual-degree test, a core theorem underlying MIP* = RE, in 63 days. The final library contains 126,367 lines of Lean code, all generated by agents. Beyond providing a verified foundation for quantum complexity, the formalization corrects side conditions and intermediate error bounds in the published proof and improves the error exponent of the main theorem. The development record shows what it takes to trust proofs written by AI agents and provides reusable tools for verifying research mathematics at scale.

Orthogonal arrays (OAs) are combinatorial configurations with applications in experimental design, error-correcting codes, and quantum information. Local unitary (LU) equivalence provides a natural framework for classifying multipartite entangled states. Using the correspondence between OAs and quantum states, Goyeneche and Życzkowski [Phys. Rev. A, 2014, 90: 022316] posed the problem of determining when OAs are $LU$ equivalent. In this paper, we construct OAs from generator matrices and establish conditions for Fourier-based $LU$ equivalence of OAs and irredundant orthogonal arrays (IrOAs). For prime alphabets, we identify the Fourier partners of the linear OAs considered here with the arrays of their corresponding dual codes. This gives an explicit connection between $LU$ equivalence and coding theory. We also identify families of $LU$ equivalent OAs arising from specific classes of linear codes.

Flare is an open-source Python-based data workflow orchestration tool powered by b2luigi. It automates the workflow of Monte Carlo (MC) generators inside the Key4HEP stack, such as Whizard, MadGraph5 and Pythia8, together with fast detector simulation using Delphes. It also automates the Future Circular Collider (FCC) physics analysis software workflow. These workflows are combined, giving a user an automated pipeline from MC production to final FCCAnalyses histograms. With its customisation options and Python API, Flare simplifies executing FCC-ee analyses, especially when custom MC events are required.