Papers

Superconductivity in stoichiometric FeTe opens access to the FeTe endpoint of the Fe(Se,Te) phase diagram, yet the nature of its superconducting pairing state remains unresolved. In this work, we combine scanning superconducting quantum interference device (SQUID) microscopy, electrical transport, scanning tunneling microscopy and spectroscopy (STM/S), and mean-field calculations to investigate the local superfluid response and pairing state of FeTe thin films with tunable stoichiometry. Even in stoichiometric FeTe, we observe micrometer-scale spatial variations in both superfluid stiffness and superconducting transition temperature $T_c$, while the London penetration depth remains non-saturating down to 0.02$T_c$ and follows a power-law temperature dependence with an exponent of approximately 1-1.5. Together with a V-shaped low-energy density of states and two-gap modeling, these results indicate a superconducting state with gap nodes or deep minima, consistent with either a $d$-wave or nodal $s$-wave superconducting state. Our findings establish stoichiometric FeTe as a distinct superconducting regime that departs from the trend toward more isotropic gaps at intermediate Se/Te compositions, providing a new benchmark for modern microscopic theories of iron-chalcogenide superconductivity. Our work also reveals a crossover from weak to rapid suppression of $T_c$ as superfluid stiffness decreases, connecting FeTe to the broader phenomenology observed in unconventional superconductors.

Molecular beam epitaxy (MBE) is renowned for its potential for atomic layer control, but unexpected growth mechanisms can potentially compromise this level of precision. In this study, we employ first-principles calculations to investigate the atomistic processes governing the MBE growth of perovskite SrTiO3 and Ruddlesden-Popper Sr2TiO4 films on a SrTiO3 substrate. We systematically explore the potential molecular species in the gas phase and their reactions and diffusion dynamics on the film surfaces and layer edges. Our analyses uncover three mechanisms of importance for understanding this type of growth. First, oxygen vacancies can be dynamically induced during surface diffusion on defect-free substrate and noticeably accelerate the diffusion processes. Second, while the SrO layer is expected to grow in a single-layer growth mode, the presence of potential TiSr defects may promote the formation of SrO islands. Lastly, adsorbed Ti atoms and TiO2 molecules on the SrO bilayer can insert into SrO bilayers, resulting in an unexpected growth sequence. These findings may have broader implications for the MBE growth of metal oxide films and provide guidance for achieving improved control over their growth processes.

We construct the Bogomol'nyi equations for Abelian gauge–Higgs vortices in which the Maxwell gauge sector is replaced by Kruglov nonlinear electrodynamics, a power-law family that interpolates between Maxwell theory, Born–Infeld electrodynamics, and exponential electrodynamics, characterized by a dimensionless exponent $\sigma$. Using the stressless method, we derive a pair of first-order equations directly from the vanishing of the spatial stress tensor, without assuming the Higgs potential a priori. For generic $\sigma$, the gauge and Higgs sectors are coupled through an implicit algebraic relation. We therefore introduce a constitutive map $\Phi(Y;\sigma)$ and analyze its monotonicity and range to determine the conditions for a smooth admissible Bogomol'nyi branch. For $\sigma>1/2$, the constitutive map is strictly monotonic and unbounded, whereas for $0<\sigma<1/2$ it possesses a finite maximum; the marginal case $\sigma=1/2$ is bounded. These properties yield explicit bounds on the nonlinear parameter $\beta$ for the latter cases. We further obtain closed-form constitutive relations, BPS potentials, and gauge-field equations for six representative values of $\sigma$, spanning linear, quadratic, and cubic algebraic structures. The corresponding vortex profiles are then computed numerically. The resulting BPS string tension is purely topological, $\mu_{\rm BPS}=2\pi n$, independent of both $\sigma$ and $\beta$.

This commentary briefly reviews recent measurements from DAMPE and LHAASO on cosmic rays to explore why the spectra of different species change shape across the TeV-PeV energy range. DAMPE finds that several primary nuclei show spectral softening at a similar magnetic rigidity, while the combined proton and helium data from DAMPE and LHAASO reveal a more complex evolution at higher energies. By comparing these spectral features and composition changes, we discuss what they may tell us about the sources of Galactic cosmic rays and how these particles propagate through the Galaxy.

We investigate the low-energy band structure and topology of twisted bilayer–trilayer graphene with four stacking configurations: AB–ABC, BA–ABC, AB–ABA, and BA–ABA. Using both tight-binding and continuum models, we first establish that the two approaches show good agreement in the band structure in low-energy regime. We then study the evolution of the flat bands and their valley Chern numbers as functions of twist angle, perpendicular electric field, and the self-consistent Hartree potential. At relatively large twist angles and under electric field, we find a topological transition between the narrow bands, with the total Chern number of the flat bands following the Chern number sum rules derived from the chiral-limit description. We also observe another type of topological transition when the flat bands hybridize with adjacent remote bands, where gap closing and reopening processes lead to Chern number and charge density transfer. By constructing topological phase diagrams in the space of twist angle and electric field, we show that the perpendicular electric field provides an efficient tuning knob for controlling the stability and transitions of the Chern bands. Finally, we find that the Hartree potential mainly induce weak band shifts and reshaping in the narrow bands. However, with a combination of Hartree potential and the electric fields, the narrow bands show rich topological phase diagram. Our results clarify the interplay between the stacking, twist angle and electric field in manipulating the narrow bands and their topology in twisted bilayer–trilayer graphene, and provide guidance for engineering topological narrow bands with tunable Chern numbers in realistic twisted multilayer graphene systems.

Machine learning surrogates based on neural operators have shown broad applicability in solving forward PDE problems. However, eigenvalue problems, in which an eigenparameter and one of several valid eigenmodes must be simultaneously solved, remain difficult because standard operator learning formulations assume a unique input-output map. This work demonstrates that Fourier Neural Operators (FNOs), combined with wavelet-based encodings of PDE inputs, can learn and predict multiple eigenmodes of the elastic wave equation, corresponding to deformation modes of acoustic waves propagating through arbitrary metamaterial geometries. We provide a mechanistic explanation and experimental evidence for why wavelet encodings are well matched to the dual spatial-spectral structure of the FNO, enabling deterministic mode selection on both continuous-valued and binary-valued geometries within a single model, and for why prediction accuracy varies with geometric discontinuities. For metamaterial design, the resulting surrogate accelerates the simulation stage of the design cycle by three orders of magnitude relative to finite element analysis on a consumer-grade CPU, while preserving high fidelity. These results also carry broader implications for designing input encodings in other multi-mode PDE solvers based on spectral neural operators.

We show that finite-momentum phonons generate electronic orbital angular momentum (OAM) even without phonon axiality or chirality, with the response controlled by the phonon wave vector $q$ and frequency $\omega$. We develop a general gauge-field theory in which a unitary transformation absorbs the phonon displacement into emergent vector and scalar potentials acting on the electrons, providing a perturbative classification of the OAM response in $q$ and $\omega$. We derive $q$- and $\omega$-scaling laws for AC and DC responses. Notably, AC OAM arises even for linearly polarized phonons, with its magnitude and sign tunable by $q$. Its generation is governed by the matching between the phonon geometry and the electronic orbital texture rather than solely by the phonon angular momentum. The connection of the DC response to the electronic Berry curvature further supports that phonon angular momentum is not the only degree of freedom governing electronic OAM generation. Time-dependent tight-binding simulations under acoustic-phonon driving independently confirm the core predictions. Our results extend phonon-driven OAM beyond chiral and axial phonons and establish a wave-vector-tunable route to orbitronics, accessible with surface acoustic waves.

We study the spectral sign implication for quantum logic, defined by the nonnegative spectral projection of the operator obtained by subtracting the antecedent projection from the consequent projection. The construction agrees with classical material implication on commuting projections and compares arbitrary pairs of projections through the spectral structure of their difference. It satisfies Hardegree's four minimal implicative conditions, his law of contraposition, and a falsity condition. It differs from the standard polynomial implications in that its value need not belong to the ortholattice generated by its arguments. Within a uniform class of Borel constructions for pairs of projections, the operations satisfying entailment, contraposition, and the falsity condition correspond exactly to measurable choices of spectral branch. In the continuous subclass, these three conditions determine the spectral sign implication uniquely. In finite dimensions, the operation is also the largest among the acceptance projections of optimal projective tests for Helstrom discrimination between subspace states with priors proportional to rank. These results connect quantum implication with the operator theory of two projections and binary quantum discrimination.

We derived a resolvent operator to analyze the coupled flame-acoustic effect in a model two-stream coaxial combustor. The theoretical analysis accommodates both the hydrodynamic effect of the active flame and chamber acoustic effect, as well as their coupling effect. Utilizing the coupled thermoacoustic resolvent, we are able to identify the optimal forcing of different mechanisms and their corresponding optimal responses. When this new modeling tool is applied to a two-stream coaxial model combustor, it reveals distinctly different forcing-response characteristics in the coupled system compared to those in a purely hydrodynamic linear system. Acoustic energy peaks, indicative of resonance, are observed. Additionally, it has been found that the acoustic forcing does not maintain a rank-one property. Furthermore, the modes most receptive to the flame-acoustic coupling effect can be identified using a novel sensitivity analysis approach. Interestingly, by employing the coupled thermoacoustic resolvent, we demonstrate that forcing can be designed to negate or counteract perturbations caused by the forcing of another attribute, potentially aiding in the development of effective thermoacoustic control strategies.

The evolution of galaxy cluster abundance is a powerful probe of cosmology, but its efficacy depends on our ability to understand and control for systematics in the selection and mass estimation of clusters. We study redMaPPer-selected clusters in the Cardinal simulation, which simulates the DES Y3 observational conditions. Specifically, we investigate the line-of-sight velocity distributions of cluster member galaxies in 12,272 simulated clusters. We find that a significant fraction of clusters, 35%, have velocity dispersions that are high compared to their richness with an offset of $\sim 400$ km s$^{-1}$ between the outliers and the main population. A similar population of velocity dispersion outliers was found in the DES Y3 data. Nearly all of the outliers (98%) in a low-richness subsample have non-Gaussian velocity distributions, and they are more likely than the main population to have significant velocity substructure. These clusters also tend to have higher redshifts than clusters with typical velocity dispersions, and they show a larger scatter between halo mass and richness. Overall, our results point to a significant contamination of redMaPPer-selected samples from line of sight structure, particularly at high redshifts and low richness. Comparison to the Buzzard simulations shows similar results.

We analyze high-cadence spectropolarimetric observations of solar plage obtained with the Visible Spectro-Polarimeter (ViSP) on the Daniel K. Inouye Solar Telescope (DKIST) to investigate low-chromospheric waves sampled by the Na I D1 5896 Angstrom and Ca II 8542 Angstrom lines. Observations were taken at an oblique viewing angle, providing sensitivity to transverse motions. Magnetic oscillations within plage elements exhibit significant line-of-sight (LOS) RMS amplitudes of approximately 9 G on average in the Na I D1 line, whereas the corresponding Ca II oscillations are only marginally above the noise level. Adaptive profile tracking provided line-core intensities and Doppler velocities, the weak-field approximation provided LOS magnetic fields, and non-LTE inversions provided mass densities and formation heights. Cross-spectral analysis shows velocity-intensity phase distributions coupled at -90 degrees, consistent with compressive oscillations. The velocity phases in Na I-Ca II indicate upward propagation and the phase speeds are predominantly sub-Alfvenic, consistent with slow magnetoacoustic waves. Although the slit geometry prevents a definitive identification of the tube eigenmode, the differing magnetic phase relationships suggest a height-dependent sausage-like behavior in the coupling between the magnetic and compressive perturbations. Additionally, our inferred wave fluxes are insufficient to heat active-region plage.

Projective transcorrelation recovers the short-range electron correlation by a similarity transformation with a geminal function $f(r_{12})$, at the cost of an effective Hamiltonian containing a 3-body term. We replace the term by an effective operator of rank at most two, obtained from the two-body cumulant (2C) approximation to the three-particle reduced density matrix. The 2C 3-body energy is written without cumulants, and the effective one- and two-body interactions are derived as its partial derivatives with respect to the reduced density matrices. The truncation is assessed on the atomization and reaction energies of the HEAT set with CCSD(T), and on the CAS-pTC model, whose downfolded Hamiltonian is held on a qubit register with the number of Pauli strings reduced from the sixth power of the orbital count to the fourth.

We introduce a merger tree builder, CTree. Its key feature is the identification of progenitors using the evolutionary information encoded in object branches, rather than relying solely on the instantaneous particle membership in a single snapshot. In this sense, CTree can be described as a branch-wise merger tree builder. Specifically, CTree extracts particles associated with objects over a defined timescale and uses this information to compute the merit functions employed in the progenitor search across multiple snapshots. During this process, CTree requires only the identifiers of particles and objects. This ensures high compatibility with different halo and galaxy catalogues and also with pre-existing merger trees. To identify `core' particles that remain bound to the host halo over extended physical timescales, CTree employs a simple and efficient algorithm that does not rely on explicit radial or binding-energy information. The timescale adopted for core particle extraction and the number of snapshots used in the progenitor search can be user-configured. Basic validation tests using suites of dark matter-only simulations demonstrate that CTree produces stable and physically consistent halo merger trees, particularly in high-density regions or in simulations with high output cadence. The code is written in C++ and employs a hybrid message passing interface and OpenMP parallelization, making it well-suited for high-resolution cosmological simulations. The code is publicly available and actively maintained to improve performance, reliability, and compatibility.

Portable atomic clocks are essential in a wide variety of applications, most notably in the operation of global navigation satellite systems. Existing portable atomic clocks utilizing microwave-based interrogation schemes are now routinely eclipsed by the next generation of atomic frequency standards based on optical interrogation. While optical frequency standards demonstrate greatly improved frequency stability, they have only recently reached a level of technical maturity required to demonstrate this improved performance outside of well curated laboratory environments. Here, we demonstrate a fully autonomous and portable optical frequency standard based on an efficient dual-color excitation of the $5S_{1/2}\rightarrow5D_{5/2}$ two-photon transition in $^{87}$Rb. The standard utilizes a combination of robust, highly developed commercial-off-the-shelf telecommunications technologies and a fully integrated portable optical frequency comb, providing the optical and microwave outputs vital for interfacing with existing electronic systems and infrastructure. The system demonstrates a fractional frequency stability of $1.9\times10^{-13}$ at 1s of integration time, reaching $3.5\times10^{-15}$ at 8000s of integration time without the need for drift removal. This portable demonstrator unit marks a significant achievement in the development of Rb optical atomic frequency standards, and for the deployment of optical atomic frequency standards outside of the laboratory.

In crystals and molecules with strong coupling between the charge carriers and atomic vibrations, high order harmonics of the vibrational excitations can be observed with intensity following the Franck-Condon envelope. Here, we uncover a new regime of electron-phonon coupling in La2-xSrxCuO4 using resonant inelastic X-ray scattering. In the undoped compound, we find sharp peaks at approximately 85$\pm$5 meV, 180$\pm$7 meV, and 330$\pm$5 meV with no observable dispersion, and an absence of appreciable intensity from other modes observed in Raman spectroscopy in this energy range. The 180 meV and 330 meV excitations have energies approximately consistent with two-phonon and four-phonon in-plane Cu-O bond stretching mode, suggesting that the resonantly excited valence electrons strongly couple to this mode. These excitations exhibit significant doping dependence, eventually becoming unresolvable at 10% hole doping, where the low energy charge excitations are dominated by dispersive plasmons. The observation of selective coupling to even-ordered phonons and stark contrast with the Raman spectra indicate anomalous electron-phonon coupling beyond the Franck-Condon picture. One intriguing possibility is the existence of locally paired quasiparticles in insulating cuprates.

Designing quantum optical experiments requires searching over discrete circuit topologies and continuous parameters, often with multiple realizations of the same target state. Graph-based methods commonly address this problem by optimizing a dense graph and pruning it toward a single circuit. We introduce Grinch, a bottom-up reward-driven generative framework that learns to sample optical graphs directly from fidelity-based rewards without relying on a pre-existing training dataset. We demonstrate the framework on multipartite entangled states, graph and cluster states, and nonlocal photonic-gate targets, obtaining multiple high-fidelity optical graphs. We identify asymptotic solutions for states that cannot be generated exactly by graphs, as well as nonlocal Toffoli gate constructions requiring two ancillas. Our work presents hardware-constraint objectives, which lead to alternative constructions of CNOT and Toffoli gates when connections between ancilla nodes are restricted. These findings illustrate a reward-driven approach to quantum optical inverse design, exploring alternative circuit topologies while directly incorporating connectivity constraints into the search process.

Long Period Variables (LPVs) are Asymptotic Giant Branch stars with periods >100 days. Around one third to half of LPVs display a Long Secondary Period (LSP) that is 5-10 times the length of the main periods. The exact cause of LSPs are unknown, with one potential explanation lying in cross-harmonics caused by the interaction of two simultaneously occurring periods. In this paper, we use the Fourier analysis software VStar to examine the visual range photometric light curves obtained through the American Association of Variable Star Observers of a sample of 5 stars. We find that one star, V CVn, displays a secondary period over 20 times the length of its main period, inconsistent with traditional LSPs. To test if cross-harmonics can result in an LSP or VCVn's extra-long secondary period, we then construct evolutionary tracks and pulsation models of LPVs using Modules for Evolution in Stellar Astrophysics (MESA) and GYRE. After examining the interactions of the fundamental pulsation mode and the first 4 overtones with each other, we do not find evidence that LSPs or V CVn's extra-long secondary period could be caused by cross-harmonics.

Interlayer twisting in van der Waals (vdW) layered materials generates moire superlattices, unlocking unique opportunities for engineering their electronic and mechanical functionalities. Here, building on two key insights - the invariance of the potential energy of complete moire tiles during sliding, and the symmetry-breaking effect induced by the slider edge - we propose the concept of edge energy fluctuation (EEF) and demonstrate that the EEF governs the sliding energy barrier of finite-sized sliders. Interestingly, we found that even at a fixed twist angle and sliding direction, significant frictional anisotropy emerges when the slider edge is cut along different directions, resulting in distinct friction scaling laws. Furthermore, we present a friction engineering paradigm for twisted layered material interfaces through the deliberate introduction of hierarchical edges, offering a promising route for friction control in superlubric devices.

Quantum critical lattice models retain universal information about their lattice symmetries beyond the bulk data of their infrared conformal field theory (CFT). We probe these lattice symmetry remnants by comparing the spatial and temporal entanglement of two Euclidean-evolved states from the same critical model. At large length scales, short-range initial states define conformal boundaries and boundary CFT (BCFT) organizes the universal low-lying entanglement spectrum. In the temporal construction, the translation invariance along Euclidean time requires a uniform state. Moreover, the time slice $\delta \tau \rightarrow 0$ forces a split-gate basis, resulting in a new regular uniform symmetry-preserving transfer representation. For the Ising and Potts chains, onsite symmetries result in the same BCFT structure in the spatial and temporal constructions. The spin-$1/2$ XXZ chain instead realizes the Lieb–Schultz–Mattis (LSM) constraint differently in the two Euclidean quantization. A $U(1)$-preserving spatial state has a doubled unit cell and inequivalent entanglement cuts, whereas the temporal state remains uniform and alternates between translation relation related Dirichlet sectors with integer and half-integer compact-boson zero modes. Breaking $U(1)$ removes the zero mode and the alternation. Thus microscopic symmetry and anomaly data remain visible in universal entanglement by constraining the boundary realization of the infrared CFT.

Long-baseline optical links for space interferometry and satellite quantum networks rely on heterodyne phase tracking under Doppler motion and gravitational frequency shifts. These relativistic shifts can generate large detector-frame beat-frequency offsets over finite readout windows and thereby constrain the temporal precision of front-end phase readout. We develop a detector-frame framework for this problem using an effective two-mode signal–local-oscillator model in which relativistic motion rescales the local-oscillator frequency. Within this setting we derive closed-form Mandelstam–Tamm and Margolus–Levitin bounds for representative Gaussian resources and connect global state distinguishability with the operational precision of heterodyne phase tracking. In the bright-local-oscillator regime we identify a geometric–operational mismatch: the joint optical state can evolve on arbitrarily short global timescales while the relevant information rate is set by the measured detector record. Combining this result with an open-loop transient-acquisition analysis, we show that white phase noise and relativistic beat-frequency drift that is approximately constant over the acquisition window generate a cube-root scaling benchmark for the optimal pre-lock open-loop integration window and the minimum residual phase error. These results establish detector-frame benchmarks for quantum-limited heterodyne timing in relativistic optical links and clarify how global dynamical bounds enter task-restricted continuous optical measurements.

We investigate the geometry of extreme Kerr-Newman black holes and its role in selecting distinct black hole states. Motivated by Smarr's question of what physical information is encoded in event-horizon symmetries, we identify, besides the Smarr extreme family, a special family in which the mass, charge, angular momentum, and irreducible mass are constrained by a single irrational number. In the Christodoulou diagram, this family is selected by a discrete symmetry of appropriately scaled charge and angular-momentum variables. The local differential geometry of the event horizon provides an additional selection principle, which, up to the discrete symmetries (Q \rightarrow\pm Q) and (J \rightarrow\pm J), identifies a unique extreme Kerr-Newman black hole exhibiting the highest degree of local spherical symmetry compatible with the rotating Kerr-Newman geometry. Remarkably, for this distinct extreme configuration, all relevant physical and geometrical quantities, including the energy, electric charge, angular momentum, and irreducible mass, are solely related through the golden ratio. We also examine reversible and irreversible transformations and the associated extractable energy. Intrinsic horizon geometry can therefore constrain the macroscopic parameters and single out distinct extreme Kerr-Newman configurations.

Electroencephalography (EEG) is a noninvasive technology that is widely used to monitor brain states, and many efforts are focused on developing reliable and efficient data analysis methods for EEG recordings. Here, we apply ordinal analysis to the EEG recording of the resting state of 109 healthy subjects measured in two different conditions: with eyes closed (EC state) or eyes open (EO state). We study the robustness of the temporal permutation entropy ($PE$) and the spatial permutation entropy ($SPE$) with respect to the presence of blinking artifacts in the EO recordings, the duration of the recordings, and the number of EEG channels analyzed. We perform a paired statistical test to assess whether these quantities differ significantly in the EO and EC recordings of the same subject. We find that $PE$ and $SPE$ perform surprisingly well, as they detect significant differences when calculated from the raw signals, even within a short time interval ($PE$) or from a reduced number of electrodes ($SPE$).

Targeted alpha therapy will require a large expansion of ${}^{212}$Pb and ${}^{225}$Ac production. We propose neutron- and photon-driven routes that convert ${}^{230}$Th, ${}^{231}$Pa, ${}^{232}$Th, and ${}^{237}$Np into generator parents ${}^{228}$Th and ${}^{229}$Th. The most direct ${}^{225}$Ac route is ${}^{230}$Th(n,2n)${}^{229}$Th. A 10 MW deuterium-tritium (D-T) neutron source irradiating thorium with a 27% ${}^{230}$Th isotopic fraction accumulates about 250 Ci of ${}^{229}$Th in six months, initially enough for five million ${}^{225}$Ac dose-equivalents per year, and its 7916 yr half-life makes it useful for millennia. This requires only $\sim$2 gigawatt-days of D-T fusion operations. Thermal-neutron irradiation of tens of grams of ${}^{230}$Th produces gram quantities of ${}^{232}$U, a decades-long source of ${}^{228}$Th for millions of ${}^{212}$Pb dose-equivalents per year. Alternate routes proceed through ${}^{231}$Pa: fusion neutrons produce 1 to 2 tonnes of ${}^{231}$Pa per gigawatt-year from ${}^{232}$Th, and a thermal reactor converts up to 0.4 g of ${}^{232}$U per gram of ${}^{231}$Pa. Each gram of stored ${}^{232}$U produces 10 mg (8.2 Ci) of ${}^{228}$Th per year. Subsequent ${}^{228}$Th(n,$\gamma$)${}^{229}$Th converts 0.07 to 0.34 g of ${}^{229}$Th per gram of ${}^{228}$Th. We also analyze the ${}^{237}$Np(n,2n)${}^{236\mathrm{m}}$Np route to ${}^{228}$Th. These pathways scale from kilowatt to megawatt D-T sources and could secure millions of ${}^{212}$Pb and ${}^{225}$Ac dose-equivalents per year.

The symmetry content of static spherical $f(R)$ gravity is reconsidered for the pure quadratic model. We first derive the radial action without prematurely eliminating the equation carried by the radial metric variable. The Schwarzschild-type gauge may then be imposed while retaining its associated gravitational constraint. For the resulting system, radial translations and one combined scaling are exact off-shell Noether symmetries. The scaling charge reduces, on the constraint surface, to a conserved radial flux of the scalar curvature. The same flux follows independently from the trace of the four-dimensional field equations. Noether invariance, the strong point-Mei criterion, and Lie invariance of the Euler–Lagrange system are examined separately. Within the full polynomial point ansatz of total degree at most two, the Lie algebra contains precisely three independent generators. The flux also separates the solution space into a nonzero constant-curvature Einstein sector, a degenerate scalar-flat sector, and a dynamical-curvature sector. In particular, the scalar-flat sector permits a Reissner–Nordström-form metric, although its inverse-square coefficient has no electromagnetic meaning in the absence of a Maxwell field.

Earth System Models rely on tunable subgrid-scale parameterizations, but optimizing these parameters is computationally expensive, particularly when nonlinear interactions require many simulations. We present a hybrid Physics-ML multi-fidelity framework that combines Green's Function Optimization (GFO) with Gaussian Process or Neural Network surrogate optimization. Using a quasi-geostrophic turbulence model, GFO first ranks parameter sensitivities in normalized coordinates and selects a reduced active subset. Nonlinear surrogates then explore this subset using inexpensive 30-day simulations before refining promising candidates with 180-day simulations. Across seven strategies and a 35-member ensemble, GFO-MultiGP and GFO-MultiNN achieved mean improvements of 64.6 percent and 65.2 percent, respectively, while reaching practical saturation after 3,060 and 2,520 simulation-days. The corresponding standalone GP and NN achieved 61.1 percent and 42.0 percent improvements and required 7,740 and 6,660 simulation-days. These results demonstrate an end-to-end sample-efficiency advantage for the tested hybrid pipelines. Because screening, dimensionality reduction, initialization, and fidelity scheduling change simultaneously, their individual contributions are not isolated.

The paper presents a consistent thermomechanical framework for strongly nonlocal continua, a type of generalized media in which a material's response at a point depends on deformation and temperature gradients within its neighborhood. Such dependence is responsible for localization phenomena having an intrinsic size, and nonlocal modeling also serves as a practical regularization tool to prevent mesh dependence. Nonlocality is of the integral type, using a kernel function that gives the relative influence of neighboring points on a central point. The paper develops three sources of nonlocality: (1) nonlocal momentum balance equations; (2) nonlocal conservation laws (including the first and second laws of thermodynamics); and (3) a material's nonlocal constitutive structure. Balance equations are derived using the principle of virtual power, permitting non-smooth force and displacement fields and non-smooth boundary surfaces with indistinct normal directions. The balance equations differ from those of classical local continua. Conservation laws also differ from those of local continua, with the mechanical power and heating at a point being averaged over its neighborhood. These laws are developed for processes that are sufficiently slow to minimize additional meso-scale kinetic energy due to internal turbulence. Stress, entropy, and dissipative forces are obtained as averaged derivatives of the free energy function with respect to strain, temperature, and internal variables. An example is presented of a stretched elastoplastic bar with a small defect, and nonlocality is shown to impart a characteristic size to the deformation pattern.

Gravitational-wave denoising must handle the full diversity of spinning, precessing binaries, since the recovered waveform underpins parameter estimation, tests of general relativity, and population studies. Matched filtering achieves this at a cost that becomes prohibitive as next-generation detectors push event rates higher; deep learning offers real-time reconstruction, but current methods are developed on narrow parameter spaces, precluding principled comparison and reliable deployment. We present the first controlled comparison of five neural-network architectures for gravitational-wave denoising, trained identically across the full astrophysically-motivated spinning binary-black-hole parameter space. A unifying principle emerges: matching network structure to the spectral anatomy of a coalescence – inspiral, merger, ringdown – outperforms brute-force model scaling. Our Multi-Scale Frequency-Aware architecture embodies this via dedicated parallel branches per frequency regime, achieving the best fidelity while using fewer parameters than larger models. It generalizes from simulated training to real LIGO-Virgo-KAGRA data without retraining, recovering merger morphology across confirmed events spanning three observing runs and both detectors, despite training on a single detector's simulated noise. We construct population-level uncertainty bands from denoising residuals, validate their calibration, and stress-test the framework on extended mass ratios and a spin population resembling hierarchical-merger remnants. Applied to real noise with no known signal, the network suppresses its output almost everywhere, with rare exceptions traced to noise transients rather than a general weakness – indicating the statistic discriminates signal from noise and motivating a future detection study. Released weights give a deployable, reproducible benchmark for future extensions.

This editorial introduces the topical collection arising from the Lemaitre Conference 2024 - the second in a series of meetings dedicated to the scientific legacy of Georges Lemaitre - held at the Vatican Observatory in Castel Gandolfo, 17-20 June 2024, fifty-seven years after Lemaitre's death and on the eve of the centenary of his foundational 1927 paper on the expanding universe. The nineteen contributions collected here address the most pressing open problems at the interface of cosmology, gravitation, and quantum theory: the Hubble tension and the future of ${\Lambda}$CDM in light of recent DESI data; inflationary cosmology and dark-energy model-building in string theory and supergravity, together with the Swampland constraints that bound them; the observer-dependence of the quantum-cosmological wave function; the removal, or consistent crossing, of spacetime singularities - from the canonical quantization of Lemaitre's own 1933 dust model to string-theoretic pre-Big-Bang bounces and many-body constructions of singularity-free black-hole cores; primordial black holes and their gravitational-wave signatures; the search for a background-independent formulation of quantum gravity and a first-principles account of horizon thermodynamics; and the foundational status of the quantum-to-classical transition in gravitational contexts. A proposal for lunar-based cosmological observations, and a historical reconstruction of the genesis of Lemaitre's primeval-atom hypothesis, complete the collection. A recurring unifying thread was the legacy of Lemaitre himself - who first distinguished coordinate from physical singularities and coined the term "horizon" - whose pioneering vision continues to guide research at the frontier of cosmology and fundamental physics.

We tabulate, on the diagonal, the $n$th power of the primitive approximation for the pair Coulomb density matrix on a sphere, with up to $n=5$, and we discuss its behavior at particles contact as $n$ grows. Our results show that even on a curved surface quantum statistical physics is fundamentally different from its classical counterpart. If in the latter one needs to artificially introduce a regularization of the divergent attractive Coulomb potential preventing particles contact, for example with a hard core, in the former this is not necessary.

We investigate the late-time accelerated expansion of the Universe in power-law $f(Q)$ gravity, $f(Q) = Q + 6\gamma H_0^2 \left(\frac{Q}{Q_0}\right)^n$, combined with two dynamical dark energy parametrizations, Barboza-Alcaniz (BA) and Jassal-Bagla-Padmanabhan (JBP), which allow a smooth evolution of the equation of state beyond the standard constant $\omega$ assumption. We derive analytical expressions for the Hubble parameter and the dark energy density, and constrain the model using Pantheon$^+$ Type Ia Supernovae, DESI DR2 Baryon Acoustic Oscillations, and Cosmic Chronometers. Going beyond purely geometrical probes, we incorporate Redshift Space Distortion (RSD) measurements to test the growth of cosmic structures and distinguish modified gravity from General Relativity through the effective Newton's constant. Both parametrizations reproduce the observed late-time acceleration and remain consistent with growth data, with only mild deviations from $\Lambda$CDM over low and intermediate redshifts. Notably, both configurations yield $G_{\rm eff} < G$, indicating suppressed growth of matter perturbations. These results establish power-law $f(Q)$ gravity with BA and JBP parametrizations as a viable and versatile alternative to $\Lambda$CDM across both background and perturbative regimes.