AI for Science

We develop a stochastic analysis of the sine-Gordon Euclidean quantum field $(\cos (βφ))_2$ on the full space up to the second threshold, i.e. for $β^2 < 6 π$. The basis of our method is a forward-backward stochastic differential equation (FBSDE) for a decomposition $(X_t)_{t \geqslant 0}$ of the interacting Euclidean field $X_{\infty}$ along a scale parameter $t \geqslant 0$. This FBSDE describes the optimiser of the stochastic control representation of the Euclidean QFT introduced by Barashkov and one of the authors. We show that the FBSDE provides a description of the interacting field without cut-offs and that it can be used effectively to study the sine-Gordon measure to obtain results about large deviations, integrability, decay of correlations for local observables, singularity with respect to the free field, Osterwalder-Schrader axioms and other properties.

When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a novel numerical formulation for simulating incompressible viscous flows at low Reynolds numbers in the presence of deformable interfaces. Our method employs a vorticity-stream vector formulation that significantly simplifies the fluid solver, transforming it into a set of coupled Poisson problems. The body-fluid interface is modeled using a phase field, allowing for the incorporation of various free-energy models to account for membrane bending and surface tension. In contrast to existing three-dimensional approaches, such as Lattice Boltzmann Methods or boundary-integral techniques, our formulation is lightweight and grounded in classical fluid mechanics principles, making it implementable with standard finite-difference techniques. We demonstrate the capabilities of our method by simulating the evolution of a single vesicle or droplet in Newtonian Poiseuille and Couette flows under different free-energy models, successfully recovering canonical axisymmetric shapes and stress profiles. Although this work primarily focuses on single-body dynamics in Newtonian suspending fluids, the framework can be extended to include body forces, inertial effects, and viscoelastic media.

We derive exact identities for open systems connecting two equilibrium endpoints without imposing microscopic reversibility, detailed balance (DB), fluctuation-dissipation structure, or local detailed balance (LDB) on the driven dynamics. The identities express the Hamiltonian of mean force (HMF) free energy differences through exponential moments and an explicit chi-squared overlap between the endpoint marginals. In the frozen-coupling regime, the HMF shift reduces to a bare-system increment and admits a trajectory-level heat-work-reference decomposition. The exact relations then reduce the problem to a scalar-action law. A maximum-entropy construction gives a Bessel-form scalar-action law, independent of the microscopic system, environment, and number of degrees of freedom at the level of the variational reconstruction. This law provides three outputs from the same sampled configurations: the HMF free energy difference, the endpoint-overlap burden, and a Hessian uncertainty estimate. Since many systems in biology, chemistry, physics and engineering violate the underlying assumptions of the standard Jarzynski identity, we validate the framework on a reduced-dimensional model with a non-Liouvillian, phase-space-compressing ramp followed by underdamped Langevin relaxation. The standard Jarzynski work estimator fails for this ramp because phase-space preservation is broken and no compensating Jacobian correction is included, whereas the present endpoint identities recover the exact HMF free energy difference, and the variational construction reproduces it within its local uncertainty.

We investigate the ground-state properties of ultracold two-component Fermi gases in the presence of a transverse harmonic potential, focusing on the strongly interacting regime in which pairs of fermions form tightly bound molecules. Using the fixed-node diffusion Monte Carlo method, we calculate the equation of state and density profiles for the full fermionic system, which allows us to address the importance of finite-range corrections arising from the internal fermionic structure of the dimers. We interpret the results in terms of a molecular Bose gas in quasi-two-dimensional confinement and compare them with theoretical predictions for a weakly interacting two-dimensional Bose gas, identifying the range of validity of mean-field and beyond-mean-field descriptions. We also develop an analytical theory for the transverse density profile, capturing its broadening with increasing interaction strength. This work provides a benchmark for an effective bosonic description of strongly bound fermionic dimers and offers new insights into confinement-induced dimensional effects.

In Markov networks, measurement blackouts with unknown frequency compromise observations such that thermodynamic quantities can no longer be inferred reliably. In particular, the observed currents neither discern equilibrium from non-equilibrium nor can they be used in extant estimators of entropy production. Our strategy to eliminate these effects is based on formally attributing the blackouts to a second channel connecting states. The unknown frequency of blackouts and the true underlying transition rates can be determined from the short-time limit of observed waiting-time distributions. A post-modification of observed trajectory data yields a virtual effective dynamics from which the lower bound on entropy production based on thermodynamic uncertainty relations can be recovered fully. Moreover, the post-processed data can be used in waiting-time based estimators. Crucially, our strategy does not require the blackouts to occur homogeneously or symmetrically under time-reversal.

The requirement that a trapped spacetime domain forms in finite time for distant observers is logically possible and sometimes unavoidable, but its consequences are not yet fully understood. In spherical symmetry, the characterization of the near-horizon geometry of these physical black holes is complete and shows marked differences from their eternal counterparts. Whether these differences lead to observable signatures remains unclear. We construct an approximate near-horizon metric that encapsulates them and is suitable for modeling. The timelike apparent horizon of physical black holes provides a natural surface for a consistent membrane description: we obtain closed-form expressions for the redshift, proper acceleration, and extrinsic curvature, and assign a two-dimensional viscous-fluid stress tensor via junction conditions. These results also provide an additional perspective on the relation between Rindler and near-horizon geometries. Among dynamical generalizations of surface gravity, only a subset applies to these models. We complete their analysis and recover the intuitive definition of surface gravity -- the acceleration in the frame of a near-horizon observer, redshifted to infinity -- directly from the membrane acceleration.

Photonic resonances enable control over light-matter interactions, but many key phenomena only emerge in the strong-coupling regime where light and matter excitations fully hybridize. To distinguish between weak and strong coupling, one conventionally studies real-frequency spectra of the hybrid system. However, these spectra only provide indirect estimates of the underlying resonant dynamics, as the resonances reside at complex frequencies. To overcome this contradiction, we demonstrate that photonic resonant states provide a framework for unambiguously distinguishing between weak and strong coupling. Upon tracing the resonant states through the complex plane while changing the resonator geometry, their trajectories undergo a qualitative change at the onset of strong coupling. Instead of passing each other in the complex frequency plane with only perturbative interactions, the resonant states swap positions. Assuming a single dominant photonic resonance, we derive an effective Hamiltonian that captures the interaction with multiple material resonances, including direct access to coupling rates from overlap-integrals. Our analysis reveals that, unlike most coupled-oscillator models commonly employed, hybridization not only introduces off-diagonal coupling but also shifts the bare eigenfrequency of the photonic mode. We apply our approach to planar and spherical silver resonators filled with a molecular material whose properties were extracted from quantum-chemical simulations.

Organisms that locomote by propagating waves of body bending can maintain performance across heterogeneous environments by modifying their gait frequency $ω$ or wavenumber $k$. We identify a unifying relationship between these parameters for overdamped undulatory swimmers (including nematodes, spermatozoa, and mm-scale fish) moving in diverse environmental rheologies, in the form of an active `dispersion relation' $ω\propto k^{\pm2}$. A model treating the organisms as actively driven viscoelastic beams reproduces the experimentally observed scaling. The relative strength of rate-dependent dissipation in the body and the environment determines whether $k^2$ or $k^{-2}$ scaling is observed. The existence of these scaling regimes reflects the $k$ and $ω$ dependence of the various underlying force terms and how their relative importance changes with the external environment and the neuronally commanded gait.

We present a numerical model of fractal-structured aggregates in low-Reynolds-number flows. Assuming that aggregates are made of cubic particles, we first use a boundary integral method to compute the stresses acting on the boundary of the aggregates. From these external stresses, we compute the stresses within the aggregates in order to gain insights on their breakup, or disaggregation. We focus on systems in which aggregates are either settling under gravity or subjected to a background shear flow and study two types of aggregates, one with fractal dimension slightly less than two and one with fractal dimension slightly above two. We partition the aggregates into multiple shells based on the distance between the individual cubes in the aggregates and their center of mass and observe the distribution of internal stresses in each shell. Our findings indicate that large stresses are least likely to occur near the far edges of the aggregates. We also find that, for settling aggregates, the maximum internal stress scales as about 7.5% of the ratio of an aggregate's apparent weight to the area of the thinnest connection, here a single square. For aggregates exposed to a shear flow, we find that the maximum internal stress scales roughly quadratically with the aggregate radius. In addition, after breaking aggregates at the face with the maximum internal stress, we compute the mass distribution of sub-aggregates and observe significant differences between the settling and shear setups for the two types of aggregates, with the low-fractal-dimension aggregates being more likely to split approximately evenly. Information obtained by our numerical model can be used to develop more refined dynamical models that incorporate disaggregation.

Adiabatically eliminating the quantum degrees of freedom in a mixed quantum-classical system produces an effective force in the classical equation of motion. The elimination can be made to any order in the adiabatic parameter, generating a series of higher order forces. By applying a sequence of near-identity unitary transformations to the quantum state, we derive a hierarchy of increasingly accurate effective actions for the classical variables. The third order Euler-Lagrange equation is non-Newtonian as the force depends on the jerk, the third order time derivative of position. We find that the third order terms induce a special kind of Kawaguchi geometry on the space of classical variables. This geometry is characterized by an almost symplectic structure and a differential line element that depends on the acceleration in addition to the velocity. Our results can be used to efficiently capture higher order nonadiabatic effects in molecular dynamics simulations.

Altermagnetism, characterized by momentum-dependent spin splitting and zero net magnetization, has so far been explored mainly in weakly or moderately correlated d-electron systems. How symmetry-allowed altermagnetic band splitting manifests in heavy-fermion materials, where magnetic exchange competes with Kondo correlations, remains unclear. Here we use high-resolution angle-resolved photoemission spectroscopy (ARPES) to investigate CeNiAsO, a Kondo-lattice system that was predicted to be a candidate for p-wave altermagnetism. Fermi surface mapping and polarization-dependent ARPES show that the experimentally observed itinerant bands are mainly derived from Ni 3d orbitals, while resonant photoemission reveals that the Ce 4f states remain predominantly localized with residual c-f hybridization. Ultra-low-temperature measurements reveal no resolvable near-Fermi-level p-wave-like exchange splitting on the Ni 3d-derived conduction bands across the successive antiferromagnetic transitions. These experimental observations cannot be captured by an itinerant-4f band-structure description, which predicts a sizable p-wave splitting in the itinerant bands. When the localized Ce 4f character is incorporated, our band structure calculations indicate that the itinerant Ce 4f band weight is shifted away from the Fermi level and the p-wave-like splitting on the Ni 3d-derived bands is reduced to the few-meV scale. These results establish CeNiAsO as a strongly correlated f-electron setting in which the magnetic symmetry allows p-wave-like band splitting, but localized 4f electrons strongly suppress its observable itinerant single-particle signature.

A regularized Boussinesq equation is studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi-Pasta-Ulam lattice with a general cubic interaction force. Explicit periodic traveling wave solutions in terms of Jacobi elliptic functions are classified, and their solitary-wave, kink, and trigonometric limits are obtained. The Whitham modulation equations describing slow modulations of periodic traveling wave solutions are derived using an averaged variational principle. The convexity (strict hyperbolicity, genuine nonlinearity) of the resulting hydrodynamic-type equations is examined numerically in general and analytically in the solitary-wave and harmonic limits. In particular, the loss of hyperbolicity and the formation of complex conjugate characteristic speeds is shown to lead to modulational instability of periodic traveling waves. The onset of modulational instability is verified by numerical computations of linearized spectra for periodic traveling waves and initial value problems that also reveal additional short-wave instabilities.

Arrays of neutral atoms present a promising system for quantum computing, quantum sensors, and other applications, several of which would profit from the ability to load, cool, and image the atoms in a finite magnetic field. In this work, we develop a technique to image and prepare $^{87}$Rb atom arrays in a finite magnetic field by combining EIT cooling with fluorescence imaging. We achieve an average readout fidelity of $99.7(1)\,\%$ at $98.2(3)\,\%$ survival probability and up to $68(2)\%$ single-atom stochastic loading probability in a 2.3 G magnetic field, with performance validated at fields up to 10 G. We further develop a model to predict the survival probability, which also agrees well with several other atom array experiments. Our technique cools both the axial and radial directions, and will enable future continuously-operated neutral atom quantum processors and quantum sensors.

Two-path complementarity in polarized interferometric fields is reconsidered by retaining the complete path--polarization density matrix instead of reducing the description to the path degree of freedom from the outset. The familiar relation connecting the Cartesian visibility components, path predictability, and reduced-state mixedness is recovered as a marginal consequence of the reduced path state and is not interpreted as a new complementarity law. Attention is focused instead on the full path--polarization description in a real reference basis adapted to the path and linear-polarization degrees of freedom. Within this framework, the normalized purity separates naturally into path, polarization, and path--polarization-correlation contributions, while the antisymmetric sector provides a sector-resolved measure of cohesion. The resulting decomposition identifies which parts of the complete state store phase-sensitive interferometric coherence and which contributions are removed when polarization is traced out. The formalism therefore provides a sector-resolved accounting of complementarity within the full path--polarization state and clarifies the connection between reduced visibility loss, polarization marking, path--polarization correlations, and quantum-eraser recovery. The present article establishes the framework and associated purity decomposition; a more detailed exploration of full path--polarization complementarity and its dynamical aspects is left for future work.

We determine the fully resolved equilibrium density profiles for two binary hard-sphere crystal structures using classical density functional theory through the White Bear II functional from fundamental measure theory. While for the substitutional crystal, in which some hard spheres are replaced by spheres of slightly smaller diameter, the density profiles are rather similar to the single-component case (narrow Gaussian peaks centered at fcc lattice sites), we observe a more complex behavior for the case of interstitial solid solutions, where the small species is fairly delocalized in the unit cell. Further, we compute the species-resolved inhomogeneous two-body direct correlation functions, depending on two three-dimensional vectors, for these two types of binary crystals. The large--large components are mainly determined by the vacancy concentration $n_\text{vac}$ and show a characteristic magnitude $\sim 1/n_\text{vac}$. Based on this observation, we propose a simple geometric picture. The components of the direct correlation function involving the small spheres substantially differ in interstitial solid solutions from those of the substitutional crystal.

Surfactants are amphiphilic molecules that are generally anisotropic rather than spherical. Their orientation is therefore governed by the interplay between shear-induced reorientation, thermal rotational diffusion, and energetic alignment with the interface. The relative importance of these processes is characterized by the rotational Peclet number, $Pe_r$. We show that this microscopic coupling between flow and surfactant orientation can give rise to new macroscopic interfacial phenomena, including a shear-dependent effective surface tension and non-trivial droplet deformation. To investigate this mechanism, we develop a phase-field model that incorporates both the surfactant concentration and its local average orientation (polarization field). Using perturbation theory, we derive an analytical expression for the effective surface tension, which depends not only on the surfactant concentration but also on the local shear rate. We then employ a hybrid numerical method to study the deformation of a surfactant-covered droplet under imposed shear flow. For small $Pe_r$, droplet deformation can be accurately captured by a modified Taylor and Maffettone-Minale theories. For large $Pe_r$, shear-induced reorientation strongly distorts the surfactant polarization, and the droplet deformation progressively approaches that of a pure (surfactant-free) droplet.

The surface states of certain topological phases can be linked to a quantum anomaly: the violation of a classical symmetry by a field theory via a non-conserved current. This has been generalized to the case of a non-Hermitian (NH) chiral anomaly affecting the surfaces states of an NH Weyl phase. Here, we show that the NH anomaly inflow is mediated by continnum Landau modes (CLMs): special eigenstates exhibiting both spatial localization and a continuous spectrum, contrary to the usual distinction between bound and free states. The number of anomaly-induced surface modes scales with the sample volume rather than its surface area, which is shown to be tied to the unusual multiplicity of the CLMs. The other properties of the CLMs, including their normalization conditions and localization scale, closely match the predictions of the NH field theory. Finally, we discuss the conditions under which these phenomena can be probed experimentally using metamaterials.

Accurate epidemic forecasting requires models that account for the layered and heterogeneous nature of real social interactions. The basic reproduction number $\mathcal R_0$, as calculated from models that assume homogeneous mixing or single-layer contact structures, has limited applicability to complex social systems. Here, we derive an expression for $\mathcal R_0$ in the context of multiplex networks, enabling the analysis of disease transmission across multiple social layers. We adapt the Degree-Based Mean-Field (DBMF) SIR model for single-layer complex networks to the multiplex setting, where each layer is characterized by its own degree distribution and infection rate. Using the Next Generation Matrix method, we derive an analytical expression for the basic reproduction number $\mathcal R_0$. Numerical integration of the multiplex DBMF equations shows that $\mathcal R_0=1$ marks the epidemic threshold and governs the behavior of key outbreak indicators as expected. In addition to the exact expression for $\mathcal R_0$, we introduce an approximation, denoted by $τ$, which is simpler to compute and admits a more transparent interpretation in terms of the epidemiological and topological parameters of the system. Stochastic agent-based simulations support these findings, demonstrating a direct correspondence between $τ$ and the average number of secondary infections generated during the early stages of an outbreak, consistent with the epidemiological interpretation of $\mathcal R_0$. This work provides a robust generalization of $\mathcal R_0$ for layered contact structures, offering a more realistic basis for epidemic forecasting and the design of intervention strategies.

AI systems can increasingly automate scientific workflows, but the reasoning that links prior evidence, generated ideas, experiments and final claims often remains implicit inside model inference. Here we introduce Xcientist, a research harness that externalizes research synthesis and experimental validation into inspectable, contract-governed processes. Xcientist organizes literature evidence, idea states, implementation plans, ablation records and repair traces as persistent research artifacts, so that generated mechanisms can be grounded, executed, tested and revised without losing their evidential basis. We identify claim drift as a failure mode of automated research, where runnable artifacts no longer support the mechanism originally claimed. Across training-free memory systems, graph-structured traffic forecasting and multi-scale physics-informed neural networks, Xcientist preserves traceable trajectories from problem formulation to mechanism design, validation and bounded revision. These results suggest that AI scientists should be evaluated not only by their final artifacts, but by whether their synthesis and validation processes remain attributable, inspectable and scientifically accountable.

This paper studies the clustering behavior of weakly interacting diffusions under the influence of sufficiently localized attractive interaction potentials on the one-dimensional torus. We describe how this clustering behavior is closely related to the presence of discontinuous phase transitions in the mean-field PDE. For local attractive interactions, we employ a new variant of the strict Riesz rearrangement inequality to prove that all global minimizers of the free energy are either uniform or single-cluster states, in the sense that they are symmetrically decreasing. We analyze different timescales for the particle system and the mean-field (McKean-Vlasov) PDE, arguing that while the particle system can exhibit coarsening by both coalescence and diffusive mass exchange between clusters, the clusters in the mean-field PDE are unable to move and coarsening occurs via the mass exchange of clusters. By introducing a new model for this mass exchange, we argue that the PDE exhibits dynamical metastability. We conclude by presenting careful numerical experiments that demonstrate the validity of our model.

A two-dimensional topologically nontrivial state of noninteracting electrons, such as the surface state of a three-dimensional topological insulator, is predicted to realize a topological superconductor when proximity-coupled to an ordinary $s$-wave superconductor. In contrast, noninteracting electrons partially occupying a Landau level, with Rashba spin-orbit coupling that lifts the spin degeneracy, fail to develop topological superconductivity under similar proximity coupling in the presence of the conventional Abrikosov vortex lattice. We demonstrate, through exact diagonalization, that introducing in this model a repulsive interaction between electrons induces topological superconductivity at half-filled Landau level for a range of parameters. This appears rather surprising because a repulsive interaction is expected to inhibit, not promote, pairing, but suggests an appealing principle for realizing topological superconductivity: proximity-coupling a composite Fermi liquid to an ordinary $s$-wave superconductor.

Altermagnets are a newly identified class of magnetic materials that combine vanishing net magnetization within the unit cell with spin-split electronic states. Their theoretical description relies on symmetry properties of the bulk band structure. Surfaces and thin films, however, inherently break these symmetries. Here, we investigate the consequences of such symmetry reduction for the electronic structure of bulk altermagnets near the surface and of thin films. When the surface coincides with a symmetry plane of the bulk altermagnetic order, the resulting two-dimensional Brillouin zone exhibits spin-degenerate bands, corresponding to conventional antiferromagnetic behavior. In all other cases, the symmetry of the altermagnetic order is reduced, leading to modified spin splitting. Remarkably, we discover a thin-film geometry of a $g$-wave altermagnet with a particular surface orientation that enables a $d$-wave spin splitting, which is commonly accompanied by the spin-splitter effect, suggesting the functionalization of non-$d$-wave altermagnets by surfaces. Our findings demonstrate that symmetry breaking at surfaces and in thin films fundamentally reshapes altermagnetic spin textures, providing a tunable platform for controlling spin-dependent electronic phenomena.

We present a first-principles study of the natural optical activity of the gyroelectric Pb$_5$Ge$_3$O$_{11}$ crystal, explicitly accounting for spin-orbit coupling (SOC) effects. We derive a new analytical expression for the gyration coefficients within the recent framework of long-wavelength density-functional perturbation theory [Phys. Rev. Lett. \textbf{131}, 086902 (2023)], which significantly improves computational efficiency by reducing the number of required response functions and includes spin-orbit coupling effects. We use this implementation to investigate the evolution of Pb$_5$Ge$_3$O$_{11}$'s optical rotation across the ferroelectric double-well, from the paraelectric $P\bar{6}$ phase to the ferroelectric $P3$ phase. Our results demonstrate that, in addition to the substantial renormalization of the double-well energy, spin-orbit coupling contributions play an equally crucial role in the natural optical activity, largely through purely electronic contributions, while SOC-induced structural relaxation effects are minor.

We report an experimental investigation of the magnetic microstructure of iron oxide multicore assemblies by means of polarized small-angle neutron scattering (SANS). Guided by a recently developed analytical theory for vortex-state magnetic nanoparticles, we provide a quantitative comparison between the measured and calculated cross sections, revealing signatures that are consistent with vortex-type magnetization configurations at low applied magnetic fields. In particular, the field evolution and the characteristic isotropic ring-type feature of the spin-flip scattering intensity at intermediate momentum transfers are in line with the formation of flux-closure states. The latter are stabilized by the interplay of exchange, Zeeman, and magnetostatic energies. The methodology allows for a statistically significant characterization of vortex states in densely packed nanoparticle systems, thereby complementing surface-sensitive techniques that are commonly limited to the observation of spin structures in individual particles.

Thermally driven quantum-orders observed in exceptional instances may redefine the role of thermal-fluctuation from a source of decoherence to a resource for coherent-state engineering. While preliminary signs of counterintuitive temperature-rise-triggered superconductivity manifested in CeCu2Si2, ErRh4B4, Ho1.2Mo6S8 and (La,Ce)Al2, their critical-temperatures (Tc-inv) remain below Kelvin-range, precluding substantial applications. Here, we report field-modulated inverse-superconducting-transitions above 4He-cooling-limit in Eu-based infinite-layer nickelates (EuxNd1-xNiO2 and EuxPr1-xNiO2) grown on a substrate under both overdoped and underdoped regimes. Paradigmatically, superconductivity with zero-resistance is confined between Tc-inv (2.6-5.4 K) and another higher normal-Tc, rising and decreasing with applied magnetic-field, respectively. Starting from the resistive-state below Tc-inv, the inverse-superconducting-transition is driven by not only temperature-rising, but also current-density, while superconductivity further vanishes at higher temperature and current thresholds. The Kelvin-range inverse superconducting transition is plausibly explained by temperature-induced alternating dominance of effective magnetic-fields arising from Eu2+4f7 related compensations relative to the upper-critical-field. Furthermore, an extended-phenomenological-framework is also supported by reemerged superconductivity below 300 mK under magnetic-field, giving rise to an unprecedented temperature-induced reentrant superconductivity. Our findings establish magnetic-interaction-reconfigured high-Tc systems as fertile platforms for exploring quantum phenomena that reverse thermal-decoherence paradigm, also enabling antithetical-designs to unlock untapped application-scenarios for quantum-phase-transition devices.

Recent tunneling measurements on $β$-PdBi$_2$ reported a magnetic field induced phase transition from a fully gapped to a nodal superconducting state. We develop a microscopic theory of superconductivity in this multi-band material, taking into account spin-orbit coupling and Zeeman splitting. We show that there are two attractive pairing channels in this system: an s-wave and a p-wave. At zero magnetic field, s-wave superconductivity wins. At a finite field, this channel becomes less favorable because Fermi surfaces split, and the gap symmetry changes to p-wave. We show that at a higher field, the excitation spectrum of a p-wave multi-band superconductor becomes gapless, with nodal points located in between the split Fermi surfaces. We argue that this behavior accounts for the experimentally observed field-induced nodal superconductivity in $β$-PdBi$_2$.

Moiré multi-layers of transition metal dichalcogenides have been shown to exhibit optical responses that are endowed with a richness that is absent in single monolayers. Much of this can be attributed to the Moiré superlattice that modulates the electronic landscape of these heterostructures. Strongly coupled layer-hybridized excitons in $\text{MoSe}_2 / \text{WS}_2$ heterobilayers have been shown to exhibit enhanced optical nonlinearities. In this work we strongly couple layer hybridized excitons and trions in n-doped $\text{MoSe}_2 / \text{WS}_2$ heterobilayers inside an optical microcavity. We find that the additional Lindhard screening from dopant electrons and the formation of trions result in a strikingly non-monotonic nonlinear response. The absence of electron capture in the Moiré superlattice plays a crucial role, promising very large second-order nonlinearities. In this work, trion polaritons manifest as high velocity hot polaritons, reaching nominal diffusion lengths approaching 100 microns.

Cryogenic hydrogen isotope fuel layers with high structural integrity and atomic-scale smoothness are prerequisites for symmetric implosion and ignition in inertial confinement fusion (ICF). Using deuterium (D$_2$) as model fuel, we perform large-scale molecular dynamics simulations with a Feynman-Hibbs corrected Silvera-Goldman potential to describe nuclear quantum effects at low temperatures, systematically investigating D$_2$ crystallization inside spherical ablator capsules. By varying substrate lattice constant from 3.1 angstrom to 3.9 angstrom, we demonstrate that lattice matching dictates the transition from coherent epitaxial growth to polycrystalline formation, establishing it as the primary design principle for high-performance targets. When the substrate lattice closely matches the equilibrium hexagonal-close-packed (HCP) spacing of cryogenic D$_2$ (approximately 3.5 angstrom), D$_2$ forms coherent layer-by-layer epitaxial growth consistent with Ostwald's stepwise nucleation theory, yielding HCP-dominated near-single crystals with minimal dislocations and ultra-smooth inner surfaces. In contrast, large lattice mismatch destabilizes coherent growth and causes island-like growth, producing polycrystalline structures with mixed HCP/FCC phases, elevated defects, and greatly increased surface roughness. Radial stress analysis shows that interfacial stress from mismatch localizes within 2-3 molecular layers near the interface, triggering subsequent defect-mediated growth. These findings highlight substrate lattice matching in regulating confined solid growth and crystallization quality, establish it as a key principle for ablator inner-surface engineering in ICF cryogenic targets, and offer atomic guidance for growing high-quality single-crystal deuterium-tritium (DT) fuel layers with optimal smoothness.

We demonstrate that assimilating Neural Network (NN)-predicted surface nitrate leads to a major improvement in phytoplankton short-range (1-5 day) dynamical model forecasts for the North-West European Shelf (NWES) seas. We show that assimilation of only ocean color chlorophyll-$a$ in the current Met Office NWES operational system can lead to excess surface nitrate concentrations in the post-Spring bloom period and these are a major reason behind some known, fast-growing biases in NWES phytoplankton forecasts during late Spring and Summer. Assimilating observations of nitrate would potentially help address this, but NWES nitrate data are typically not available in sufficient abundance to be effectively assimilated. We have therefore used a recently developed and validated neural network (NN) model predicting surface nitrate concentrations from a range of observable variables and assimilated the NN-predicted nitrate within a research and development version of the Met Office's NWES operational forecasting system. As a result of nitrate assimilation the phytoplankton 5-day forecast skill improves by up to 30%. We show that although much of this improvement can be achieved by using a weekly nitrate climatology predicted by the NN model, there is a clear advantage in using flow-dependent nitrate data. We discuss the impacts of this improvement on a range of additional eutrophication indicators, such as dissolved inorganic phosphorus and sea bottom oxygen. We argue that it should be feasible to upgrade this approach to a fully hybrid machine learning - data assimilation within the near-real time NWES operational forecasting system.

Identifying Pareto optimal solutions is critical to support multi-objective decision-making. We introduce the first anytime Multi-Objective Multi-Armed Bandit algorithm for the Pareto Set Identification problem, taking a Bayesian approach: Top-Two Pareto Front Thompson Sampling (TTPFTS). We benchmark TTPFTS against state-of-the-art fixed-budget Pareto Set Identification algorithms on synthetic environments. Next, we demonstrate its practical utility in a challenging multi-objective molecular discovery setting by efficiently exploring an ultra-large synthesis-on-demand molecular library. Furthermore, we introduce a novel uncertainty quantification metric that estimates our algorithm's confidence in the predicted Pareto set. We demonstrate that this metric effectively proxies true performance, yielding a robust methodology for monitoring learning progress in complex settings. Finally, we complement these empirical findings with a theoretical proof of the algorithm's asymptotic correctness.