AI for Science

We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a direct numerical reconstruction method for the Radon transform of $q$, which can then be inverted using standard X-ray tomography techniques to determine $q$. Our implementation introduces a spectral regularization procedure to stabilize the numerical differentiation step required in the reconstruction, improving robustness with respect to noise in the boundary data. We give rigorous justification and optimal stability estimates for the regularized spectral differentiation of noisy measurements, which may be of independent interest. Numerical experiments demonstrate the feasibility of recovering potentials from boundary measurements of nonlinear waves and illustrate the advantages of the Radon-based reconstruction.

Granular creep is the slow, sub-yield movement of constituents in a granular packing due to the disordered nature of its grain-scale interactions. Despite the ubiquity of creep in disordered materials, it is still not understood how to best predict the creep-to-failure regime based on the forces and interactions among constituents. To address this gap, we perform experiments to explore creep and failure in quasi two-dimensional piles of photoelastic disks, allowing the quantification of both grain movements and grain-scale contact force networks. Through controlled external disturbances, we investigate the emergence and evolution of grain rearrangements, force networks, and voids to illuminate signatures of creep and failure. Surprisingly, the force chain structure remains dynamic even in the absence of observable particle motion. We find that shifts in force chains provide an indication to larger, avalanche-scale disruptions. We connect these force signatures with the geometry of the voids in the pile. Overall, our novel experiments and analyses deepen our mechanical and geometric understanding of the creep-to-failure transition in granular systems.

The emergence of neutral collective modes is a hallmark of correlated quantum phases but is often challenging to probe experimentally. In two-dimensional flatband systems, charge responses have been intensively investigated yet neutral excitations remain largely unexplored. In particular, intervalley coherent state (IVC) features a neutral Goldstone mode due to spontaneously broken valley U(1) symmetry. While IVC state has been proposed as a unifying theme across graphene and semiconductor based systems, its defining feature, the neutral Goldstone mode, remains elusive in experiment. Here we investigate space and time resolved transport of neutral modes in twisted WSe2 moire superlattices through a novel ultrafast imaging technique. We uncover two new propagating collective modes with very different velocities, which emerge near the van Hove singularity (VHS) in both intermediate (3.5 to 4 degree) and large (around 5 degree) angle twisted WSe2. The fast-propagating mode has a large speed of about 3 km/s and is consistent with a Goldstone mode for an IVC state, while the slow-moving mode is likely a gapped amplitude mode. They can be understood as the spin-valley analogues of collective modes of a superfluid, whose propagation is imaged for the first time in a condensed matter system. Our study demonstrates a powerful new approach for probing charge-neutral modes in quantum materials and offers key insights into the interplay between charge and spin-valley physics in moire superlattices.

The Doyle-Fuller-Newman (DFN) model resolves internal electrochemical states in lithium-ion batteries with high fidelity. However, the numerical solution of its governing equations is computationally prohibitive for real-time deployment, limiting scalability from individual cells to pack and fleet-scale applications. While machine learning surrogates can substantially reduce inference latency through GPU acceleration, most existing approaches learn solution approximations tied to specific operating conditions rather than learning generalizable state-evolution dynamics. This work presents a systematic comparison of four neural network architectures (MLP, ResNet, U-Net, FNO) formulated as autoregressive state-transition operators that predict full DFN internal states across a wide range of operating conditions. To ensure a controlled architectural comparison, all models are trained under a unified framework using multi-step unrolling and current-conditioning, isolating the impact of spatial inductive bias. Results demonstrate that the U-Net's multi-scale feature hierarchy achieves a mean final-step nRMSE of 3% averaged across all internal state variables after 300-step autoregressive rollouts, while providing a 5.38x speed-up over the numerical solver. These findings highlight spatial inductive bias as a critical determinant of surrogate performance, advancing the development of surrogates for internal state observability for next-generation battery management systems and digital twins.

Long-span roadway bridges exhibit highly localized structural responses under vehicular loading, making repeated FE analysis computationally expensive for applications such as influence surface generation and structural digital twins. Existing SciML approaches struggle to accurately capture these localized responses. To address this challenge, this study proposes an adaptive-trunk DeepONet for localized structural response prediction in large-scale bridge systems. The framework dynamically constructs a load-dependent learning domain using a KNN strategy, allowing the network to focus on structural influence zones. The trunk network is further enhanced using distance-aware features that encode the geometric relationship between the load and structural nodes. A physics-based full-field reconstruction is incorporated through a stiffness-informed Schur complement formulation, enabling predictions at adaptive nodes to be extended to the entire structural domain. To enable scalable training, response data are generated using a reduced-order equivalent shell model that preserves the dominant global behavior while significantly reducing computational cost. The proposed framework is validated on both a benchmark bridge model and the real-world Mussafah Bridge. Results show that the method achieves FEM-level accuracy with relative errors below 5%, while reducing the total response evaluation time (including full-field reconstruction) by approximately 60x; excluding the post-processing reconstruction step, the AD-DeepONet inference is up to four orders of magnitude faster than FEM. In addition, the framework enables rapid generation of full-field responses, influence lines, and influence surfaces under arbitrary vehicular loading configurations, demonstrating strong potential for large-scale bridge analysis and digital twin applications.

WepresentatwolevelSchwarzmethodasanalternativetoAlgebraicMultigridmethod(AMG) used as the last level (coarse) solver of the p-multigrid pMG preconditioner for pressure Poission equation resulting from Spectral/Finite element descretization of incompressible Navier-Stokes eqaution. Proposed Schwarz method consits of a local problem in the original pMG coarse space and a global coarse problem. Main contribution of the paper is a novel, structured and a non-nested coarse space for the global coarse problem. Structured nature of the proposed global coarse space enable communication-free interpolation between the original p-multgrid coarse space and the global coarse problem. We demonstrate the effectiveness of the proposed method compared to the state of the art AMG solver BoomerAMG by a series of experiments performed using Nek5000/RS, a suite of highly scalable incompressible Navier-Stokes solvers, on Summit/Frontier supercomputers at Oak Ridge Leadership Computing Facility.

We introduce the Frontier decoder, a pruned dynamic-programming decoder for sparse quantum decoding problems. Frontier processes error variables in a chosen order, merges prefixes with the same residual syndrome and logical label, and approximates logical-coset posterior masses by retaining only a narrow scored frontier. Without pruning, the recursion is exact ordered inference with exponential complexity. In the code-capacity setting, the decoder reaches thresholds close to optimal for the surface code and the color code. In the circuit-level noise model, it achieves state-of-the-art performance with a very small average retained list size: less than 100 for the gross code $[[144,12,12]]$ at a physical error rate of $0.001$. When the list size is constant, the decoder has linear complexity, suggesting the possibility of low-latency implementations.

In this article we revisit regularity results for eigenfunctions in the discrete spectrum of the electronic Schrödinger equation and study their consequences for approximation complexity. In particular, for the convergence to the complete basis set limit, it can be shown that the curse of dimensionality in the leading algebraic exponent can be mitigated. That is, for general sparse grid constructions, the main term of the convergence rate with respect to the number of degrees of freedom is independent of the number of electrons. These insights indicate potential benefits for classical numerical solvers of the electronic Schrödinger equation and also for quantum-computing approaches through new qubit-efficient wavefunction encodings.

Reliable quantum control in the presence of decoherence requires policies that combat the effect of environmental noise on the controlled dynamics. Open quantum systems under continuous monitoring generate classical measurement records whose drift depends on the noise experienced by the system; the records of two evolutions sharing the same decoherence channels differ only in this drift, so Girsanov's theorem yields a closed-form, differentiable estimator of the KL divergence between their trajectory distributions. We instantiate this estimator with two physically motivated reference measures, yielding two regularizers that both drive the system toward states where the effects of decoherence are minimal: the Wiener KL (KL_W), which is empirically more effective under certain conditions on the noise model, and the drift-variance regularizer (R_DV), which works for all noise models. Both are qualitatively distinct from existing penalties on control fluence or smoothness: they penalize the observable consequences of control on the decoherence channels rather than the control amplitude itself. The regularizers outperform unregularized gradient-based and reinforcement-learning baselines across a range of open quantum systems -- including single- and multi-qubit benchmarks and a multi-qubit chain calibrated to a published snapshot of the IBM Kingston processor -- along several axes of evaluation: final-state fidelity, robustness to mismatch in the assumed noise model (gains grow from +17 pp at training noise to +27 pp under 2.5x noise mismatch), and occupation of forbidden states. The regularizers reduce infidelity by up to 50%, with ~16% gains on the calibrated IBM Kingston chain.

Mathematicians understand a PDE solution through mathematical structures rather than tables of computed values. Historically, this has been the product of mathematical analysis, carried out by hand for each problem individually. Neither numerical simulation nor neural networks produce those structures directly. We propose Agentic Symbolic Search (ASYS), a prior-guided framework in which an agent translates PDE theory, public problem constraints, and accumulated search experience into testable differentiable symbolic programs. The mathematical forms are refined under evolutionary search, while their continuous parameters are fit by gradient-based optimization. This makes the search an automated form of inductive-bias injection rather than blind symbolic regression. For problems with known analytical forms, ASYS recovers these forms naturally; for other problems, ASYS constructs analytical approximations which can guide mathematicians toward further analysis. In our experiments, across five problems spanning bounded dynamics, finite-time blow-up, and free-boundary focusing, ASYS produces interpretable representations, including a geometric interface formula for Allen-Cahn 2D dynamics and a nine-parameter contraction law for Keller-Segel chemotactic blow-up, in settings where no closed-form description was previously available. ASYS shows the possibility of a new paradigm for characterizing PDE solutions, beyond handcrafted analytical solutions, mesh-based numerical solutions, and neural network approximations.

The sub-Ohmic spin-boson model exhibits three distinct dynamical regimes in its spin population dynamics, classified as coherent, incoherent, and pseudo-coherent. Whether these regimes correspond to distinct spin-bath entanglement structures remains an open question. Here we address this using tree tensor network states with projector-splitting time evolution (TTN-TDVP-PS), scanning a broad grid in the sub-Ohmic $(s, α)$ plane. We find that the spin entanglement entropy $S_\mathrm{spin}(t)$ reaches a stationary plateau on a timescale shorter than the polarization relaxation, enabling construction of a stationary entropy landscape from the stationary value $S_\mathrm{stable}$. Within this scalar entropy landscape, the entropy ridge broadly follows the population-based phase boundary at small $s$, but does not reproduce the two-branch structure at large $s$. The ridge remains single-valued within the incoherent region rather than separately tracking both population-based transitions. The Bloch-sphere representation provides a geometric interpretation of this behavior. The entropy plateau corresponds to trajectories settling onto constant-radius shells, with the ridge marking the parameters of smallest stationary Bloch radius. Mode-resolved bath entanglement shows that low-frequency modes dominate the environmental entropy scale and that coherent dynamics enhance bath-mode correlations beyond direct spin--mode correlations. These results establish the stationary spin entanglement entropy as a physically informative observable that complements population-based classifications of dissipative quantum dynamics.

High-quality single-photon sources, realized through saturable emitters, photon blockade, or heralded pair generation, are indispensable building blocks for photonic quantum platforms. Although these mechanisms suppress multiphoton emission through distinct principles typically captured by analytical models, their practical implementation is constrained by conflicting requirements for purity, brightness, and indistinguishability, which must be balanced within high-dimensional design landscapes. Here, we propose a computational framework for optimizing competing metrics of single-photon sources. Building on a Liouville-space adjoint formulation that efficiently evaluates multiple objectives in Markovian open quantum systems, we develop a Jacobian-based update, which ensures first-order monotonic reduction of multi-objective costs. By incorporating simulated annealing to escape gradient-vanishing plateaus, our framework achieves a design success rate of nearly 60 % for photon blockade with g2(0) smaller than 0.1 and theoretically bounded brightness across a broad parameter space, without any analytical guidance. This framework provides a general recipe for multi-objective design of open quantum systems.

We introduce SEA-PINN, a novel architecture that incorporates a Squeeze-Excitation-like attention mechanism into physics-informed neural networks to dynamically recalibrate the importance of neurons across layers. A key feature of SEA-PINN is its highly stable initialization. On 17 out of 20 benchmark problems, SEA-PINN exhibit nearly negligible variance and significantly reduced initial loss, establishing a quasi-deterministic and favorable starting point for optimization. Notably, without employing Fourier feature embeddings or periodic activation functions, SEA-PINN attained competitive accuracy (83\% vs. 90\% improvement relative to FNN-PINN on the high-frequency case 7) as compared with TSA-PINN-a model specifically engineered for high-frequency problems via learnable frequencies in sinusoidal activations. Furthermore, integrating SEA-PINN into TSA-PINN boosted performance by 42.49\%. These results underscore SEA-PINN as a lightweight plug-in module that enhances nonlinear representation power, promotes more robust and efficient convergence, and strengthens the overall reliability of physics-informed learning.

Squeezed vacuum lets gravitational-wave detectors and other quantum sensors surpass the standard quantum limit, and is optimal in the loss-limited regime; phase noise breaks this optimality. Numerically optimizing the quantum Fisher information across the loss and phase-noise landscape, we identify non-Gaussian states that outperform any Gaussian state. These fall into three classes: Fock-like, cubic-phase-like, and states with discrete rotational symmetry. Limiting the average number of photons in the input state to $\bar{n}=5$, with $1-η= 5\%$ photon loss and 200 mrad phase noise, the non-Gaussian advantage reaches up to 2.2 dB. Furthermore, we observe that the non-Gaussian advantage can persist even when the measurement strategy is homodyne detection.

In this work, we develop a state estimation framework for two-dimensional Rayleigh-Bénard (RB) convection that combines a stable Galerkin reduced-order model (ROM) with an extended Kalman filter (EKF). The ROM, constructed from controllability modes of the linearised Boussinesq equations, provides the nonlinear dynamical model for the filter prediction step. Direct numerical simulations (DNS) are used to generate synthetic measurements for data assimilation. We assess filter performance across periodic, quasiperiodic, and chaotic regimes, demonstrating that the filter tracks the most energetic modes with high fidelity and achieves time-averaged reconstruction errors below $14\%$ for velocity and $9\%$ for temperature. We apply the ROM-based EKF to a hybrid simulation scenario where the system state is assimilated from coarse PIV-like velocity measurements. It is shown that velocity observations alone suffice to reconstruct the state, including the temperature field. Finally, we exploit the Kalman gain matrix to develop a greedy sensor placement strategy that progressively removes the least informative sensors. The algorithm reveals a clear hierarchy among sensor types and can be used to derive skeletal observation configurations. It also provides guidance on which measurement variables and spatial locations are most informative for state correction. The present framework is general, and may be applied to other quadratic Galerkin ROMs for state estimation.

We analyze planar Lagrangian transport and scalar-gradient organization in a supersonic, reacting hydrogen-air temporal mixing layer using time-resolved mid-plane data from a three-dimensional direct numerical simulation. The analysis combines forward/backward finite-time Lyapunov exponent (FTLE) fields, operational FTLE-ridge skeletons, Cauchy-Green deformation measures, shear-LCS metrics, and planar hyperbolic geodesic-LCS extraction to examine how finite-time stretching structures the reacting shear layer. The time-resolved FTLE ridges identify repelling and attracting finite-time transport skeletons in the constrained two-dimensional slice, from which ridge geometry, intersection occupancy, persistence, and scalar-conditioned transport are quantified. Hyperbolic geodesic LCS are extracted from Cauchy-Green tensors reconstructed from planar flow maps as strainlines seeded at high-$λ_{\max}$ normal maxima, providing a variational counterpart to the operational FTLE-ridge skeleton. We then relate the transport skeleton to temperature, mixture fraction, and a reaction intermediate. The results show localized forward/backward ridge overlap, strong scalar-gradient enrichment, finite-time geodesic LCS that occupy the same high-strain transport skeleton, residual direction-dependent separation from a time- and cross-stream-stratified null model, and scalar-response lags that remain compact relative to decorrelation and FTLE-integration scales. Together, these results provide a transport-oriented characterization of coherent structures and their role in mid-plane mixing within a compressible reacting shear flow.

Laser wakefield accelerators (LWFAs) provide extremely large accelerating gradients for compact electron accelerators and photon sources but are limited by dephasing, where trapped electrons outrun the accelerating phase of the wakefield. Flying-focus pulses can eliminate dephasing by driving a wake at the vacuum speed of light, but these pulses involve tradeoffs such as varying spot size, long duration, or large plasma volume. Here we show that a spatiotemporally structured laser pulse propagating in a plasma waveguide can drive a wakefield at the vacuum speed of light while maintaining a constant spot size and ultrashort duration. The pulse is formed by superposing plasma-waveguide modes with appropriately selected frequencies. Compared with flying-focus approaches, the waveguide substantially reduces the required plasma volume. Scaling laws and quasi-3D particle-in-cell simulations show that the single-stage energy gain increases linearly with the number of modes used to construct the pulse, enabling larger energy gains or shorter stages than standard LWFA.

The accurate prediction of laminar-to-turbulent transition is critical for the design of aerodynamic and turbomachinery systems, yet widely used experimental benchmarks, such as the ERCOFTAC T3 series, lack the full-field, three-dimensional, and time-resolved data required for modern model development. To address these limitations, this study presents a high-fidelity numerical database of bypass transition in boundary layers, generated using wall-resolved implicit Large Eddy Simulations (iLES) to rigorously mimic the ERCOFTAC T3 flat-plate experiments. Computations are performed using a high-order compressible Navier-Stokes solver across multiple configurations, encompassing a range of freestream turbulence intensities and both zero and varying pressure gradients. The numerical results demonstrate satisfactory agreement with legacy experimental data for skin friction, mean velocity, and fluctuation profiles. Finally, the resulting database is utilized to evaluate the predictive capabilities of standard Reynolds-Averaged Navier-Stokes (RANS) transition models (SA-BCM and $k-ω-γ$), revealing systemic flaws in predicting transition onset and length. This highlights the dataset's value as a foundational resource for the calibration, assessment, and development of next-generation, physics-informed machine learning transition closures.

We demonstrate that caustic microlensing occurring in a liquid jet efficiently drives linear, nonlinear, and high-energy-density phenomena. In the linear regime, caustics provide localized focusing, distinct from external high-NA optics. In the nonlinear regime, they enhance the input field at the liquid-air interface and boost surface-sensitive processes. In the high-energy-density domain, caustic-driven localized laser absorption generates gigapascal shocks using microjoule femtosecond pulses, with scalability up to repetition rates of 0.2 MHz. Caustic-driven fluidic microlensing offers opportunities for surface nonlinear optics, ultrafast science, and high-energy-density physics.

Modern stellarators are typically designed by optimizing the shape of the plasma boundary surface, with the parameters taken to be Fourier amplitudes. Many promising optimization algorithms such as Bayesian methods require bound constraints on the parameters and are most efficient when each parameter is scaled similarly to the others. With the typical Fourier parameterization, it is unclear how to set these bounds: wide constraints lead to self-intersecting boundaries and frequent failures of the MHD equilibrium calculation, while tight bound constraints limit expressiveness. To address these issues, here we propose two new parameter spaces for stellarator optimization. Both begin with a dataset of existing stellarator boundaries. In the first approach, a quantile transformation is applied to each Fourier degree of freedom, mapping the data distribution to a uniform distribution on the unit interval. In the second approach, principal component analysis (PCA) is applied to points on the boundaries, followed by a quantile transformation. For both approaches, the transformed variables become the degrees of freedom, naturally bounded to [0, 1]. The PCA method has the additional benefit of dimensionality reduction, with high expressiveness for a small number of parameters. The methods are demonstrated via Bayesian optimization for good alpha-particle confinement with guiding-center tracing inside the optimization loop, using asynchronous parallelization. These optimizations yield stellarator configurations with excellent fast-particle confinement in fields that can be far from quasisymmetric or quasi-isodynamic.

Rydberg atom simulators, in both analog and digital modes, have attracted significant recent interest due to their versatile geometric reconfigurability. In this work, leveraging this feature, we propose two complementary approaches, one for each mode, to characterize emergent fermions in critical quantum many-body systems. In the analog mode, we assemble the Rydberg atoms in a "developable" (namely, preserving local couplings) Möbius band geometry to realize antiperiodic boundary conditions, where fermionic states reside. Spectroscopic measurement in this sector then reveals universal energy ratios of the bosonic and fermionic states. In the digital mode, we carry out a fermionic version of Kibble-Zurek ramping with a quantum circuit, directly addressing the fermionic scaling form. Reconfigurability allows an exponential speed-up of this task, with an $O(\log L\log\log L)$ circuit-depth overhead. Our work establishes the Rydberg atom simulator as a uniquely powerful platform to attack the notoriously difficult issue of experimentally probing emergent fermions that are nonlocally defined in a bosonic system.

Quantum quenches drive edge states far from equilibrium, yet whether the memory of a topological initial state survives in a non-integrable, interacting system has remained largely unexplored. We study this question in the bond-alternating XXZ chain -- an interacting Su--Schrieffer--Heeger model hosting symmetry-protected topological edge modes with markedly enhanced boundary magnetization -- and analyze quenches across all combinations of single-particle and many-body initial and final Hamiltonians. The results organize by a single distinction as we rigorously establish in this work: whether the post-quench Hamiltonian is free or genuinely interacting. For a free post-quench Hamiltonian, the dynamics is solved exactly by a correlation-matrix approach; the boundary-mode return amplitude decays as $t^{-3/2}$, and initial interactions enter only through a dressed one-body density matrix. For a genuinely interacting post-quench Hamiltonian, finite-time stability bounds prove that away from local resonances the first-dimer magnetization remains stable on time windows growing as arbitrarily large powers of the inverse inter-dimer coupling. Matrix product state simulations across all four protocols show that interactions in the final Hamiltonian markedly extend finite-time boundary memory -- with local suppression near the isotropic $SU(2)$ point -- revealing a many-body protection mechanism in a non-integrable system where scrambling would otherwise wash out initial-state memory fast.

We present the exceptional phenomenon of complete absence of Anderson localization, and perfect transmission of particles, in a completely disordered diamond-dot chain. We analytically show a proof for the condition to observe this exceptional phenomenon, based on a transparent window emerging from a geometrical condition. We support our theoretical prediction by numerical simulations and direct experimental observation of the transmission probabilities of the light in a femtosecond laser-written diamond-dot photonic lattices. We additionally show that for a $π$ effective magnetic flux, extreme localization of the light in the same system may occur, independently on the specific geometry. Our results open up an excellent platform for controlling the transmission of energy from ballistic to zero transmission, in a completely disordered lattice system..

Foliated topological orders in three dimensions are layered systems in which anyons are free to move within a layer but cannot hop between them. A simple model with such a phase is a stack of decoupled two-dimensional electron gases in a strong magnetic field, each in the same fractional quantum Hall state. By focusing on the case of filling $ν=1/3$ of the lowest Landau level in each layer, we show that (i) the limit of decoupled Laughlin states is stable upon introducing interlayer interactions and (ii) the system can enter a spontaneously layer-trimerized foliated non-Abelian Fibonacci phase. We support our claims by numerical exact diagonalization of up to 10 layers as well as perturbative analytical calculations. Specifically, we show that the foliated Fibonacci phase exists in the 9-layer system with pseudopotential interactions within and between neighboring layers. We identify the phase via quasihole counting and by calculating the overlap with a model wave function which we derive from the associated conformal field theory. Our numerical results suggest the possibility of realizing these phases in layered van der Waals crystals in strong magnetic fields, as well as in multilayer heterostructures.

Tomography allows one to estimate the density matrix describing the state an ensemble of quantum systems are prepared in (for example, polarization tomography determines the polarization state of a beam of identically prepared photons). In general, it is not possible to uniquely decompose the density matrix into its pure state components. Agarwal et al. proposed a protocol which, for a mixture composed of any two pure states of a qubit (with arbitrary probabilities), allows an observer to infer not only the density matrix but the identity of those specific pure states and their weights - the additional requirement being that the qubits arrive in pairs, where both qubits in each pair are in the same state. We experimentally demonstrate this learning-from-pairs concept using photons in the polarization degree of freedom. We use tomography to measure a sequence of single photons and make use of their time-of-arrival information to 'pair up' the photons after the measurement. From here we are able to infer the photons' polarization states and their respective probabilities, and we demonstrate this for various different choices of polarization states and ratios. Finally, we investigate our ability to discriminate between two equal mixtures of distinct pairs of orthogonal polarization states. We find that on the order of approx. 10e4 photons is typically enough to achieve tomography fidelities of approximately 0.9999. This is sufficient to discriminate between two different preparations of the same mixed state, differing by angles of less than 5 degrees between the pure states used in the two preparations.

We investigate the propagation profile of positive solutions to \begin{equation*} u_t-du_{xx}=f(t,u) \mbox{ for } t>0,\ x\in(g(t),h(t)), \end{equation*} where $f(t,u)$ is monostable in $u$ and $T$-periodic in $t$, and the free boundaries $x=g(t), \ x=h(t)$ are determined by the Stefan condition $g'(t)=-μu_x(t, g(t)),\ h'(t)=-μu_x(t,h(t))$, coupled with $u(t, g(t))=u(t, h(t))=0$. For a special nonlinearity satisfying the strong KPP condition, the long-time behavior and asymptotic spreading speed of this problem were considered by Du, Guo and Peng \cite{DGP}. In this paper, by employing new techniques, we extend the results of \cite{DGP} to general monostable nonlinearities beyond the KPP framework and at the same time we obtain more precise description of the propagation profile: we prove the existence and uniqueness of a semi-wave and show that the spreading solution converges to this semi-wave as time goes to infinity.

For nearly a century, the transition state has been thought to lack an exact quantum counterpart: recrossing-free, one-way flux seems to require simultaneous knowledge of position and momentum. We show that this obstruction is illusory. The exact quantum flow contains a transition-state geometry: stable and unstable manifolds meeting in a unique bounded quantum transition-state trajectory that anchors a dividing surface carrying one-way quantum probability flux. The geometric framework of classical reaction dynamics survives in exact quantum mechanics, in a fundamentally quantum form.

Virtual accelerators and digital twins are increasingly essential tools for accelerator operations, controls development and verification, and model-based optimization. However, current implementations are often tightly coupled to specific simulation codes, facilities, and applications, resulting in fragmented, ad hoc solutions that are difficult to reuse or extend. To address this, we expand the LUME Python package to include standardized implementation and deployment of virtual accelerators and digital twins across heterogeneous simulation backends and control system interfaces. At the core of this change is the introduction of LUMEModel abstraction, which defines a fixed, simulator-agnostic API and a variable system that encodes metadata such as units and data types/validation. This design enables standardized interaction with physics-based simulators, surrogate models, and differentiable simulations, while supporting both Python-native workflows and IOC-based operation via EPICS using the lume-pva package. Facility- and simulator-specific details are encapsulated through extensible transformer layers, allowing consistent control-system semantics to be mapped onto diverse simulation engines. We describe the LUMEModel architecture, variable system, and package ecosystem, and present representative use cases including model interchangeability, staged and chained simulators, and continuous integration testing. This work will make implementing and using virtual accelerators easier and more flexible.

Rare $α$-particle-induced charge clusters appear in LSST images as compact, PSF-like sources with a median FWHM of $0.\!\!^{\prime\prime}95$ and median ellipticity consistent with zero, closely resembling unresolved astrophysical point sources. These events are detected in both dark and science exposures at a rate of approximately $10^{-12}\ \mathrm{pixel}^{-1}\ \mathrm{s}^{-1}$. Their collected charge and morphology are consistent with energy deposition from $\sim$5 MeV $α$-particles in silicon CCDs, and their spatial distribution across the focal plane suggests a localized material origin, plausibly associated with trace radioactive contamination in the cryostat aluminum. Despite their deceptive appearance, we demonstrate that a simple broadness statistic based on fourth-order moments cleanly separates these events from stellar PSFs, enabling efficient rejection in coadded images and real-time alert streams. Such charge clusters do not impose an intrinsic bright-end contamination floor for Rubin transient searches, as genuine fast astrophysical events would exhibit characteristically different morphological signatures.

An atomic Josephson junction realized with dipolar bosons in a double-well potential can be described by an extended Bose-Hubbard model in which dipolar interactions generate an effective on-site interaction and nearest-neighbor pair tunneling. Using mean-field theory and exact diagonalization, we investigate how this correlated process affects zero-temperature equilibrium and dynamical properties of the system. In equilibrium, we show that pair tunneling induces ground-state parity modulations and significantly reshapes the phase diagram, producing qualitative changes in the quantum phase transitions toward NOON and phase-NOON states, as well as quantitative shifts of the critical points. Out of equilibrium, we demonstrate that it modifies the conditions for macroscopic quantum self-trapping, and assess its impact by comparing mean-field and fully quantum evolution, including the emergence of dynamical quantum phase transitions.