Hydraulic fracture (HF) propagation in naturally fractured formations is strongly influenced by local stress states near pre-existing natural fractures (NFs). The role of NF-induced shear deformation and stress redistribution in controlling HF trajectories remains poorly characterized. This study investigates how NF-induced stress redistribution governs HF-NF interactions through coupled laboratory experiments and poroelastic extended finite element simulations on intact and pre-fractured PMMA specimens under plane-strain conditions. Digital image correlation provides full-field measurements of displacement and strain evolution during mechanical loading and hydraulic fracturing. Under fixed-base, lateral confinement, and vertical compression boundary conditions, inclined NFs induce asymmetric stress redistribution and shear deformation, generating distinct local stress states prior to fluid injection. The results demonstrate that the HF trajectory is governed by the sign and spatial distribution of shear stress and shear strain components generated by NF orientation relative to the far-field maximum principal stress. Shear deformation that promotes compressive stress development adjacent to the NF causes the HF to deflect away, whereas shear deformation that reduces the effective normal stress along the NF promotes fracture attraction and linkage. Corresponding numerical reproduction of HF curvature in pre-fractured specimens requires mixed-mode (Mode I-II) fracture energy release criteria, while the intact specimen propagates in pure Mode I. Overall, the findings reveal a transition from tensile opening to shear-assisted mixed-mode propagation as local stress states evolve due to the presence of NFs, providing a mechanistic basis for predicting and controlling fracture trajectories in subsurface stimulation and storage applications.

The problem of optimal sizing and power scheduling in microgrids subject to uncertainties is well known to the control community. Commonly, the optimal control problem is cast as a mixed-integer program to model the logical constraints arising in energy storage systems, and is then solved approximately using numerical methods such as the scenario approach. In this paper, we propose and compare two formulations of a robust microgrid sizing and power scheduling optimal control problem with logical constraints and uncertainties in the user's power demand, solar power generation, grid electricity prices and battery efficiencies. The first formulation uses binary variables and big-M constraints, leading to a mixed-integer linear program. The second formulation casts the problem as a continuous nonlinear program through an exact smooth reformulation of the logical constraints, consisting of additional modelling variables and non-convex constraints. We then propose a novel local reduction algorithm, extending an existing method, to solve both problems. The two formulations are compared by evaluating the solutions returned by local reduction using 100,000-sample Monte Carlo simulations and achieve promising results, with both averaging feasibility rates above 90%.

Modern Artificial Intelligence (AI) workloads deployed across the heterogeneous tiers of an edge--cloud continuum must satisfy multi-dimensional Service Level Objectives (SLOs) over latency, throughput, and output quality. For each incoming task, the scheduler picks both a target node and a processing mode (e.g., full or reduced inference precision). We call this class of problems \emph{Continuous Multi-Mode Scheduling} (CMMS). Comparing CMMS algorithms fairly is difficult because prior studies typically evaluate each controller in its own stack, under a single workload, and without reporting per-decision overhead. To close these gaps, we present an open source benchmark platform that features (i) a unified controller interface, (ii) a closed-loop workload driver covering multiple workload patterns, and (iii) dual-metric SLO scoring that reports raw SLO (overall compliance) and steady-state SLO (compliance during stable operation) separately. Running six controllers across five cluster configurations and two load regimes (424 episodes), we find that controller rankings are strongly configuration-dependent: a deep reinforcement-learning winner under light workloads loses to a rule-based heuristic by nearly 29 percentage points once load intensifies, at roughly 500$\times$ the per-decision operational overhead. We further show that separating raw from steady-state SLOs exposes switching costs that a single aggregate score would otherwise conflate.

Large language model (LLM) agents increasingly act on a user's behalf -- reading personal files, calling tools, transacting with external services -- possibly leaking personally identifiable information (PII) across trust boundaries at every step. Privacy here is a property not of a single output but of an entire trajectory, and three properties make it hard: leakage is cumulative, as individually innocuous releases accumulate across honest-but-curious or colluding sinks into inferences about a protected secret; bidirectional, as a malicious observation can inject instructions that turn the agent's own reasoning model against the user; and task-dependent, as the same field is necessary for one recipient yet gratuitous for another. Per-release contextual-integrity filters, information-flow controls, and posterior-leakage monitors each address part of this but none controls cumulative, inference-based leakage at runtime. We recast agent privacy as \emph{posterior-risk control} and present OCELOT, a runtime mediator that budgets how much an adversary's belief about a secret may improve across a trajectory, rather than filtering outputs. Its mechanism, \emph{Witness-Verified Declassification}, separates judgment from trust: an untrusted, locally fine-tuned defender model inspects each candidate release and emits structured evidence -- labeled atoms and proposed declassification operators -- which a deterministic verifier audits, charging a certified min-entropy cost for the chosen variant and authorizing the least-disclosing useful release under a sink-trust-weighted budget recorded on a tamper-evident ledger. Across diverse agent benchmarks and recent defenses, OCELOT attains significantly lower leakage at higher task utility, resists adaptive injection, jailbreak, cumulative inference, and sink collusion, and adds only modest overhead.

We consider a movable conducting plate of finite mass, between two fixed ones, whose mechanical degrees of freedom are treated quantum-mechanically and bound to its equilibrium position by a harmonic potential. The movable wall is thus subjected to quantum fluctuations of its position. This creates a system of two sub-cavities separated by the movable fluctuating plate, and two massless one-dimensional scalar fields, one in each sub-cavity. This system is described by an appropriate generalization of the Law Hamiltonian. The presence of the movable wall yields an effective plate-fields interaction, as well as an effective interaction between the field modes. We obtain, at the second order in perturbation theory, the ground state of the interacting system and the reduced density operator of the fields in each sub-cavity by tracing out the wall's degrees of freedom. We calculate the entanglement between two field modes, one in each cavity, by evaluating analytically the negativity; we then evaluate numerically also the total multimode negativity. Our results show that in both cases the fields in the two sub-cavities are entangled, in contrast to the case in which the wall is fixed in space. We discuss the amount of the field entanglement present as a function of relevant physical parameters of the system such as the mass and oscillation frequency of the movable wall, its distance from the fixed walls and the frequencies of the field modes considered.

We develop a large-signal stability analysis for a sampled-data, optimization-based secondary controller for inverter-interfaced distributed energy resources in virtual power plants.

In 1988, Las Vergnas conjectured that if $M$ is a binary matroid with bicycle dimension $d$, then for $0 \leq k \leq d$, the $k$th derivative of the diagonal Tutte polynomial $T(M;z,z)$ evaluated at $z=-1$ is an integer multiple of $2^{d-k}$. While this was rapidly disproved for binary matroids and for graphs in general, extensive computations strongly suggested that it might be true for planar graphs. In this paper we prove that this is indeed the case. To do this, we consider a stronger divisibility property that we call the LV property, and a larger class of graphs, namely the class of delta-wye-reducible graphs. By a detailed analysis of how a delta-wye exchange affects the coefficients of the diagonal Tutte polynomial, we show that delta-wye-reducible graphs have the LV property. That Las Vergnas' conjecture holds for planar graphs immediately follows because planar graphs are delta-wye reducible and the LV property is stronger than Las Vergnas' divisibility conditions.

Expectiles provide a class of asymmetric location functionals that incorporate the magnitude of deviations and admit a natural geometric interpretation. Building on their structural consistency with the convex stochastic order, this paper introduces a family of integrated expectile functionals for measuring risk, dispersion, and inequality. The proposed functionals admit analytical representations as integrals of expectiles across asymmetry levels. For a distinguished subclass of these constructions, a geometric representation is available: the resulting quantities can be expressed as weighted areas of star-shaped sets encoding the distributional asymmetry of a random variable. This approach yields a new class of expectile-based inequality indices, constituting a natural counterpart to classical Gini-type measures while preserving desirable monotonicity and consistency properties. Empirical counterparts are derived in closed form and admit explicit decompositions over finite samples. The framework extends naturally to multivariate settings through directional expectile constructions, leading to measures capable of capturing genuinely joint forms of multivariate dispersion and inequality.

A cyclic meander is an embedded oriented loop in the plane intersecting a fixed infinite line, or circle, transversely in a linearly ordered set of $2n$ points. By keeping track of the order in which the loop visits these points, the cyclic meander induces a cyclic permutation on these marked points. Correspondingly, given a permutation on $n$ letters, one can ask whether or not a cyclic meander induces the permutation in this manner, and if not, what is the most efficient way of doing so if we allow more points of intersection? This process gives a way of associating to a permutation on $n$ letters a measurement of complexity of the permutation in question. The principal result of this work shows that the maximum of this quantity, the \emph{meander number}, over all cyclic permutations on $n$ letters, is bounded above and below quadratically in $n$. This result resolves a conjecture of Schwartz~\cite{richtpss} in relation to his work on the topological salesman problem. We conclude this work by constructing families of cyclic permutations on $n$ letters whose meander numbers realize a continuum of growth rates between linear and quadratic.

The cooling number measures the speed at which a slow-moving influence or contagion spreads on a graph. In this paper, we investigate the cooling number of four classical graph products: the Cartesian product, the strong product, the lexicographic product, and the direct product. We also determine the cooling number of a disconnected graph in terms of the cooling numbers of its components. We conclude with open problems.

STFT-based speech enhancement typically adopts overlapping analysis frames. While overlap is essential for stable STFT processing, it makes adjacent frames highly correlated, causing redundant computation in lightweight models. We propose Half-frame-rate Adaptive Learnable Operator (HALO), a causal plug-in module that halves the internal frame rate without altering the STFT procedure. Broadly applicable to many lightweight models, HALO applies adaptive rate reduction before the backbone and restoration afterward, reconstructing the full-rate spectrum on the original STFT grid. Both reduction and restoration are implemented with lightweight dynamic convolutions. By halving the processed frame rate, HALO reduces backbone compute cost with no added algorithmic latency, freeing budget for channel widening. Experiments on the DNS3 dataset show consistent gains across diverse lightweight models under matched complexity, demonstrating the effectiveness of reducing overlap-induced redundancy.

This note is a tutorial on the deterministic version of the Kalman filter (state estimator), which is formulated as finding the state trajectory consistent with the system's equations with the minimal amount of $L^2$ process and measurement uncertainty. As stated, this is an input signal design problem with linear dynamics and an objective that is affine-quadratic in the state and inputs. The first step is to convert this problem to one with a purely quadratic objective by embedding in a larger system using ``homogeneous coordinates''. This converts the problem to a purely quadratic (i.e. an LQR) problem, but with non-standard initial or final state constraints. This latter problem can then be solved using a version of the matrix Differential Riccati Equation (DRE) for the larger LQR problem. The second step is a partitioning of this larger problem, which then yields the optimal dynamic observer and the DRE of the traditional Kalman filter. For comparison, the solution of the traditional LQ-tracking (Servomechanism) problem is also treated using a similar construction.

Machine learning (ML) of electronic Hamiltonians offers a unified route to electronic wave functions and physical observables. We introduce a Hamiltonian learning framework built on electronic features derived from the superposition-of-atomic-potentials (SAP) approximation, an efficient self-consistent-field initial guess that captures essential electron-electron screening. SAP quantities define a symmetry-adapted intrinsic atomic orbital learning basis and provide physics-informed inputs to an orbital-based graph neural network that predicts converged Kohn-Sham Fock matrices. To extend the approach to larger basis sets, we further develop a downfolding scheme that predicts large-basis electronic structure from minimal-basis features. On the QM9 dataset, the model accurately reproduces frontier and core orbital energies, dipole moments, and the full density of states. For organic charge-transport materials, it yields accurate intermolecular transfer integrals for benzene, tetracyanoquinodimethane (TCNQ), and tetrathiafulvalene (TTF) dimers, and transfers to unseen substituted-benzene heterodimers with a mean absolute error of 4.8 meV. These results establish SAP-based ML of electronic Hamiltonians as a transferable and scalable tool for high-throughput electronic-structure prediction.

In arXiv:2311.10069, Matolcsi et al. show that the fractional chromatic number of the plane is at least 4. Their proof uses a 27-vertex unit-distance graph in the Moser lattice, with geometric fractional chromatic number exactly 4. We show that this bound is tight for graphs in the Moser lattice by exhibiting geometric 4-colorings of the entire lattice. The same colorings also extend to the entire Moser ring.

Economic decisions often depend on many noisy estimates of neighborhood effects, school quality, and hospital performance. Shrinkage estimation can reduce this noise by pooling information across related units. When units are related through geography, adjacency, or shared characteristics, the main challenge is not only how much to shrink, but which relationships should guide pooling. We use Stein's Unbiased Risk Estimate (SURE) to select among and average over flexible shrinkage estimators, allowing researchers to compare candidate definitions of relatedness without treating any one prior, covariance model, or adjacency rule as the true model for the latent parameters. Under regularity conditions stated directly on the estimator maps, SURE selection performs nearly as well as the best rule in a candidate class. The SURE-chosen weighted average likewise performs nearly as well as the best fixed weighted average of trained candidates, including nonlinear shrinkage rules whose fitted values use the full vector of noisy estimates. In an application to Opportunity Atlas economic mobility data from 20 commuting zones, the best individual spatial specification varies across zones, and the SURE-chosen average reduces reported SURE-estimated mean squared error by about 27% relative to the best-performing non-spatial empirical Bayes benchmark.

We realize two-dimensional magnetically-assisted Sisyphus laser cooling of an asymmetric top molecule (ATM), calcium monoamide (CaNH$_2$). Vibrational state closure is achieved with $41.1 \pm 6.3$ photons scatters using optical pumping of the $X[3_1]$ state. Photon-cycling measurements show good agreement with branching ratios determined by dispersed fluorescence spectroscopy. Rotational closure is maintained by driving the $X[1_{11}] \to A [0_{00}]$ transition. The observed absence of additional state leakage channels broadens the scope of molecular laser cooling to include ATMs, which are the most general geometric class of molecules and possess the richest internal structure. Future applications of quantum controlled ATMs include new quantum information platforms and searches for physics beyond the Standard Model.

Kinetic collisionless plasma equations are commonly solved via spectral methods in velocity space. The most commonly used spectral method is based on Hermite polynomials with a Maxwellian weight, as this basis efficiently represents near-Maxwellian distributions with relatively few degrees of freedom. An alternative approach uses Legendre polynomials, which are better suited for resolving strongly non-Maxwellian features. In this paper, we propose a mixed method that combines the Hermite and Legendre expansions. The mixed method is particularly advantageous for problems in which non-Maxwellian features are localized in velocity space, such as beams and plateaus. We demonstrate analytically and numerically that the mixed method conserves total mass, momentum, and energy by imposing certain constraints. The numerical results show that, for the same number of degrees of freedom, the proposed mixed method can achieve improved accuracy in comparison to the individual Hermite or Legendre methods, while maintaining comparable computational cost.

Conventional beamforming techniques primarily steer energy along desired directions or focus it at specific locations. These techniques become fragile when facing frequent blockage and highly dynamic propagation environments. In this article, we present caustic beamforming as a new paradigm for wireless beam control. First, we classify representative caustic beams according to their underlying mathematical origins and present three unique properties, namely self-bending, self-healing, and near-field non-diffracting. Building on these propagation properties, we then propose several application scenarios in sixth-generation (6G) networks. We undertake two case studies focused on physical layer security and service stability that highlight the capability of caustic beams to bypass potential eavesdroppers, deliver more uniform coverage, and sustain blockage-resilient links. We further discuss the enabling hardware architectures that facilitate practical deployments, and finally outline key open challenges regarding caustic beams that require further research.

ShrinkageTrees is an R package for Bayesian tree ensembles in survival analysis and causal inference. The package implements Bayesian additive regression tree models for right- and interval-censored survival outcomes within an accelerated failure time (AFT) framework, with optional decomposition into prognostic and treatment-effect components for causal inference. Two complementary forms of regularisation are available: regularisation of the tree structure, via depth-penalising priors and Dirichlet splitting priors, and regularisation of the step heights, via global-local shrinkage priors. ShrinkageTrees provides the first implementation of the Horseshoe Forest, which places a horseshoe prior on the step heights. These regularisation strategies extend Bayesian tree ensembles to high-dimensional settings. An efficient Rcpp backend, multi-chain MCMC, and S3 methods support the full workflow: fitting, prediction, causal effect estimation, and convergence diagnostics.

This paper extends a previous work in which the rank-2 co-Higgs bundles on a Hopf surface are classified based on the data of the underlying vector bundle. The aim of the paper is to study the Poisson 3-folds that can be constructed from these co-Higgs bundles by describing their symplectic leaves.

This paper presents a theoretical framework for multi-band localization for a single-path single-input multiple-output (SIMO) system. We derive closed-form Cramer-Rao bounds (CRBs) for angle-of-arrival (AoA) and distance for uniform linear arrays (ULAs), and an intermediate matrix-form formulation for arbitrary array shapes. We also develop benchmark single- and multi-band maximum-likelihood (ML) estimators for AoA-Distance, leveraging a structured Levenberg-Marquardt (LM) refinement procedure. A key contribution is an analytical characterization of the threshold SNR (TSNR) for the proposed estimators. This is the SNR threshold at which the estimator transitions from "off the chart" to CRB-approaching performance, for both TDoA and distance estimation. Numerical simulations confirm that the proposed single- and multi-band estimators achieve the CRB at SNRs above the predicted TSNR, and that multi-band processing simultaneously improves estimation accuracy and reduces SNR requirements. The resulting framework provides a rigorous foundation for next-generation multi-band localization and can be readily extended to elevation estimation, distributed arrays, and multi-path environments.

A quantum repeater segment is a basic building block of a quantum repeater, generating buffered entanglement of quantum memories to connect quantum repeater cells. It also enables the connection between quantum computers. In the implementation we present here, photons emitted from two co-trapped free-space coupled $^{40}$Ca$^+$ ions are converted to the telecom-C band and interfered after transmission over 440$\,$m of optical fiber (220$\,$m per arm), where a photonic Bell measurement is performed to create entanglement between the memories. With this scheme we generate an entangled $\left|Ψ^+\right\rangle$ Bell state with $\ge 68(8)\,$% fidelity, highlighting trapped $^{40}$Ca$^+$ ions as a promising quantum repeater hardware platform.

We study the next-to-leading order electroweak corrections to $e^+e^- \rightarrow W^+W^-$ from dimension-six two-fermion top-quark operators in the Standard Model Effective Field Theory. We compute analytical and numerical results for future electron-positron colliders, focusing on the proposed LEP3 and FCC-ee that will operate at centre-of-mass energies below the $t \bar{t}$ production threshold. We compare the indirect sensitivity arising from virtual corrections to $WW$ production to that from $ZH$ production, and to the current constraints from LEP and LHC data. We show that NLO corrections can provide competitive sensitivity to these operators. This work represents a first step towards the systematic computation of electroweak corrections to $W$-pair production at lepton colliders in the SMEFT, whose impact can then be properly assessed in global analyses.

Altermagnetic $α$-MnTe with Néel vector along the $y$-axis exhibits a finite anomalous Hall conductivity (AHC) and weak ferromagnetism along the $z$-axis. As already demonstrated in the bulk, there is the breaking of the C$_6$ symmetry by the in-plane Néel vector, leaving a C$_2$-type magnetic symmetry. The surface of $α$-MnTe breaks the C$_2$, leaving only a time-reversed mirror symmetry with respect to the $x=0$ plane. Therefore, we demonstrate that on the surface, the interplay between breaking of the crystal symmetry and Néel vector orientation produces a reduction of the space group from hexagonal P6$_3$/mmc to orthorhombic Amm2. As a result, the surface exhibits not only a polar distortion along the $z$-axis, but also a polar distortion and a weak ferrimagnetism along the $y$-axis. To describe the surface of MnTe in an accessible way, we simplify the problem and examine the effect of the in-plane electric field in bulk MnTe. Moreover, as a doped ionic semiconductor, the properties of MnTe can be influenced by lattice polarization under an applied electric field. We investigate the interplay between the intrinsic anomalous Hall effect and lattice polarization, showing that polarization effects can substantially affect the AHC. Since the electric field breaks inversion symmetry, this contribution from the lattice polarization coexists with the non-linear anomalous Hall effect, highlighting the rich transport phenomenology of altermagnets.

The standard in Earth-observation tasks today is having near real-time access to surface images in response to changing conditions. For instance, as urban environments interface more with wildlands and wildfires become less predictable, their tracking with satellite resources becomes essential. This requires the coordination of increasingly large constellations of satellites, giving rise to challenging computational problems. With wildfire detection and tracking as a backdrop, we investigate the power of special purpose and novel computing paradigms to tackle the ensuing satellite scheduling problems, making a compelling case for quantum algorithms. We bring quantum scheduling algorithms closer to implementation by examining both the emerging iterative quantum algorithm framework, which comes with analytic guarantees compared to some classical algorithms, and distributed quantum computing methods whose relevance is on the rise as utility-scale problems begin to get solved with quantum computers. Drawing strength from several computing fronts, we develop a distributed/parallelization scheme in conjunction with the quantum algorithm design and apply these techniques to real-world datasets for wildfire detection. While our quantum subprocesses are currently too small to see significant quantum advantage, our results validate the utility of these techniques, and continue forging the path toward distributed quantum computing.

In the Born-Oppenheimer approximation for QCD, the exotic hidden-charm tetraquark meson $χ_{c1}(3872)$ is a near-threshold bound state in Born-Oppenheimer potentials associated with an isospin-0 adjoint meson. The $χ_{c1}(3872)$ is the $1^{++}$ member of a heavy-quark spin-symmetry multiplet whose other members have $J^{PC}$ quantum numbers $0^{++}$, $1^{+-}$, and $2^{++}$. We introduce a simple model for the Born-Oppenheimer potentials that interpolates between the adjoint-meson potential at short distances and the triplet-meson-pair potential at large distances. We take into account the spin splittings of charm mesons nonperturbatively for the first time by solving the diabatic Schrödinger equation. We also take into account the spin splittings of the adjoint meson as well as a narrow avoided crossing with the quarkonium potential. We tune the energy of $χ_{c1}(3872)$ to the $D^* \bar{D}$ threshold and then calculate the spin splittings of the other members of the multiplet and their decay widths into charm-meson pairs. We also calculate the energies and decay widths of the corresponding multiplet of hidden-bottom tetraquarks. These calculations provide a template for the quantitative analysis of all hidden-heavy hadrons using the Born-Oppenheimer approximation for QCD.

Laser-induced forward transfer (LIFT) is a nozzle-free laser-assisted printing method that provides an advanced manufacturing route for spatially selective deposition of functional inks, nanoparticle suspensions, polymers, hydrogels, biological materials, and other difficult-to-nozzle formulations. The apparent simplicity of LIFT, however, conceals a strongly coupled laser-liquid interaction. Laser energy is absorbed within a confined donor architecture, converted into thermal and plasma responses, and then transformed into bubble-mediated motion of the donor material. The cavitation bubble provides the transient mechanical bridge between optical energy deposition and the hydrodynamic ejection process. This chapter presents LIFT from a multiscale perspective centered on bubble dynamics and material ejection. It first reviews major LIFT donor architectures. Then, it examines how donor ribbon design, absorbing-layer properties, laser parameters, material rheology, control bubble inception/growth, jet formation, droplet breakup, and final deposition. Modeling approaches are discussed as tools for connecting experimental observations across time and length scales, ranging from reduced-order estimates to interface-resolving simulations and data-driven process maps. As one illustrative mechanistic example, thermal-only, plasma-mediated, and coupled plasma-thermal-thermoelastic frameworks for early-stage bubble inception are briefly compared to show how different inception assumptions can provide initial conditions for downstream bubble growth and jetting models. This chapter concludes by identifying opportunities for bubble-aware donor design, time-resolved diagnostics, benchmark datasets, and predictive LIFT process maps based on intermediate bubble and jet observables.

Preference learning refers to the learning of latent patterns from ranking and preference data of different kinds. Typical aims of preference learning are to infer a shared consensus ranking, to learn individual-level preferences, and to perform unsupervised clustering. The Mallows model is among the few approaches that can achieve all these objectives jointly. Previous work has developed computationally tractable methods for Bayesian inference based on a MCMC Metropolis-Hastings scheme, where clustering is performed via a finite mixture of Mallows models. Inference on the number of clusters is then conducted a posteriori. Here we propose a Bayesian nonparametric Mallows model, based on a Dirichlet process mixture model. This allows joint inference on the number of non-empty clusters and on the clustering allocation, as well as posterior inference on cluster-specific parameters. The implementation of the proposed sampling algorithm is integrated into the existing R package BayesMallows, which also supports data in the form of incomplete rankings and pairwise comparisons. Simulated data show good performance of the nonparametric model compared to a finite mixture model in terms of recovery of the correct number of clusters, while empirical data on movie ratings show the model's effectiveness in providing personalized movie recommendations on discarded ratings.

The realization of on-chip photonic circuits requires scalable and deterministic single-photon emitters (SPEs) at room temperature, which remain a challenge in van der Waals materials. In this work, we report a novel three-step fabrication process for the generation of spatially controlled SPE arrays in hexagonal boron nitride (hBN). The process comprises site-selective gallium (Ga) focused ion beam milling, nanoscale conformal carbon deposition over the patterned regions, and subsequent thermal annealing. The synergistic combination of these steps resulted in a site-correlated emitter yield of ($\sim 89\%$) across 100 fabrication sites. Second-order autocorrelation measurements revealed pronounced three-level emitter dynamics where the best emitters exhibited high purity ($g^{(2)}(0)=0.15 \pm 0.09$).To the best of our knowledge, this is the first lithography-free, direct-write approach combining Ga-ion milling, selective carbon engineering, and thermal annealing to deterministically generate \hBN{} \SPE{}s. The reproducibility of the method is validated across multiple independently fabricated samples. These results establish a scalable, lithography-free pathway toward on-demand SPE arrays relevant to integrated quantum photonics.

This study investigated how additively manufactured nozzles with body-centered cubic lattice structures reduce the flame flashback propensity in a hydrogen jet flame burner. Five different configurations of a jet flame combustor were investigated, with a focus on mixing duct walls incorporating porous media. The nozzles were manufactured by the powder bed fusion of metals using a laser beam process. The lattice parameters were varied by the volume fraction and the strut diameter. For the experiments, pure hydrogen was used as fuel under atmospheric conditions at various equivalence ratios and Reynolds numbers of 9,000 - 12,000. Flow field measurements, flame imaging, and spectral proper orthogonal decomposition of the flame dynamics were employed to identify possible transition mechanisms from a stable operation to flashback. The flow fields and the flame shapes showed only minor effects from wall modifications, preserving general flow characteristics across configurations. The flow dynamics in the combustion chamber were dominated by large-scale coherent structures in the shear layer, specifically Kelvin-Helmholtz instabilities. The results demonstrated that the nozzle with the coarsest porous wall structure significantly improved the flashback resistance compared to a nozzle with a solid wall. It is concluded that the primary mitigation mechanism was a cooling effect by unburnt mixture flowing through the porous media. The findings confirmed that the integration of lattice structures through additive manufacturing provides a viable strategy for hydrogen flashback mitigation by manipulating the coupled interaction between the flame and the thermal conditions of the wall.