Papers

Thermosolutal dendritic solidification involves interface evolution, solute diffusion, heat transfer, and melt flow over markedly different time scales. In lattice Boltzmann simulations, a single numerical time interval may place different transport processes in unfavorable relaxation ranges, while asynchronous updates require consistent transfer of phase-change contributions. To address these issues, a unified multirate multiple-relaxation-time lattice Boltzmann method is developed for thermal, solutal, and thermosolutal dendritic solidification. The coupled fields share a common moment-space framework but evolve at different update rates. The concentration and temperature source terms are separated into transport-related and phase-change contributions, and each resolved phase increment is used to immediately transfer the corresponding solutal and latent-heat contributions. The method reproduces characteristic dendritic morphologies and tip-velocity trends under pure diffusion and forced convection, with weak sensitivity to the tested update factors. Directional solidification over Lewis numbers \(Le=1\)–\(1000\) captures the transition from nearly planar to cellular and strongly branched growth, including vertically aligned dendrites and solute-rich interdendritic channels for saline water, in qualitative agreement with experiments. Source-coupling ablation shows that delayed coarse-step transfer produces increasingly strong local source pulses and eventual loss of numerical stability as time-scale separation increases, whereas phase-step instantaneous transfer remains stable over the tested conditions. These results demonstrate the applicability of the proposed framework to dendritic solidification with strongly separated transport time scales. The source code is publicly available in the DendriteLBM repository.

We investigate the weak and strong field gravitational lensing of light by a primary hair black hole (BH) solution obtained within the framework of the gravitational decoupling (GD) approach. In this method, the BH solution is constructed by introducing geometric deformations to a known seed spacetime, which, in the present case, is the Schwarzschild geometry. The deformation functions are determined by imposing the dominant energy condition, leading to the emergence of two characteristic parameters, the primary hair $Q$ and the coupling constant $\alpha$, both of which deform the Schwarzschild spacetime. To explore the lensing properties of this BH, we employ the Gibbons-Werner approach in the weak field regime and Bozza's formalism in the strong field regime. In the weak field limit, we derive the deflection angle up to second-order corrections and find that the coupling parameter $\alpha$ contributes more significantly to the leading-order deflection than the primary hair parameter $Q$. The primary hair is also found to exhibit an effectively repulsive gravitational behavior. In the strong field regime, we compute the deflection angle of photons propagating near the photon sphere, where the deflection diverges logarithmically, allowing photons to complete multiple loops around the BH and form relativistic images. Using the supermassive BH Sgr A* as the astrophysical lens, we further investigate the strong lensing observables, namely the asymptotic angular position $\vartheta_{\infty}$, the angular separation $s$, and the relative magnitude $r_{\mathrm{mag}}$. We also constrain the primary hair parameter $Q$ for different values of the coupling constant $\alpha$ using the shadow observations of Sgr A* reported by the Event Horizon Telescope (EHT) Collaboration.

We present a systematic study of nuclear ground-state properties obtained with the Skyrme quark-meson coupling (SQMC) energy density functional and compare them with results from the SLy4d Skyrme parameterisation. The SQMC functional is constructed using the quark-meson coupling (QMC) model, which incorporates the internal quark structure of the nucleon and results in a significant reduction in the number of free parameters. We investigate binding energies, two-nucleon separation energies, charge radii, and quadrupole deformations across a broad range of nuclei. Particular attention is devoted to the isovector dependence of the spin-orbit interaction derived within the QMC model, and its impact on the binding energies of neutron-rich nuclei relevant to the r-process. We find that the SQMC functional provides a reasonable description of nuclear ground-state properties in comparison with SLy4d.

Reconstructing the stress field of a planar viscoelastic flow from optical measurements loses its direct evidence wherever optical coverage is interrupted, and no improvement in optical precision restores an observation that was never made. We characterize what a second, velocity channel adds, and what neither channel can supply. Two calibrated optical components determine the local deviatoric stress pointwise, while velocity constrains spatial stress variation through momentum balance, so the two channels are complementary rather than redundant. The isotropic part of the stress is unobservable to both: the divergence of an isotropic field is a pure gradient, which the Leray projection annihilates, so every representable isotropic mode lies in the joint null space. That accounts for the null space exactly when the optical field is complete, and bounds it from below otherwise, since finite incomplete sampling and aperture zeros can remove further directions. We verify the count directly on three discretizations. In paired synthetic tests with finite measurement apertures, spatially correlated noise and optical stripe dropout, adding velocity reduces the mean whole-domain deviatoric error from 50.40% to 27.82% at 3% reference noise, and the improvement survives shared gaps, inverse-grid refinement at fixed physical sampling, and a constitutively generated stress field. The improvement does not rest on how the regularization parameter is chosen: it holds under both the expected-norm discrepancy rule and generalized cross-validation, and we report each selection with its position in the search interval, which is where the two rules differ.

The mass and redshift distributions of merging binary black holes (BBHs) bear imprints of their astrophysical formation channels. Whether the BH mass distribution evolves with redshift, however, remains an open question. In this paper, we employ copula functions, which describe the dependence between variables independently of their marginal distributions, to probe the dependence structure between the primary mass and the redshift of BBH mergers. We construct five population models by coupling the marginal distributions of primary mass and redshift with the Gaussian copula, the Clayton copula, or one of its three rotations, and we constrain their hyperparameters using 235 BBH events from GWTC-5.0. For comparison, we also adopt a baseline model in which the primary mass and redshift are assumed independent. Among the copula-based models, only the model with the $180^\circ$ rotated Clayton copula, which couples higher primary masses preferentially with high redshifts, exhibits evidence for a nonzero correlation, with its copula parameter deviating from the independence limit at more than $1\sigma$ significance. Importantly, the constraints on the Hubble constant ($H_0$) derived from these models are mutually consistent within the $68\%$ confidence level; the baseline model yields $H_0=74.3^{+13.7}_{-19.6}~\mathrm{km\ s^{-1}\ Mpc^{-1}}$, indicating that allowing for a mass–redshift dependence does not significantly bias the $H_0$ inference with the current dataset. Bayesian model comparison favors the baseline model over all copula-based alternatives, with log-Bayes factors corresponding to weak to moderate evidence against the latter on the Jeffreys scale. Our results thus imply that the current GWTC-5.0 sample remains consistent with no redshift evolution of the primary mass distribution over the redshift range probed.

We develop a Schrödingerization algorithm for quantum linear systems problems in two higher dimensions. The earlier LC-Schrödingerization approach represents the solution as a time integral of a homogeneous convection response and implements this integral by a linear combination of unitaries (LCU) over evolution times. We instead use Duhamel's principle to incorporate the integral into an inhomogeneous convection equation with zero initial data. Fourier projection in the convection variable and Schrödingerization in a second auxiliary variable then realize the solution without the separate LCU step. A joint choice of the kernel and recovery procedure gives an evolution time independent of the target accuracy, a uniformly bounded $L^2$ kernel normalization, and accurate recovery on a fixed interval. We establish the periodization and discretization bounds and analyze the interval recovery probability. With block preconditioning, we retain a single logarithmic precision factor and obtain linear condition-number dependence without variable-time amplitude amplification. Under exact oracle access and given a valid constant-factor solution-norm estimate, the algorithm uses $\mathcal O(\kappa_A\log(1/\varepsilon))$ queries to each original input oracle, with constant success probability and $\ell^2$ state error at most $\varepsilon$. The matrix-query bound matches the standard worst-case scaling when the supplied norm bounds are tight. UnitaryLab simulations on positive-definite and indefinite systems demonstrate the solution accuracy and probability gain from interval recovery.

This thesis studies the intersection of quantum computing and artificial intelligence in two directions: quantum methods for machine learning and machine learning methods for quantum systems. For quantum machine learning, Neural Quantum Embedding learns data representations that increase the trace distance between embedded class ensembles, lowering an embedding-dependent bound on empirical risk and improving classification on noisy quantum hardware. A training objective based on the Hilbert-Schmidt inner product extends this approach to deterministic quantum computation with one qubit (DQC1) and is demonstrated on an NMR quantum processor. A margin-based generalization analysis then connects quantum neural network performance to quantum state discrimination. In the studied benchmarks, margin distributions predict generalization more reliably than parameter-count metrics. For quantum systems, a Mamba-based neural decoder for surface codes matches a reproduced Transformer baseline in memory experiments while reducing inference-cost scaling from quartic to quadratic in code distance. Under an explicit decoder-induced-noise model, it achieves lower logical error rates and a higher effective threshold. For neural quantum states, stochastic reconfiguration is interpreted as tangent-space ridge regression, with its diagonal shift controlling the bias-variance trade-off under finite Monte Carlo sampling. Multi-shift stochastic reconfiguration reduces checkpoint-local validation residuals and update variance relative to fixed-shift SR, at additional computational cost. Together, these contributions show how learned representations, statistical control, and hardware constraints shape the exchange between quantum computing and machine learning.

We trained 64 independently seeded networks in four configurations, continuing each to sustained convergence or a 40,000-epoch ceiling. We then asked whether an RSB-inspired distribution of pairwise weight overlaps changes across the grokking transition. It is the alignment step, not the overlap statistic, that determines what this registered probe can report. The registered implementation permutes hidden units without the corresponding bias and head-internal permutations and therefore does not preserve the network function. Every q_wt value computed through this alignment inherits the defect; q_fn does not, because it is computed from predictions of the unpermuted models. The numerical-precision requirement also failed, and an audit found protocol deviations. Consequently, the pre-registered rule gives no verdict: registered outcome UNDETERMINED (reason code C0_INSTRUMENT_INVALID). These data provide neither a confirmatory null nor a validated reading of the Parisi order parameter. Only frac40 cleared the 12/16 checkpoint-completeness requirement. For this configuration, a post-hoc criterion applied to the same data gave a Hartigan-dip interval containing zero (95% CI for Delta dip = [-0.017, 0.034]), whereas the overlap standard deviation increased by a factor of about 5.6. A post-hoc calibration assigns the dip test zero power at the simulated separations; the interval is therefore uninformative, not evidence of no change. The standard-deviation ratio is the only statistic here with power at the observed effect. Ensemble loss was near-flat only under the pre-specified 1% threshold. Finally, grokking rates of 0/16, 11/16 and 16/16 remain descriptive because train fraction is confounded with split identity.

A moving object breaks the fundamental property of constant per-pixel count rates in an astronomical image read out up-the-ramp. In this paper, we show how to fit a moving object's path across a detector as that detector is read out nondestructively. We write the full likelihood function for every pixel subject to a constant count rate plus a time-dependent count rate due to a moving source. Assuming the moving source to be point-like and assuming the effective point-spread function to be known, we are left with four parameters that enter the likelihood nonlinearly: two for position and two for velocity. All remaining parameters can be optimized using closed-form expressions. Our approach extracts maximal information on a moving source's position and speed and enables the source to be accurately removed from the image. We investigate the dependence of flux, position, and velocity precision on the target's speed and the readout pattern. We also find a small, positive bias on the recovered flux due to the need to fit for an uncertain position and speed. Our approach can be used for space-based images with minor Solar system bodies in the foreground, e.g.~from Roman and JWST, or for ground-based observations with satellites in the foreground. We demonstrate the promise of our method with a fit to an asteroid track observed serendipitously by the NIRISS instrument on JWST, comparing it to the performance of the JWST pipeline. Python code implementing our approach is available at https://github.com/t-brandt/moving_source. The total computational cost to fit the track of a moving object is $\sim$1 second on a 2023 Macbook Pro.

Optical chirality quantifies the geometrical twisting of electromagnetic fields and underlies chiral light-matter interactions, yet its conventional formulation captures only the spin-associated chiral geometry of light. We introduce orbital optical chirality and derive its continuity equation, revealing physical properties distinct from those of angular momentum. For vortex beams, spin and orbital optical chiralities follow the spin and orbital indices, respectively. Applied to a twisted nanorod dimer, orbital optical chirality gives rise to vortex dichroism through quadrupolar hybridized modes, while dipolar modes exhibit only circular dichroism. These results establish a unified framework for optical chirality and provide access to chiral geometries beyond those resolved by spin optical chirality alone.

We study the thermal partition function of the critical large-$N$ $O(N)$ model on rotating $S^1\times S^2$. Rotation makes the saddle latitude dependent, with its leading profile governed by the local temperature. Using a Weyl-covariant hydrostatic expansion, we determine the partition function through four-derivative order in high-temperature and semi-universal limits. In the near-light-speed limit, the geometry around the equator reduces to a pp-wave and captures the expected semi-universal behavior of the partition function. We compute the corresponding theory-dependent residue directly on this limiting geometry, both at high and low temperatures. The high-temperature result agrees with the near-light-speed limit of the sphere calculation, while the low-temperature expansion reveals interaction-dependent corrections arising from the response of the saddle to the thermal source.

The synthesis of superheavy nuclei (SHNs) lies at the forefront of nuclear physics, enabling researchers to probe the limits of nuclear stability and the influence of shell effects. This review summarizes recent theoretical advances in understanding SHN formation and decay, emphasizing time-dependent density functional theory (TDDFT) and its extensions as microscopic tools to describe heavy-ion dynamics. Hybrid approaches combining TDDFT with coupled-channels, Langevin, and statistical models are discussed as means to connect microscopic predictions with experimental observables. The roles of fusion hindrance, quasi-fission, and multinucleon transfer are examined in terms of dissipation, shell structure, and deformation effects. Recent progress in computational power has enabled three-dimensional time-dependent mean-field (and beyond) simulations that include pairing and fluctuation dynamics. Perspectives are given on future developments toward a fully predictive description of superheavy element synthesis and the exploration of the upper limits of the nuclear landscape.

Evaluating spin Hamiltonians with dense, long-range interactions requires repeated global summation over many pairwise couplings, making energy evaluation costly on conventional electronic hardware. Here, we realize a planar optical architecture that evaluates such interaction energies directly in momentum space. For translationally structured couplings, the interaction kernel is encoded in the spatial transmission of a subwavelength-thick planar optical element placed in the Fourier plane. Pointwise spectral weighting followed by total-power detection reduces the quadratic spin Hamiltonian to a single optical signal, avoiding repeated digital multiply-accumulate operations during energy evaluation. We experimentally apply this approach to frustrated finite-range models and fully connected spin systems with oscillatory long-range couplings. The measured energies agree closely with numerical calculations, while optical annealing reproduces low-energy configurations and landscape statistics, reaching a normalized solution quality of 99.9%. These results establish momentum-space planar optics as a compact physical computing primitive for global-interaction problems in statistical physics and optimization.

We study the scaling behavior of the eigenvalues of correlation matrices, which characterize the entanglement of a subsystem with its complement part of a total pure state. A most distinguishing feature of entanglement entropy is its logarithmic dependence on the subsystem size for the groundstate of one-dimensional critical systems. Despite its robust universal character and relevance to a wide range of topics, a thorough understanding of this result requires sophisticated mathematical physics techniques or conformal field theory. The aim of our work is to shed light on this from the underlying eigenvalue distribution perspective. The central object is the correlation matrix, which takes the form of Toeplitz or block-Toeplitz matrix. We develop a circulant matrix approximation in the large matrix dimension limit, thus allowing for the individual eigenvalues behavior to be analysed analytically. We find that for both free lattice fermions and transverse field Ising chain, eigenvalues in the bulk of the eigenspectrum scales as $1/L_A$ with the subsystem size. Together with the extensivity of the entropy function, it explains the robust $\log_2 L_A$ scaling of entanglement at criticality. Perturbing from the entanglement-free limit of the Ising chain, we find a smooth crossover behavior to `non-critical' scaling that is characterized by a very slow logarithmic dependence rendering it seemingly a constant entanglement value expected of non-critical systems.

We investigate a long-lived scalar $S$ that triggers a strongly first-order electroweak phase transition (SFOEWPT) in the singlet scalar extension of standard model (SM). A sufficient small mixing angle between $S$ and the SM-like Higgs boson $h$ naturally leads to a long lifetime for $S$. We focus on the mass range $m_S>m_h/2$, where the dominant production channel at the LHC is the Higgs-mediated process $gg\to h^*\to SS$ with an off-shell $h$. By analyzing the finite-temperature effective potential, we identify the parameter space realizing an SFOEWPT and calculate the associated gravitational-wave spectra, finding that part of the parameter space can be probed by LISA. We further study the LHC sensitivity to the long-lived $S$ using the ATLAS detector and proposed far detectors, including ANUBIS, CODEX-b, FACET, FASER2, MoEDAL-MAPP1 and MAPP2, and MATHUSLA. The combined sensitivity of the main detector and far detectors, particularly ANUBIS and MATHUSLA, allows a large fraction of the SFOEWPT parameter space to be probed for $10^{-10}\leq \sin\theta\leq 10^{-5}$, with $m_S$ up to $250~\mathrm{GeV}$. For $\sin\theta\leq 10^{-11}$, however, the SFOEWPT parameter space becomes inaccessible to both the main detector and the far-detector searches.

In this paper, we study the analogue of the Kolmogorov scale in surface gravity wave turbulence, characterized by the cutoff wavenumber $k_c$ at which the power-law inertial range transitions into the dissipation range. We perform numerical simulations of the primitive dynamical equations with a broad-scale dissipation of magnitude $\gamma_0 k^2$ in spectral space to establish the relation between $k_c$ and $\gamma_0$. Our results show a scaling $k_c\sim\gamma_0^{\beta}$, where $\beta$ depends on the slope $\alpha$ of the power-law spectrum. We find that $\beta(\alpha)$ agrees more closely with the prediction obtained by balancing the nonlinear and dissipation terms in the dynamical equations than with that based on the kinetic equation. This observation reveals that non-resonant triad interactions play a more significant role than resonant quartet interactions in the formation of $k_c$.

Trapped-ion quantum networks rely on efficient ion-photon interfaces, while objective-based free-space collection systems must balance high photon collection with sufficient working distance for practical integration with ion-trap hardware. Here, we design and characterize an ion-photon interface with a long working distance of 26.15 mm and a high numerical aperture of 0.5. The core of the interface is a photon-collection objective consisting of six commercial spherical lenses with optimized spacing. The interface achieved an overall fiber-coupled photon-detection efficiency of (1.29$\pm$0.09)% from the ion to the detector and maintains fiber coupling over several hours without active realignment, supporting stable operation of the ion-to-fiber interface. Photon-correlation measurements show clear antibunching in the fiber-coupled fluorescence, confirming the preservation of non-classical photon statistics. These results demonstrate a practical implementation of a long-working-distance photon collection interface for trapped-ion quantum network experiments.

Topological wave systems have largely evolved along two distinct paradigms: gapless topological semimetals and gapped topological insulators. While topological semimetals support bulk transport, they generally lack intrinsic selectivity among propagation channels; topological insulators enable robust transport but confine it to narrow interfaces, limiting spatial utilization. Here, we theoretically demonstrate and experimentally realize time-reversal-invariant spin-valley photonic half-semimetals (HSMs), which exhibit a dual semimetal-insulator topology within a single bulk band structure. In HSMs, the bandgap closes selectively in spin-valley space: for a given spin (valley), one valley (spin) is semimetallic while the other remains insulating. This coexistence of spin- and valley-resolved gapless and gapped band structures makes HSMs fundamentally distinct from both conventional semimetals and insulators. As a defining bulk phenomenon, an HSM functions as a spin-valley-locked beam splitter, intrinsically enabling valley-selective spin routing. Moreover, when four complementary HSMs are assembled into a periodic superlattice, the same dual topology enables reciprocal spin-valley-resolved multilane helical transport with 100% spatial utilization. These results establish HSMs as a platform for selective bulk wave control and multichannel topological transport beyond conventional topological phases.

Scaling quantum control for atoms, ions, and solid-state emitters requires gigahertz-frequency spectral control of high-power visible light in a volume-manufacturable platform. Silicon nitride photonics provides high power handling and CMOS-foundry compatibility but has no intrinsic mechanism for high-speed modulation. Integration with piezoelectric materials enables acousto-optic phase modulation, and mechanical resonant enhancement has made it efficient at gigahertz frequencies. However, a single resonance restricts the modulation waveform to a single tone, imposing Bessel-function sideband amplitudes and limiting frequency-shifting efficiency to 33.9%. Here we engineer a silicon nitride acousto-optic microstructure to support harmonically spaced resonances at 1.14 GHz and 2.28 GHz, each strongly optomechanically coupled to a 730 nm guided optical mode, so that tailored non-sinusoidal modulation waveforms can be resonantly synthesized. By piezoelectrically controlling the two mechanical amplitudes and their relative phase, we demonstrate 50% conversion to one sideband (1.5x the single-tone theoretical maximum), a flat seven-line comb, and a frequency shift with 60 dB carrier and 53 dB image suppression - to our knowledge the highest reported for an integrated modulator. The devices are fabricated in a 200 mm CMOS foundry, and we measure 91.7% yield without post-fabrication tuning across 36 devices from three wafers. We also show how the technique can be straightforwardly scaled to three or more harmonics. This result overcomes the trade-off between resonant enhancement and spectral programmability, with important consequences including improved single-qubit gate efficiency for hyperfine qubits.

The possibility of describing neutrino masses through a single multiplet of modular forms in a modular symmetric framework is reanalysed. The minimal model achieving this is Feruglio's model based on modular $A_4$ symmetry, which contains a chiral flavon triplet $\phi$, with all neutrino masses and mixing determined by a superfield triplet of modular forms $Y(\tau)$. We point out that, in local supersymmetry, these superfields by themselves allow an additional $R$-parity-violating contribution to neutrino masses originating from the Kähler potential of the model. The $R$ violation manifests through a bilinear term $\epsilon_i L_i H_u$ in the effective superpotential, with parameters $\epsilon_i$ determined in terms of $Y(\tau)$ and its derivatives. The Kähler potential also mixes neutrinos with the fermionic component of $\phi$, leading to seesaw neutrino masses when these fermions are massive. Two separate cases are analysed, with neutrinos obtaining mass through the Weinberg operator or through the $\phi$-induced seesaw. Unlike the original model, adding the $R$-violating contribution allows accurate reproduction of neutrino mixing angles and mass ratios for both the normal and inverted orderings in either case, with the Weinberg operator predicting a sum of neutrino masses close to the cosmological limit and the seesaw mechanism predicting ones comfortably below it.

Recent advances in engineered quantum platforms have enabled the realization of bosonic Laughlin states at $\nu=1/2$ and brought non-Abelian topological phases within experimental reach. A central theoretical challenge is to develop a unified framework connecting lattice fractional quantum Hall (FQH) model states, exact parent Hamiltonians, and experimentally accessible interactions. We systematically construct Hermitian parent Hamiltonians for which continuum lowest Landau level (LLL) model states sampled on lattice sites are exact zero modes. Using these model manifolds as quantitative references, we find that, within the projected lattice LLL at the flux densities studied, short-range density interactions stabilize Laughlin ground-state manifolds at $\nu=1/3$ and $1/4$, while two-body onsite repulsion supports a Moore–Read triplet at $\nu=1$. Full multiband calculations reveal a sharp contrast: the Laughlin manifolds remain robust against interband mixing on the studied tori, whereas the Moore–Read triplet becomes less spectrally isolated and eventually undergoes a level crossing with competing states near the interband scale. Our framework provides a theoretical foundation for using lattice model states to guide the search for experimentally accessible Abelian and non-Abelian FQH states.

The realization of a scalable quantum network (QN) hinges on the efficient distribution of entanglement across heterogeneous hardware platforms. While traditional QN frameworks are often restricted to single-encoding schemes, relying exclusively on either discrete (DV) or continuous (CV) variables, such segregated architectures limit the capacity and interoperability of large-scale systems. Here, we propose a scalable hybrid entanglement distribution scheme that bridges these domains by mapping hybrid entanglement swapping and concentration at DV-CV interfaces onto a unified set of series and parallel graph rules. We demonstrate that our hybrid approach exhibits a potential performance advantage over traditional point-to-point generation of maximally entangled states, achieving enhanced end-to-end entanglement within series-parallel topologies. These results provide a robust theoretical foundation for designing resource-efficient, interpretable architectures for the future quantum internet.

We investigate axial gravitoelectromagnetic perturbations of charged black holes surrounded by dust-like Kiselev-type anisotropic matter in Rastall gravity. We derive the axial matter compatibility condition and construct a compatible response by holding the covariant anisotropy-direction vector unperturbed. The resulting gravitational and electromagnetic perturbations obey two coupled Schrodinger-type master equations. An r-independent algebraic decoupling exists in the Reissner-Nordstrom and general-relativistic dust-like limits; additional radial structure obstructs it in generic charged Rastall backgrounds with nonzero surrounding matter. We prove axial mode stability under the adopted closure for every nonextremal background satisfying the stated exterior conditions, covering all physical axial multipoles. A matrix S-deformation excludes exponentially growing coupled modes for l >= 2, while the physical electromagnetic dipole has a positive effective potential. A Chebyshev pseudospectral calculation, validated against the Reissner-Nordstrom spectrum and spectral convergence, determines the fundamental frequencies. In the parameter ranges examined, increasing the Rastall coupling lowers both the oscillation frequency and the damping rate in the small-coupling region; in the large-coupling region, the oscillation frequency rises while the damping rate varies nonmonotonically. A larger charge generally raises the oscillation frequency, whereas stronger surrounding-matter contributions produce longer-lived modes.

We construct a sequence of finite Rodriguez-Villegas transforms converging locally uniformly to the Riemann $\xi$-function in the critical strip. The input is a positive symmetric profile on the unit interval obtained from the Riemann theta kernel through convolution with the hyperbolic-secant kernel and the logistic coordinate. The profile is a Stieltjes function of $x(1-x)$. Its Bernstein polynomials produce reciprocal numerators and exact finite functional equations. The same numerators admit an exact realization as fermionic supertraces, while the Bernstein polynomials are normalized Gibbs traces.

We propose a two-stage production method to overcome existing supply-constraints for the alpha-emitter $^{149\mathrm{g}}$Tb, a promising candidate for Targeted Alpha Therapy (TAT) with no existing globally scalable production pathway. Although awaiting experimental measurement of the $^{150}$Gd(p,2n)$^{149\mathrm{g}}$Tb cross section, the proposed method could produce $^{149\mathrm{g}}$Tb at clinical scale and beyond on readily available proton cyclotrons, enabled by production of the extinct but long-lived isotope $^{150}$Gd, a pure alpha emitter with a 1.79 million year half-life. Stage one generates $^{150}$Gd feedstock by irradiating natural Eu or enriched $^{151}$Eu with $\gtrsim$10 MeV protons, neutrons or photons. Stage two produces $^{149\mathrm{g}}$Tb from fabricated $^{150}$Gd targets by driving the $^{150}$Gd(p,2n)$^{149\mathrm{g}}$Tb reaction with $\gtrsim$14 MeV protons, accessible on over 700 reported cyclotrons worldwide. Fast fusion neutrons appear to offer the most scalable pathway for $^{150}$Gd production: even with a large $^{149 \mathrm{g}}$Tb dose size of 1 GBq and 40 million administered doses/yr, we estimate this would require neutrons produced by only 6.8 megawatts of steady-state deuterium-tritium power to produce the required $^{150}$Gd, far below expected capacity in the next decade. The route described here, if validated, would enable $^{149\mathrm{g}}$Tb supply at the scale needed to support clinical development of $^{149\mathrm{g}}$Tb-based TAT.

Resolving how ensemble growth kinetics emerge from particle- and grain-level dynamics is essential for predictive control of nanocrystal synthesis. Here, time-resolved four-dimensional scanning transmission electron microscopy (4DSTEM), extended into five dimensions (5DSTEM) through continuous acquisition, is used to simultaneously resolve morphology, crystallographic orientation, and lattice strain during Au nanocrystal growth in aqueous HAuCl4. Although ensemble growth follows surface-reaction-limited kinetics, individual nanoparticles exhibit distinct pathways, including continuous growth and discrete coalescence through oriented attachment. These pathways display characteristic orientation dynamics, with stable or gradually selected orientations during continuous growth and abrupt reconfiguration followed by alignment during coalescence. At the ensemble level, the out-of-plane orientation distribution is established early and remains stable, whereas in-plane orientations remain broadly distributed without global alignment. Tensile strain develops progressively from particle surfaces and interfaces, directly linking lattice distortion with evolving morphology and crystallographic structure. By connecting ensemble kinetics with particle- and grain-resolved structural evolution, 5DSTEM provides a general framework for uncovering heterogeneous growth mechanisms and for relating synthesis pathways to structure-dependent properties in functional nanomaterials.

Extracting Gaussian information from data is well understood, but characterizing non-Gaussianity is challenging. We introduce HAWCS, a healpy-based Python package for efficiently computing wavelet scattering transform coefficients from full-sky maps. These coefficients provide compact summary statistics that are sensitive to higher-order structure and interactions across angular scales. We test the implementation on controlled Gaussian and non-Gaussian fields and demonstrate its computational efficiency. We then apply HAWCS to thermal Sunyaev-Zeldovich maps derived from Planck observations and four simulations, quantifying and comparing their higher-order statistical properties. We also use the method to expose the signatures of gravitational lensing in cosmic microwave background (CMB) temperature maps. These results demonstrate that HAWCS is a practical tool for validating component-separation pipelines and cosmological simulations, and a promising summary statistic for characterizing non-Gaussian structures beyond the power spectrum. These coefficients could also be used to constrain or generate simulated maps that reproduce the same statistical features of real data.

An unusual object in the sky raises two related questions: what kind of object it is and what physical process drives its motion. Departures from a gravity-only trajectory can provide evidence, but the same apparent acceleration may be generated by distinct dynamical mechanisms. We formulate this as an identification problem and establish conditions for identifiable uniqueness among three reference classes: inert dynamics, impulsive forcing, and active stabilization such as a controlled spacecraft. The distinction rests on how each class responds to disturbances. Although different mechanisms can produce similar average trajectories, the specified reference models imply different stochastic responses around those trajectories. We show when these differences uniquely determine the dynamical class from the observed trajectory and when several classes remain observationally compatible.

We present a variety of possible observational sequences from planet detection to characterization (i.e., survey strategies) for the initial exoEarth detection and characterization survey phase of the Habitable Worlds Observatory. An array of survey strategies were collated by the HWO Exoplanet Survey Strategies Task Group; by investigating and comparing expected resultant exoEarth yields for multiple survey strategies, we can better understand the most efficient strategy to characterize multiple planets in unconventional ways. We present eight varied survey strategies, presented as steps of Detection, Photometry, Orbit Measurement, and/or Characterization, including discussion of possible shortcomings and benefits of each strategy. We present exoEarth yield calculations from the Altruistic Yield Optimizer (AYO) and the Exoplanet Open-Source Imaging Mission Simulator (EXOSIMS) for select strategies, with initial considerations of thermal emission and detector noise. Herein, a yield is the expectation value given the astrophysical assumptions of the number of planets that meet the observational criteria during the survey. We find that AYO and EXOSIMS find the highest yields for H2O at 0.9 microns, although the calculated yields vary. When allowing for wavelength optimization within AYO, we find that H2O is most optimal to observe at 0.9 microns when given the full range of VIS and NIR values, with an expected exoEarth yield of 29.1. H2O and O2 dual characterization is possible at the expense of yield planet loss, with a calculated possible yield of 20.9 in the VIS. The characterization of CH4 and CO2 in the NIR result in the lowest exoEarth yields at 19.9 and 6.4 possible expected planets, respectively. Future work updating AYO and EXOSIMS is necessary to explore further survey strategies that follow different observation procedures, some of which is currently underway.

I connect two literatures developed independently: the path-measure formulation of non-equilibrium statistical mechanics, where a trajectory action decomposes into a time-antisymmetric (entropic) and time-symmetric (frenetic) sector, and the stochastic modelling of ribosomal traffic on messenger RNA. The biological target is a proposed intervention – antisense oligonucleotide (ASO) interference with wobble-uridine (U34) modification of transfer RNA – whose intended effect is not to abolish translation but to perturb its timing, driving ribosome collisions and collision-triggered transcript decay preferentially on high-flux, codon-biased transcripts. Dynamical-activity and large-deviation analyses of generic lattice exclusion models – notably the symmetric and totally asymmetric simple exclusion processes – are well established. To my knowledge their formalization specifically for ribosomal traffic queues, translation elongation, and collision-triggered no-go decay remains unoccupied; this paper addresses that narrower gap, not the general one. Two claims here are load-bearing and untested. First, selectivity: transcripts whose loss is therapeutically desirable are separable, by vulnerable-codon-pair burden, from transcripts whose loss is toxic. Second, non-redundancy: the frenetic decomposition yields predictions, specific to ribosomal queueing and collision-triggered decay, not already obtainable from rate-level exclusion-process models or existing activity/large-deviation analyses of exclusion processes. This paper establishes neither. It specifies both as falsifiable tests with pre-registered decision rules, including outcomes under which the framework should be abandoned or narrowed. It is a research programme proposal, not a result. No new experimental, computational, or bioinformatic results are reported.