Papers

I present a reduced-order approach for incorporating distributed thermal dynamics into nonlinear optical-microcavity simulations without repeatedly solving the time-dependent heat equation. A harmonic finite-element heat solve is used to obtain the thermal transfer function, which is introduced into the time domain through either a rational approximation or an impulse-response convolution. The method is validated against heat-equation-coupled finite-element simulations for prescribed TE1-mode heating and for nonlinear silicon microcavity dynamics. For the feed-forward TE1 tests up to 100 MHz and simplified cavity dynamics, the error remains below 4%. The reduced models reproduce the local self-pulsation dynamics, although long-time phase alignment is sensitive to the spatial definition of the thermal transfer function and to impulse-response truncation. These results establish a physics-based route for retaining multi-timescale thermal memory while substantially reducing the cost of coupled optical–thermal simulations.

Low-lying electronic states of different spins can be thermally populated in open-shell molecules, allowing optical absorption to begin from several initial states. We formulate their canonical optical response using the electronic levels and one-body matrices of spin-adapted time-dependent density functional theory. Boltzmann populations determine the contribution of each initial state, while transition density matrices determine its coupling to the final states. Absorption and stimulated emission then give the temperature-dependent strength of every allowed transition. Transition matrices are evaluated from the calculated first-order excitation amplitudes, with the additional mixed second-order electronic response omitted by this approximation identified explicitly. The resulting response function provides spin-resolved polarizabilities and absorption spectra with definite total spin assigned to each participating electronic state. Applications to diradicals provide a qualitative interpretation of their temperature-dependent absorption spectra.

Cavity-based x-ray free-electron lasers (CBXFELs) require tunable x-ray cavities to broaden their practical utility and enable access to a wider range of scientific applications. We propose and analyze a compact tunable non-coplanar x-ray cavity based on six Bragg-reflecting crystals arranged as two three-crystal backscattering units. The three-dimensional geometry provides a substantially larger tuning range than planar bowtie cavities while maintaining a compact transverse footprint. We derive analytical expressions for the cavity geometry, crystal kinematics, and polarization-dependent Bragg reflectivity both in the intrinsic and eigenpolarization bases. For a given Bragg reflection, the ultimate photon-energy tuning range is 100%, from $E=E_{_{H}}$ at backscattering to $E=2E_{_{H}}$ at Bragg angle $\theta=\pi/6$. Practical geometrical and polarization constraints reduce the directly usable range to approximately 45%, while operation in the cavity eigenpolarization basis can extend it to approximately 65%. By combining fundamental and harmonic diamond reflections, and using reflections from different crystallographic families, the accessible photon-energy range can be extended from about 3~keV to approximately 20~keV. These results establish non-coplanar multi-crystal cavities as a viable route toward compact, broadly tunable x-ray resonators for future CBXFELs.

Magnetic reconnection in partially ionized plasmas is an important channel for energy release. While the plasmoid instability is well characterized in 2D fully ionized plasmas, its behavior in the presence of neutral-dominated plasma remains poorly understood in the nonlinear, high-Lundquist-number ($S = 10^5$) regime. We present high-resolution ($16384 \times 4096$ cells) two-dimensional two-fluid (ion $+$ neutral) simulations of Harris-sheet reconnection with upstream plasma beta $\beta = 2$, comparing fully ionized and partially ionized (ionization fraction $\xi = 10^{-1}$ and $10^{-2}$) regimes. Neutral-ion decoupling accelerates the linear tearing stage and alters the plasmoid hierarchy: the large-scale “monster” plasmoid that dominates the fully ionized case is suppressed, and the sheet instead fragments into a dense chain of sub-scale plasmoids. Below the neutral-ion decoupling scale $\ell_{\rm dec}$, ions concentrate into the plasmoids, reaching peak overdensities $\rho_i/\rho_{i,0} \approx 10$ ($\xi = 10^{-1}$) and $3-5\times10^{3}$ ($\xi = 10^{-2}$), while the neutrals remain comparatively smooth. This local pile-up raises the ionization fraction and recouples the two fluids within the plasmoids. Measured from the out-of-plane electric field at the reconnection sites, the reconnection rate in the $\xi = 10^{-2}$ case achieves $R_{\rm rec}\approx0.01$, whereas the $\xi = 10^{-1}$ case rises to a rate $\approx0.02$ and further $0.035$ when apparent coalescence occurs. In the $\xi = 10^{-2}$ case, the ambipolar drift drives a rapid ion inflow $\sim0.5\,v_{A,0}$ into the layer at the same reconnection sites, far above the neutral inflow velocity $\sim0.1\,v_{A,0}$. Here, $v_{A,0}$ is the upstream total Alfvén speed.

The vector spherical harmonics (VSH) are crucial ingredients for representation of arbitrary vector fields in curvilinear coordinate systems throughout mathematical physics. Performant, efficient computations of the VSH are essential to high-performance computing applications that utilize spectral analysis, including magnetohydrodynamics (MHD) simulations for geophysics and astrophysics. The free open-source FORTVSH library provides a catalog of numerical routines for evaluating various VSH forms and related mathematical functions. This manuscript establishes the theoretical basis, addresses the computational need for efficient VSH solvers, and presents a comprehensive overview of the FORTVSH routines.

This is the first in a series of papers aimed at understanding the statistics of coalescing particles in turbulent flow and their relation to collisionless ghost particles. We perform three families of Direct Numerical Simulations (DNS) under identical flow conditions: ghost particles without mutual interactions; particles that coalesce upon collision with lost monomers replenished at random positions (CR); and particles with the same collision-coalescence kinetics without replenishment (CN). All analyses are monodisperse and concern only monomers. Across $St=0.01\text{-}3.0$, the ghost-particle system has higher collision kernels ($K$) and radial distribution functions (RDFs, $g(r)$) near contact than the coalescing systems. A velocity-filtered RDF, $g_{\mathrm{G}}^{(-)}(r)$, provides a reasonable estimate of the CR contact RDF, $g_{\mathrm{CR}}(d)$. We show that the residual discrepancy between $g_{\mathrm{G}}^{(-)}(d)$ and $g_{\mathrm{CR}}(d)$, and between the corresponding kernels, arises from correlations among successive collisions in the ghost-particle system. A history-filtered ghost-particle kernel, excluding such correlations, reproduces the coalescing-system kernel. We introduce a collision-correlation time $\tau_{\mathrm{cc}}$ that quantifies how long current collisions influence future events and find that it has a finite, narrow range across the studied $St$. Filtering particles with collisions within a period comparable to $\tau_{\mathrm{cc}}$ yields a history-filtered RDF that reproduces those of both coalescing systems. Finally, the fraction of repeated collisions involving identical particles decays exponentially with $St$. These results unify the coalescing and ghost-particle systems as a history-filtered framework.

Within the framework of gravitational thermodynamicization, we investigate the propagation of charged scalar fields in static two-dimensional black-hole spacetimes. Starting from the scalar-field action, we derive the exact radial wave equation and show that a neutral, massless, minimally coupled scalar field in a genuinely two-dimensional geometry exhibits neither an angular-momentum barrier nor superradiant amplification. For a charged scalar field, the condition for amplification is governed by the electrostatic potential evaluated at the event horizon. In the case of the charged two-dimensional string black hole, the horizon electrostatic potential is directly related to the Hawking temperature, implying that the superradiant frequency window is determined by the thermodynamic state of the black hole. We further formulate a near-horizon residue criterion that provides a coordinate-independent characterization of the superradiant threshold. When a reflecting outer boundary is imposed, necessary frequency conditions for unstable modes are derived, together with an upper bound on their growth rates. Numerical calculations verify the corresponding flux relation and clearly distinguish superradiant scattering from genuine superradiant instability.

Recent results from the Dark Energy Spectroscopic Instrument (DESI) have suggested that dark energy, long considered to be a cosmological constant, may actually be \lq{}dynamical\rq{}. To clarify what follows from these results, we distinguish three claims: (D1) the data disfavour the \LCDM expansion history; (D2) within the phenomenological Chevallier–Polarski–Linder (CPL) parametrisation, the data prefer $(w_0,w_a)\neq(-1,0)$; and (D3) there exist one or more genuine dynamical dark-energy degrees of freedom in the matter-sector, within GR and coupled to the standard sectors only gravitationally, whose dynamics account for the departure from the \LCDM expansion history. We demonstrate that DESI establishes D2, which supports D1, but does not establish D3. The \lq{}designer\rq{} construction in $f(R)$ gravity provides a gravitational realisation of the same background history, so that no observable determined solely by that history can discriminate, even in principle, between its \lq{}matter\rq{} and \lq{}gravitational\rq{} readings. Furthermore, non-minimally coupled models admit regular effective phantom-crossing realisations of the relevant phenomenology, while the selected crossing places additional pressure on a single-component, minimally coupled realisation of the matter-sector reading. We characterise the resulting underdetermination between matter and gravitational interpretations—exact at the level of background history, but breakable beyond it—and draw the corresponding norm for survey reporting.

Hypersonic vehicles and atmospheric-entry bodies can experience radio-frequency communication blackout when shock-heated gas surrounding the vehicle becomes sufficiently ionized that plasma cutoff and collisional attenuation restrict electromagnetic transmission. Magnetic-window approaches attempt to reduce this loss by exploiting the anisotropic dispersion of a magnetized plasma, in which selected right-hand or whistler-like modes may propagate along preferred directions. This paper develops a reduced-order scaling model for magnetic-window transmission through a finite-thickness hypersonic plasma sheath when the magnetic source is represented as an onboard axial dipole. The model gives a closed-form estimate of the collisionless angular aperture, compares the underlying projected-cyclotron criterion with full cold-plasma dispersion roots, and extends the aperture estimate to a loss-limited cone using a collisional optical-depth approximation. A simplified neutral-density, speed, and ionization closure is used only to generate qualitative parametric maps and sensitivity trends. The results clarify how dipole-field decay, sheath thickness, radio frequency, vehicle scale, electron density, and collisions jointly constrain the candidate transmission window. The contribution is intended as a screening framework for selecting cases for full-wave electromagnetic simulation, nonequilibrium aerothermochemistry, antenna-coupling analysis, and laboratory validation, rather than as a demonstrated engineering solution to plasma blackout.

As a liquid approaches its glass transition, its dynamics turns heterogeneous: mobile and immobile regions coexist, and the four-point susceptibility $\chi_4$ that quantifies this heterogeneity grows sharply. Interpreting that growth is subtle, because the collective signals experiments record, such as a tagged particle's trajectory, an overlap function, or a mean field, are generated by the same particles they describe. Here we compute exactly what conditioning on such a shared record does to the population that produced it, for a broad class of stochastically observed systems; the guiding example is a tagged particle and the cage of $z$ neighbors that drives its force history. Using a Girsanov path transformation, we prove that the conditioning multiplies the independent joint law of the $z$ trajectories by exactly one term: a centered-square penalty along the single collective direction the record can see. Any fixed pair of particles stays nearly independent, with covariance falling as $O(z^{-1})$ and mutual information as $O(z^{-2})$, the property known as propagation of chaos, yet the $z(z-1)$ weak pair correlations add coherently into a finite suppression of collective fluctuations, the Schur shield $D - C = -C^2(aI + C)^{-1} \preceq 0$. An exactly solvable Brownian model calibrates the construction. The physical consequence is a calculable baseline for dynamical heterogeneity: conditioning itself contributes a computable, nonpositive amount to the susceptibility of a conditioned ensemble, so the genuine cooperative signal is the excess of the measured $\chi_4$ over this baseline rather than over zero, a comparison that existing simulation data can already perform.

The chemical potentials of multi-component mixtures underlie many physical and chemical phenomena, but remain challenging to compute. The S0 method enables the computation of chemical potentials from equilibrium molecular dynamics simulations, by leveraging the thermodynamic relationship between particle number fluctuations and derivatives of chemical potentials, followed by numerical integration along different compositions. Here we generalize the S0 method from two-component mixtures to neutral multi-component mixtures. We first extend the statistical mechanical formalism to high-dimensional compositional space, and then introduce a Gaussian process integration scheme combined with active learning to efficiently integrate chemical potentials and sample diverse compositions. We use this method to compute the mixing free energies of a molten metal alloy, and the solubilities of two paracetamol polymorphs in water-ethanol solvents. The extended S0 method provides a practical and scalable route for computing chemical potentials in neutral bulk multi-component mixtures from atomistic simulations.

We study magnetoelastic coupling in stripe-domain magnetic states of $3\,\mathrm{\mu m}$-thick YIG thin films grown on a GGG substrate. Broadband ferromagnetic resonance reveals low-frequency stripe-domain magnon branches modulated by a field-independent phonon comb with a frequency spacing of $3.5\,\mathrm{MHz}$, matching the value predicted for confined thickness-shear modes of the GGG substrate. Analytical fitting yields coupling rates that vary between $0.33$–$0.54\,\mathrm{MHz}$ and cooperativities of order $10^{-1}$, indicating that the system is in the weak-coupling regime without resolvable avoided-crossing gaps. Magnon-phonon mode-overlap calculations using finite-element simulations show that the weak coupling arises from phase and domain-sign cancellation: the local magnetoelastic coupling is sizable, but more than $99\%$ of the coherent overlap cancels across the stripe texture. Fully coupled simulations further demonstrate phonon-mediated excitation of a remote YIG layer and show that efficient propagating-phonon generation requires spatially asymmetric magnon modes, establishing magnetic texture as a control parameter for magnon–phonon coupling.

Message passing is exact for progressive epidemics on trees: infection is unidirectional, and a node's neighbours are uncorrelated in the cavity graph. A recurrent disease breaks this even on a tree due to backtracking. A node infects a neighbour, recovers, and is reinfected by it, so infection traverses an edge in both directions. Unrolled along a time axis, the outward and return transmissions together with the node's own persistence in time form a closed cycle in the space–time graph, correlating the states that ordinary message passing assumes independent. We treat these correlations by solving the dynamics exactly inside a ball of radius d about an edge and closing the ball's boundary with a single conditional per-edge message. For fixed-period susceptible–infected–susceptible dynamics this generates a hierarchy of closures on the endemic state indexed by d, in which the ball of radius d treats exactly every space–time cycle of spatial reach at most d and retains the remainder only through the mean rate supplied by its boundary. Linearising the resulting message map gives the endemic threshold, with an accuracy that increases with d. We compare the hierarchy against Monte Carlo simulation on random and empirical networks, finding excellent agreement.

We study radial nonlinear instability of compactly supported nonrotating equilibria of the three-dimensional Euler–Poisson system with a physical-vacuum boundary. Let $n^u(\mu)$ denote the radial instability index furnished by the turning-point theory of Lin and Zeng. Under general structural assumptions on the pressure law, suppose that $n^u(\mu)>0$ and that the equilibrium is not a mass extremum, $M'(\mu)\neq0$. Conditional on the existence of a sufficiently regular radial solution on the relevant time interval, we establish two nonlinear escape criteria. First, every perturbation with Hamiltonian strictly below that of the equilibrium exits a fixed neighborhood on a logarithmic time scale controlled by the least unstable linear growth rate. For the subclass of data for which the associated Lyapunov functional is initially nonnegative, we also obtain an explicit exponential lower bound in the weighted displacement norm. Second, sufficiently small perturbations whose Riesz projection onto the finite-dimensional unstable subspace is not too small escape on a logarithmic time scale. The second argument uses the exponential trichotomy of the linearized Hamiltonian flow and an invariant-cone estimate. In the polytropic class, the conditional estimates combine with the radial physical-vacuum local theory to yield unconditional nonlinear instability in the corresponding classical-solution topology. The results complement Jang's nonlinear instability theorem for Lane–Emden stars by treating mechanisms that do not require initial alignment with a leading growing eigenmode and by applying, conditionally, to unstable branches for general equations of state.

Adaptive loss-balancing schemes for physics-informed neural networks rest on a premise that every residual should be driven to zero. For level-set advection with an eikonal regulariser that premise fails: the eikonal term penalises deviation of $\lVert\nabla\phi\rVert$ from unity, a property transport preserves only under rigid motion; where the exact solution departs from a signed-distance function the eikonal residual of the correct answer is nonzero, and driving it to zero moves the network away from that answer. We show that standard gradient-norm balancing fails in exactly this way, its weight remaining near its initial value throughout training on benchmarks where the property is violated, and we introduce SDF-Aware Weighting (SAW), which combines a residual-quantile gate with a gradient-norm ratio so that points exhibiting legitimate departure are excluded before the surviving term is scaled. Across four three-dimensional benchmarks SAW selects an eikonal weight within an order of magnitude of the value located by an eighteen-run manual sweep, spanning four decades from $10^{-1}$ to $10^{-5}$ with a single fixed configuration. On the slotted sphere, where the initial field is non-differentiable at reentrant edges, SAW attains a lower error than any weight in that sweep. Two smooth rigid benchmarks serve as controls: SAW is worse there, as expected when its premise does not hold. An ablation with the gate disabled shows the slot is nearly entirely filled while the relative $L_2$ error reads $1.06\%$, indistinguishable from a field that never represented the slot. We give a feature-restricted measure that separates the two cases.

We present an information theoretic framework for extraordinary optical transmission through a subwavelength slit containing symmetric internal ridges. Full wave finite element spectra are interpreted with a reduced Fabry Perot model in which the ridge interfaces introduce a reactive discontinuity phase associated with modal impedance mismatch and evanescent field loading. Fisher information is used to quantify how reliably resonance positions and geometric parameters can be inferred from transmission measurements. For an isolated Lorentzian resonance under white Gaussian noise, the Fisher information for the resonance center scales linearly with the quality factor when amplitude, sampling, and noise are fixed. We also extend the formulation to correlated Gaussian noise and Poisson shot noise, showing why the resonance with the highest Q is not necessarily the most informative under realistic experimental conditions. The framework clarifies the interpretation of ridge induced effective cavity corrections and provides a reduced order route toward Fisher information driven inverse design of subwavelength resonators.

Electrode binders are conventionally regarded as inert structural components. Here, we show that in lead-free perovskite supercapacitors, the binder defines the optimal electrolyte composition. Across a factorial matrix of poly(vinylidene fluoride) (PVDF) loadings and LiTFSI concentrations in CsSnCl$_3$ electrodes, the capacitance optimum shifts systematically with binder content along a single linear relationship, described by the Interfacial Balance Rule ($\lambda+\theta=1$), where $\lambda$ and $\theta$ are the normalized lithium-supply and polymer contributions at the optimized interfacial state. The same relationship holds for hybrid MASnCl$_3$, showing that the optimum is governed by the polymer-electrolyte interface rather than the perovskite lattice chemistry. Simulations using a pre-trained MACE machine-learned interatomic potential show that PVDF adopts a planar configuration on CsSnCl$_3$ and simultaneously interacts with cationic and anionic sites. This configuration homogenizes lithium adsorption energetics, introduces fluorine-mediated coordination, and confines lithium to a two-dimensional interfacial region while preserving lateral mobility. Tuning polymer coverage through surface density and chain length reveals a finite interfacial lithium accommodation capacity that marks the onset of out-of-plane aggregation. The Interfacial Balance Rule provides a macroscopic descriptor of this finite interfacial resource, balancing polymer-mediated lithium stabilization against limited accommodation space. Binder loading is therefore an active design parameter for polymer-regulated energy-storage interfaces.

Long-range quantum network nodes require the combination of strong light-matter coupling, long coherence times and in situ spectral control at telecom wavelengths. The coherence of erbium in integrated devices is held back by its hosts, which do not simultaneously provide the weakly magnetic nuclear-spin environment and the well-defined substitutional sites found in coherence-optimised bulk crystals. Here we bring such an optimised crystal onto a photonic chip, by bonding an Er${^{3+}}$:CaWO${_{4}}$ host without an adhesive interlayer to a high-${Q}$ electro-optically tuneable thin-film lithium niobate microring resonator. At an effective temperature of ${75}$ mK and a field of only ${0.2}$ T, the bonded ensemble retains an effective homogeneous linewidth of ${289\pm34}$ Hz (${T_\text{M}=1.10\pm0.13}$ ms), with spectral diffusion proceeding at ${86\pm18}$ Hz and saturating at ${1.5\pm0.2}$ kHz. Electro-optically tuning the resonator through the erbium optical transition resolves an avoided crossing with a collective cooperativity of ${C=6.7\pm0.4}$. Exploiting superhyperfine coupling to the host's ${^{183}}$W nuclear spins, we store and retrieve optical phase information over ${5}$ s with a visibility of ${0.935\pm0.015}$. Strong collective coupling, millisecond coherence and in situ spectral tuning in a single device thus establish heterogeneous integration leveraging coherence-optimised hosts as a route to scalable telecom quantum networks.

Although the Alcubierre Warp Drive is theoretically capable of providing faster-than-light travel, it may be difficult to use for this purpose. But is it useful for slower-than-light travel? We begin by observing the that the warp bubble will act to protect the ship from dust particles and other space debris (a potentially serious hazard even at 10% the speed of light). We then explore several modifications of the Alcubierre Warp Drive, e.g. a "deflector shield", with the perspective of keeping a ship safe from collisions with particles, projectiles, rogue planets, and other dangers of space travel.

Engineering optical responses at surfaces, including reflection, absorption, transmission, and emission, is crucial for advanced photonic, energy, thermal-management, and optoelectronic applications. This thesis investigates epsilon-near-zero (ENZ) materials, particularly indium tin oxide (ITO) and titanium nitride (TiN), for controlling light-matter interactions through engineered optical coatings and nanostructures. It also explores the enhancement of optical absorption and emission in two-dimensional (2D) materials such as monolayer molybdenum disulphide (MoS2), whose atomic-scale thickness inherently limits light interaction. The research integrates theoretical analysis, finite-element simulations, nanofabrication, and experimental characterization to develop and validate ENZ-based optical platforms. An ITO-based multilayer coating is demonstrated to provide step-function-like reflectivity, with low reflectance in the visible-to-near-infrared range and high reflectance beyond a tunable cut-in wavelength, offering potential for spectrally selective energy management. Building on this, an ITO-based grating structure is developed to achieve broadband and angularly robust near-infrared absorption, demonstrating its potential for thermal-emission applications. TiN thin films are further demonstrated as an effective platform for enhancing the absorption and emission of monolayer MoS2 without complex nanostructuring. Complementary studies investigate substrate-induced strain and ion-irradiation-induced defects as approaches for tailoring the electronic and optical properties of MoS2. Overall, this work establishes ENZ materials based engineered surfaces as versatile platforms for spectral and light-matter interaction control, contributing to efficient, tunable, thermally stable, and scalable solutions for energy, thermal management, and 2D-material-based optoelectronic applications.

The prospects and the implementation of single-ion nuclear clocks of $^{229}$Th$^{q+}$ ions in their highest charge states $q=90, \ldots, 87$ are discussed. Highly-ionized-thorium clocks are ideal for tests of fundamental interactions since the ions are elementary quantum systems composed of only a few building blocks. Two cases of $^{229}$Th$^{q+}$ clocks excel: a) one-electron $^{229}$Th$^{89+}$ that combines two nuclear-clock transitions in the VUV with hyperfine IR atomic-clock transitions, and, b) fully ionized $^{229}$Th$^{90+}$ which constitutes the prototype of a nuclear clock, one without any electrons. We evaluate the feasibility of such clocks by means of quantum logic spectroscopy (QLS) in linear Paul traps. Due to its universal nature, the QLS approach allows for systematic clock comparisons using different charge states as well as different spectroscopy transitions on the same experimental platform. A valuable asset towards single-ion $^{229}$Th$^{q+}$ clocks is the process of nuclear hyperfine mixing that enables the tunability of the natural linewidth of the clock transition over more than five orders of magnitude by changing the charge state.

This paper presents a family of high-resolution weighted essentially non-oscillatory compact least-squares schemes with implicit time integration for the compressible Navier-Stokes equations on curvilinear grids. Compared with the original compact least-squares schemes, the proposed method introduces two main improvements. First, instead of enforcing the accuracy constraints over the entire computational domain, including discontinuous regions, it constructs the reconstruction matrix only along smooth reconstruction lines using an accuracy-preserving weighting strategy. This treatment effectively suppresses the persistent high-frequency oscillations observed in the original compact least-squares schemes and yields sharper profiles near discontinuities. Second, the method simplifies the shock-capturing procedure and improves efficiency by using a single set of polynomials, whereas the original compact least-squares schemes require both unlimited and limited polynomials. Combined with spectral optimization, the proposed method exhibits more favorable spectral properties than conventional weighted essentially non-oscillatory schemes. The smoothness indicators and penalty matrices are constructed through an efficient iterative procedure with modest additional cost. Numerical results for inviscid and viscous one-, two-, and three-dimensional flows demonstrate that the proposed method provides robust shock-capturing capability while maintaining high resolution in smooth regions and across contact discontinuities.

In aircraft engines, functionally graded abradable coatings are used to control blade-tip clearance, but their durability is governed by effects that are often treated separately in existing models, including temperature-dependent viscoelastic softening, progressive damage, deposition-induced microstructural modulation, and geometric tolerances. This study integrates these effects within a unified multiphysics–probabilistic framework. The solved domain is a local through-thickness coating column driven by prescribed strain and temperature histories that include thermal eigenstrain and coating–substrate expansion mismatch. The results show that periodic property modulation increases end-of-cycle damage relative to the monotonic gradient and concentrates the maximum stress within a localized modulation crest. Propagating symmetric geometric tolerances through the coupled solver produces a strongly right-skewed damage distribution and a higher classification-level exceedance probability for the modulated gradient than for the monotonic gradient. This exceedance behavior cannot be obtained from a deterministic analysis performed at nominal geometry. The implementation is verified through spatial and temporal refinement, closed-form unit tests, nested Monte Carlo convergence with Wilson confidence intervals, and a hold-out-validated polynomial response surface. Numerical verification is clearly distinguished from experimental validation, and the simulated case is presented as a generic benchmark rather than an identified material model. The framework links deposition parameters and tolerance bands to damage-exceedance risk, supporting reliability-oriented screening of graded and multilayer coating systems.

In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs). Perforated microstructures induce complex boundary conditions and fine-scale flow features that are difficult for standard neural networks to resolve. Conventional PINNs, even when combined with advanced training techniques, can suffer from a loss of accuracy and efficiency as the number of perforations increases. One important source of this difficulty is the soft enforcement of boundary conditions through penalty terms, which can lead to stiffness, gradient conflicts, and poor resolution of near-boundary flow structures. Hard constraints provide an alternative by encoding boundary conditions exactly into the network ansatz, but may introduce undesirable non-local effects due to the global nature of the approximation. To address these challenges, finite basis PINNs (FBPINNs), which are based on domain decomposition and localisation principles, are used together with hard boundary constraints that efficiently encode perforation-related boundary conditions. This approach helps mitigate spectral bias, improves overall accuracy, and exhibits convergence that is only weakly affected by the number of perforations, thereby providing an efficient and highly parallelisable neural network framework. The proposed approach is further supported with theoretical arguments, specifically focusing on the localisation and approximation properties of FBPINNs.

Quantum nonlocality, typically revealed through entanglement distribution across quantum networks, is a cornerstone of quantum information science. Long-distance distribution of entanglement requires the information carrier, i.e. flying photons, to operate in the minimum-loss telecom band of optical fiber. While extensive efforts have been devoted to the direct generation of entanglement between C-band telecom photons and various stationary spins, the verification of quantum nonlocality remains an outstanding challenge. Here, utilizing a dipole transition in rubidium atoms with a wavelength of 1530 nm and a cavity-assisted protocol, we achieve resonant excitation and direct emission of C-band telecom photons from a single atom, generating spin-photon entanglement with a measured Bell state fidelity exceeding 91.4%. We then verify Bell nonlocality by observing a Bell inequality violation of 2.455(77) > 2 using this high-quality entangled pair. These results extend the wavelength of a single-atom quantum emitter to the telecom C-band, achieving sufficiently high-fidelity spin-photon entanglement to finally verify Bell nonlocality. This work thereby provides a promising building block for a large-scale atom-based quantum network capable of distributed quantum metrology and long-distance quantum communication.

Coronal mass ejections (CMEs) from the Sun can have severe impacts on the Earth environment in the form of geomagnetic storms. These storms pose a risk to the global technological infrastructure, making the prediction of these events imperative. In this paper, we have broadened the statistical verification of the Bz4Cast tool, the first empirically-driven model to forecast solar wind magnetic vectors inside a CME prior to their Earth arrival. Twenty five CME events (between 2012 and 2016) have been tested with the Bz4Cast model, and the skills have been compared to the heuristic approach of NOAA's Space Weather Prediction Center (SWPC) G-scale for 3-day geomagnetic storm forecasts. For a broad range of scores, and within uncertainty, the Bz4Cast architecture provided the same skill as the experienced on-duty forecasters at SWPC. The most prominent difference is that the Bz4Cast architecture provides a slightly higher false alarm ratio than the SWPC 3-day forecast.

This study evaluates the sum-connectivity ($SGO$) and product-connectivity ($PGO$) Gourava indices as molecular descriptors for benzenoid hydrocarbons. Using a dataset of 30 benzenoid structures, we compare least-squares regression models for predicting $\pi$-electronic energies ($E_{\pi}$) and find that $SGO$ yields a markedly better fit than $PGO$ across molecular edge types. The indices are further assessed using three validation designs: (i) correlation analysis, in which $SGO$ exhibits strong yet non-perfect inverse correlations with standard descriptors ($M_1, M_2, SO, DSO,$ and $ABS$; $r\in[-0.9923,-0.8936]$), suggesting complementary structural information; (ii) degeneracy analysis on Octane, Nonane, and order-$10$ tree datasets, where $SGO$ attains low degeneracy rates (22.22%, 40.00%, and 42.45%); and (iii) structure-sensitivity analysis on trees of order $n=10$, showing 74% higher sensitivity than $DSO$ while maintaining a high structure-abruptness ratio ($SA = 0.474386$). Overall, $SGO$ offers a favorable balance between discriminative power and numerical stability, supporting its applicability in QSPR modeling and related theoretical studies.

The remarkable sensitivity, compressive nonlinearity, and frequency selectivity of the mammalian cochlea arise from an active process that amplifies the passive mechanical response of the basilar membrane. Outer hair cells are widely regarded as the primary effectors of this active process in the basal regions of the cochlea. This active contribution progressively decreases with increasing stimulus level. Motivated by these observations, a minimal cochlear model is investigated in which each location is represented by a forced damped oscillator with an exponential displacement-dependent active feedback. The oscillators are coupled through the cochlear fluid and also by elastic and dissipative longitudinal interactions to form a one-dimensional distributed model. The model reproduces key features of cochlear mechanics, including level-dependent amplification, compressive nonlinearity, frequency selectivity, traveling-wave propagation, and phase accumulation. Comparison with a simplified cubic nonlinear model has been carried out. Even though the cubic nonlinearity describes the response for weak stimuli, at higher stimulus levels it deviates from the exponential model and fails to reproduce the gradual transition towards predominantly passive behavior. Longitudinal coupling broadens the frequency response, modifies the traveling wave profile, and increases phase accumulation. The proposed model provides a simple physical framework for understanding how local active processes and longitudinal mechanical interactions together shape the nonlinear response of the cochlea.

Simulating the coupled, nonequilibrium dynamics of electrons and nuclei is a central challenge in chemistry, physics, and materials science, governing phenomena from photocatalysis to quantum information. The primary bottleneck has been the lack of a general, accurate, and efficient method for modeling the complete excited-state landscape: the potential energy surfaces, forces, and non-adiabatic couplings for multiple electronic states. While machine learning has revolutionized ground-state simulations and shown promise for excited states in molecules, a unified framework that solves the complete multi-state problem for general condensed matter systems has remained elusive. Here we introduce on-the-fly N${^2}$AMD (Neural network NAMD), a machine learning framework that makes on-the-fly NAMD in solids a reality. By employing an equivariant neural network to predict the system Hamiltonian, the framework delivers excited-state energies, forces, and non-adiabatic coupling vectors at a fraction of the cost of ab initio calculations. Crucially, it allows simulations with hybrid functional accuracy, a level of approach previously inaccessible for NAMD. We showcase its capabilities with three topical examples: correcting order-of-magnitude errors in carrier dynamics predicted by conventional procedure in a MoS$_2$/WS$_2$ heterostructure, simulating previously inaccessible photoinduced ferroelectric switching, and capturing real-time polaron formation in TiO$_2$ at the hybrid-functional level. On-the-fly N${^2}$AMD moves beyond the limitations of equilibrium theory, establishing a new paradigm for the predictive, first-principles design of materials operating far from equilibrium.

Motivated by recent reports of enhanced superconducting performance in several families of iron-based superconductors (IBS) processed by high-pressure (HP) synthesis, we investigate the influence of high gas pressure and high-temperature synthesis (HP-HTS) process on the structural, microstructural, electrical transport, and magnetic properties of Pr-based oxypnictide PrFeAsO1-xFx (Pr1111) using the processing conditions of 0.5 GPa for 1 h previously optimized for other IBS families. Representative underdoped (x = 0.2), optimal doped (x = 0.3), and overdoped (x = 0.5) compositions from the ambient-pressure electronic phase diagram of Pr1111 are selected to evaluate its composition-dependent effects of HP-HTS. The results demonstrate that HP-HTS enhances fluorine incorporation, improves phase formation, and produces a denser microstructure with improved grain connectivity in the underdoped and optimal doped compositions. Magnetic measurements reveal increased in the superconducting transition temperature (Tc) of ~1 K for x = 0.2 and ~6 K for x = 0.3, whereas only a marginal improvement in the critical current density is observed. Electrical resistivity measurements of the underdoped composition show a slight increase in Tc accompanied by a broader resistive transition, indicating residual structural inhomogeneity. In contrast, the overdoped composition exhibits increased impurity phase segregation, accompanied by suppression of superconductivity. These results demonstrate that the effectiveness of HP-HTS in Pr1111 is strongly composition dependent and governed by the interplay among fluorine incorporation, phase stability, and microstructural evolution, highlighting the need for further optimization of the HP-HTS processing conditions.