Papers

We present a formulation for the linear stability of the miscible Rayleigh-Taylor instability, retaining viscosity, Fickian mass diffusion, and non-Boussinesq effects. Rather than adopting the diffusive corrections of Duff, Harlow, and Hirt (1962) or relying on the viscous eigenvalue problem of Chandrasekhar (1961), the present formulation is derived directly from the incompressible variable-density governing equations. Both approaches are recovered as limiting cases, extending Morgan, Likhachev, and Jacobs (2016). The governing equations admit a time-evolving self-similar diffusive base state in which an error-function density profile is accompanied by a nonzero vertical base velocity required by the non-solenoidal constraint. Linearization yields a reduced coupled formulation for the vertical velocity and density perturbations, suitable for both theoretical analysis and computation. Within the quasi-steady-state approximation, we show that the formulation reduces, in the infinite-Schmidt-number limit, to the classical viscous immiscible theory and recovers the Chandrasekhar eigenvalue problem. At finite Schmidt number, diffusion alters the growth-rate spectrum and its high-wavenumber structure. Beyond the spectral cutoff we establish the scaling $\omega_r \sim -\lambda_m k^2$, where $\lambda_m$ is determined by the competition between the locally stratified kinematic viscosity and the reference diffusive scale. By isolating the effect of diffusion, we show that its stabilizing influence weakens with increasing density stratification. Buoyancy production becomes bimodal and shifts toward the lighter-fluid side, while pressure production grows to rival buoyancy and acts as an energy source on the heavier side of stratification. Together, these results clarify when classical diffusive corrections remain applicable and when diffusion and non-Boussinesq coupling must be retained.

Polarization-entangled photon pairs are essential resources for quantum information technologies, yet realizing compact sources with intrinsically controllable entanglement remains challenging. Van der Waals (vdW) nonlinear materials such as NbOCl2 provide atomically thin platforms for quantum light generation, yet their native crystalline anisotropies as natural materials impose limitations on accessible quantum states. Here, we develop a resonant vdW nonlinear metasurface based on NbOCl2 that exploits its intrinsic optical anisotropy to engineer polarization-dependent nonlinear responses. The anisotropic optical dispersion enables selective manipulation of resonant modes, resulting in a three-order-of-magnitude enhancement of the nonlinear response along the c axis. By further tailoring these resonant modes, we redistribute the effective second-order nonlinear susceptibility tensor between orthogonal polarization channels, balancing the spontaneous parametric down-conversion pathways along the b and c axes. This enables polarization-entangled photon generation with a measured fidelity of up to 92%. Our work establishes metasurface-enabled nonlinear optical engineering as a strategy for enhancing and controlling quantum light generation in vdW materials, providing a pathway toward scalable quantum photonic platforms.

We develop a framework to use multiparameter persistent homology (PH) to examine access to heterogeneous-quality resources and exposure to heterogeneous-severity nuisances in a geographic region. Persistent homology, which is a type of topological data analysis {(TDA)}, has been employed previously to examine resource coverage. Unlike prior approaches, which used one-parameter PH to study resource coverage and nuisance exposure, our method accounts for heterogeneous-quality resources. Our framework, which employs a computationally-efficient approximation of multiparameter PH, allows one to study access to any resource ({or} exposure of any nuisance) using any notion of quality (or severity). Using the city of Chicago as an example region, we employ our framework to detect clusters of poor access to public parks, overexposure to landfills, and both underexposure and overexposure to pubs and bars.

Understanding local electric fields at oxide interfaces is essential for linking interfacial electrostatics to device functionality, yet conventional electrical measurements infer these fields only indirectly. Here, we combine operando scanning transmission electron microscope electron-beam-induced current (STEM-EBIC) with four-dimensional-STEM (4D-STEM) to quantitatively reconstruct the bias-dependent electric field spatial distribution across an oxide Schottky junction at nanometer scale. Using La0.67Sr0.33MnO3/Nb:SrTiO3 (LSMO/NSTO) as a model system, we fabricate an electron-transparent junction on a MEMS biasing platform and verify that it retains the rectifying transport behavior. STEM-EBIC provides complementary information addressing several key limitations in quantitative 4D-STEM field mapping for heterojunctions. The reconstructed electric field profiles show a pronounced nonlinear decay within the depletion region and an extended penetration into the LSMO. These results directly reveal the deviations of oxides Schottky junction from the ideal conventional Schottky depletion model, providing experimental signatures of non-classical interfacial electrostatics. Our correlative approach enables quantitative nanoscale electric field mapping in operating oxide heterojunctions, providing a basis for linking interfacial electrostatics to macroscopic transport and guiding oxide devices design.

We investigate the spectral stability of quasinormal modes in nonconformal holographic QCD models using pseudospectral analysis. We first consider the soft-wall model, focusing on scalar and vector fields, and then extend the analysis to the analytic Improved Holographic QCD (IHQCD) model, where we study tensor glueball fluctuations. In both cases, the equations of motion are formulated as linear eigenvalue problems, allowing the instability of the quasinormal spectrum to small perturbations to be quantified through the pseudospectrum. We find that the spectral stability of the quasinormal modes exhibits a nontrivial dependence on temperature, reflecting the presence of intrinsic dimensionful scales in holographic QCD models. As the temperature increases, the magnitude of the imaginary part of the quasinormal frequencies grows, signaling an increasing decay rate and the progressive loss of coherence of the corresponding hadronic excitations. At sufficiently high temperatures, the quasinormal frequencies approach an approximately linear dependence on temperature, although this regime is reached only after the associated hadronic states have melted. We further compare the pseudospectral instability with the behavior of the corresponding spectral functions. Our results indicate that the growth of pseudospectral instability provides a complementary characterization of the loss of spectral stability and can serve as a useful diagnostic of hadronic dissociation and melting in holographic QCD.

Isoflux control in spherical tokamaks requires coordinated plasma-current and boundary regulation under coil-voltage and computational constraints. This study develops observer-based constrained model predictive control (MPC) for EXL-50U. Vacuum-vessel spatial coarsening reduces a 538-state linearized model to 40 states while retaining control-relevant responses. A Kalman observer provides full-state estimates, and MPC jointly optimizes current and boundary-flux tracking with explicit voltage bounds. Matrix precomputation, specialized solver code generation, and structured linear-system solution reduce online computation. Nonlinear free-boundary Grad–Shafranov evolutive simulations evaluate nominal operation, measurement noise, configuration mismatch, a one-step delay, and combined noise and delay against proportional–integral–derivative (PID) control and a linear–quadratic regulator (LQR). Nominal MPC root-mean-square errors are 1.126 kA for plasma current, 0.0164 m for last-closed-flux-surface geometry, and 2.463 mWb for the worst flux channel, all below both baselines. With noise, the boundary error is 0.0199 m over the common evaluation window, and regulation is sustained throughout the test. MPC completes a limiter-to-divertor transition without relinearization or retuning and maintains regulation under delay and combined disturbances. Across all five cases, mean MPC computation times are 0.413–0.441 ms, with all 99th percentiles below 1 ms. These results support joint current and isoflux regulation and millisecond-scale computational feasibility, providing a basis for future EXL-50U experiments.

We give a dynamical characterization of the Chandrasekhar mass for cold white dwarfs governed by the radial Euler–Poisson equations with the exact Chandrasekhar equation of state. This mass is the infimum of masses for which a finite-energy classical solution with a physical vacuum can contract its entire support to a point in finite time. Below it, conservation of energy prevents complete collapse. For every mass in a sufficiently small interval above it, we construct a solution whose support shrinks to the origin and whose density concentrates there with the full mass of the star. The interior approaches a collapsing Goldreich–Weber profile. Near the vacuum boundary, a different rescaling gives a limiting profile that connects the high- and low-density regimes of the pressure law. We determine this profile and show that, after adding the electron rest energy, the conserved energy equals that of the Goldreich–Weber reference solution. The proof combines matched asymptotic expansions with local existence and energy estimates that extend solutions backward from times approaching collapse to a common earlier time.

We investigate some aspects of holography in de Sitter space, pertaining to the proposal for the dual theory residing on the late-time boundary [arXiv:astro-ph/0210603v5], including a Fermionic field that satisfies the Dirac equation. The modes of the solutions near the boundary are found to possess equal and oscillatory fall-off, similar to the scalar field belonging to the principal series representation of the isometry group of de Sitter space. We evaluate, by suitably adding a boundary term to the Dirac action, the wavefunctional of the Bunch Davies vacuum in path integral formalism in terms of the projections of the field on the eigenspaces of the time-like ${\gamma}$-matrix. We validate our path-integral construction of the wavefunctional by reproducing the two-point function between the field operators in the vacuum state as computed in the canonical formalism. By appropriately identifying the boundary sources in terms of the projected components of the bulk field, we find that a single Dirac field in the bulk corresponds to a pair of primary spinor fields in the boundary theory and show that the resulting wavefunction coefficients satisfy the conformal Ward identities. We check the robustness of our holographic map under the addition of a Yukawa interaction considering the two cases where the scalar field in the interaction term belongs to the complementary series and the principal series representations of the isometry group of de Sitter space respectively.

Long-horizon micromagnetic simulation remains expensive because conventional and learned solvers typically propagate Landau–Lifshitz–Gilbert (LLG) dynamics step by step. Existing learned approaches generally retain stepwise integration or model deterministic evolution, leaving full-field, direct-horizon stochastic prediction largely unexplored. We propose FLARE, a flow-matching framework that recasts stochastic finite-time magnetization prediction as conditional transport over anchor-relative local axis-angle rotations. This rotation-space formulation respects the intrinsic geometry of magnetization dynamics and preserves pointwise unit norm by construction. By explicitly conditioning on the physical prediction horizon, FLARE directly generates full-field stochastic endpoints across multiple target times without stepwise integration. Against the strongest single-checkpoint external baseline on each metric, FLARE achieves 29.9% lower angular energy distance ($15.30^\circ$), and a 37.3% lower fair energy score (0.393). On a representative composed 5-ns two-segment protocol, FLARE achieves a $3{,}062\times$ best-batch speedup over the widely used GPU micromagnetic solver MuMax$^3$ on a single GPU.

We implement the machine-learned Skala exchange-correlation (XC) functional natively in CP2K using its Gaussian and plane-wave (GPW) and Gaussian and augmented-plane-wave (GAPW) methods. A joint one-centre reconstruction of density, density gradients, and kinetic-energy density before functional evaluation preserves mixed gradient terms and nonlocal couplings between smooth and atom-local contributions in all-electron and pseudopotential calculations. An XC-specific GAPW representation resolves rapidly varying local contributions on atom-centred grids, reducing plane-wave requirements for pseudopotential calculations. The implementation includes Brillouin-zone sampling and point-group symmetry reduction. With sufficiently flexible orbital bases, it retains the molecular benchmark accuracy of our earlier GauXC formulation. All-electron Skala-D3(BJ) calculations yield a mean absolute error (MAE) of 1.54 kJ mol$^{-1}$ against diffusion Monte Carlo for crystalline CO$_2$, NH$_3$, and urea, spanning dispersion, quadrupolar electrostatics, and hydrogen bonding. For all thirteen DMC-ICE13 phases, the MAEs are 1.16 kJ mol$^{-1}$ for absolute lattice energies and 0.82 kJ mol$^{-1}$ for the twelve relative energies to ice Ih. At fixed experimental geometries, all-electron/mixed-core calculations give a band-gap MAE of 0.43 eV on a 15-material set, substantially below commonly used semilocal functionals and comparable to widely used hybrid functionals. The LC10 benchmark nevertheless reveals systematically underestimated equilibrium lattice constants, indicating structural overbinding. This framework connects molecular Skala to condensed-phase electronic structure and enables future development using periodic many-body reference data.

Polymer informatics has matured from isolated property-prediction studies into an integrated discipline that couples data, models, and decision-making across the polymer design cycle. Yet it still falls short of a true intelligent system capable of inverse design on demand, causal reasoning across chemistry, processing, and performance, and closed-loop autonomous experimentation. This article traces a roadmap toward that goal, grounded in experience developing two complementary agentic and informatics platforms. Central to this vision is a modular, agent-directed architecture in which a polymer super-intelligence layer interprets a researcher's design question in natural language and coordinates domain-specialized tools, matched to the available data, for neat polymers, composites and formulations, solvents, and synthesis and processing. The resulting system spans the full chain from molecular design through processing to product-level performance and human perception. Orchestrated together, its generative design, synthesis-feasibility reasoning, and practicality assessment already form the decision-making core of a self-driving polymer laboratory, leaving autonomous, closed-loop experimentation as the principal step that remains. We survey emerging capabilities along this roadmap, including automated extraction of property data from the literature, chemistry-aware representation, property prediction for membranes and sustainable plastics, solubility and green-solvent recommendation, and computer-guided retrosynthetic planning, exposing the remaining gaps and the research and infrastructure investments needed to move from today's orchestrated tool ecosystem toward a genuinely super-intelligent polymer design partner.

Nonlinear oscillators exhibit rich collective phenomena including synchronization, bifurcation, and chaos. Experimentally accessing multimode nonlinear dynamics, however, remains challenging because low-order internal resonances readily induce mode locking and suppress stable multimode oscillation. Here, we demonstrate a transverse-mode-coupled optomechanical platform that combines engineered collective mechanical modes with optically controllable nonlinear interactions. The engineered transverse mechanical modes enable stable two- and three-mode self-sustained oscillations while suppressing trivial low-order internal resonances. By varying the laser frequency, we observe successive beat-frequency fractionalization ({\Delta}f/2 and {\Delta}f/3), followed by a broadband state exhibiting enhanced trajectory divergence consistent with deterministic chaos. These results establish transverse-mode-coupled optomechanical resonators as a scalable and tunable platform for exploring high-dimensional nonlinear dynamics in interacting mechanical networks.

We investigate $\mathbb{Z}_2$ symmetry restoration in a real $\lambda\phi^4$ theory confined to a finite cylindrical region undergoing rigid rotation. The finite transverse extent is imposed through Dirichlet boundary conditions, resulting in a discrete Fourier-Bessel spectrum and an explicit radial dependence of the fluctuation propagator. Using the background-field method, we derive the one-loop effective potential while retaining the spatial structure induced by the finite geometry. At finite temperature, rotation modifies the thermal mode energies through angular-momentum-dependent shifts, and the coincident-point propagator generates a position-dependent thermal self-energy that is incorporated through ring resummation. We use the resulting spatially resolved effective potential to determine the symmetry-restoration temperature $T_c(\Omega,R)$ and examine its dependence on the angular velocity and transverse size. The results show that the finite transverse size of the system modifies the symmetry-restoration temperature, leading to a nontrivial dependence of $T_c(\Omega,R)$ on $R$. An additional scaling behavior emerges when the normalized critical temperature is expressed in terms of the boundary velocity $\Omega R$: systems with different transverse sizes exhibit the same relative modification of $T_c$ when their boundary velocities are equal. This scaling persists after the inclusion of the position-dependent thermal self-energy through ring resummation, indicating that the $\Omega R$ dependence of the rotational response is maintained in the interacting finite system.

We study a charged particle moving outside a spiral (screw) dislocation in a uniform magnetic field. Although the geometry is locally Euclidean, its global screw identification couples the conserved axial and azimuthal quantities through the combination \(\mathcal{J}=\ell-\beta k\) After eliminating the cyclic coordinates, the radial motion is governed by an inverse-square term determined by $\mathcal{J}$ and a harmonic confining term generated by the magnetic field. The corresponding reduced quantum problem is exactly solvable for $q\mathcal{B}_0\neq0$, yielding an equally spaced spectrum with an orientation-dependent energy shift. The radial probability density depends on $\mathcal{J}$, and opposite values of the screw-modified quantum number have identical spatial profiles but different energies for a fixed magnetic-field orientation. The radial size scales as \(\sqrt{\langle r^2\rangle_n}\propto |q\mathcal{B}_0|^{-1/2}\), with the magnetic length setting the localization scale. At $q\mathcal{B}_0=0$, the confining term vanishes, and the problem reduces to a scale-free inverse-square system. Thus, the screw parameter enters the dynamics through the global coupling of the conserved axial and azimuthal quantities, whereas the magnetic field provides radial confinement and its orientation determines the spectral asymmetry.

An interesting question for discussion in university physics courses is whether gravity can conflict with the second law of thermodynamics. In this work, we address this question by comparing the behavior of an ideal gas in two conceptually different regimes: one in which gravitational effects can be neglected and another in which self-gravity becomes important. In the first case, free expansion provides the familiar example in which an increase in the volume accessible to the gas leads to an increase in entropy. Self-gravitating systems behave differently: gravitational contraction can reduce the volume occupied by matter while releasing energy and increasing the entropy of the surroundings. This illustrates why the usual intuition that increasing entropy necessarily corresponds to increasing spatial dispersion cannot be applied directly to self-gravitating systems. Using elementary thermodynamic arguments and a minimal amount of mathematics, we discuss this apparent tension and show how entropy must be considered for the complete system, including emitted radiation. The discussion is finally extended to black holes and Hawking radiation, where the appropriate framework is the generalized second law of thermodynamics. The analysis is intended to provide a pedagogical bridge between elementary thermodynamics and some of the distinctive thermodynamic properties of gravitating systems.

This paper investigates static, spherically symmetric traversable wormholes supported by Casimir energy within de Rham-Gabadadze-Tolley (dRGT) massive gravity. By deriving the exact shape function $b(r) = r_0 + \frac{\pi^3(-r + r_0)}{90 r r_0} - \frac{1}{2} C m_g^2 (r - r_0)[2C c_2 + c_1(r + r_0)]$, we verify that the geometry satisfies the local Morris–Thorne throat and traversability conditions, including $b(r_0)=r_0$ and $b'(r_0)<1$. For the nonzero massive-gravity parameters considered here, the resulting spacetime is not asymptotically flat, and its large-$r$ behavior is governed by the massive-gravity contributions to the shape function. The Casimir energy density $\rho = -\pi^2/(720 r^4)$ ensures the Null Energy Condition is violated throughout the throat region, as demonstrated by the negative behavior of $(\rho + p_r)$ and $(\rho - |p_r|)$ across all parameter values. Analysis of the volume integral quantifier reveals that the massive gravity parameter $m_g^2 c_2$ directly regulates the exotic matter requirement, with the integrated NEC violation becoming more negative as $m_g^2 c_2$ increases from $0.1$ to $0.5$. The mechanical equilibrium is rigorously established via the generalized Tolman-Oppenheimer-Volkoff equation, where the anisotropic force precisely balances the gravitational and hydrostatic forces. The quasinormal mode spectrum for scalar perturbations is extracted using both the analytical Mashhoon method and direct numerical integration. The effective potential forms a symmetric barrier at the throat, with the peak height increasing with the multipole number $\ell$. The damping rate $|\omega_I|$ grows systematically with increasing massive gravity parameter. These distinct spectral signatures provide robust theoretical markers for distinguishing Casimir wormholes from black holes in future gravitational wave observations.

The information-theoretic construct of synergy refers to the statistical structure that is contained in three or more variables, but not in any subset of them. Here we leverage recent advances in multivariate information theory to show that synergy is far more prevalent in complex systems than previously thought. In particular, we show that many-body systems tend to become strongly dominated by synergy as the number of subcomponents grows. At the same time, our results also reveal that commonly used tools for statistical modelling severely underestimate synergistic structures. These findings imply that synergy constitutes a prevalent, yet often invisible, informational component of complex systems. With a certain poetic licence, we interpret these results as suggesting that synergy is the dark matter of statistics - interdependencies that we know exist, but standard instruments fail to detect.

The geometric shadow of a black hole cannot observationally distinguish horizonless exotic compact objects. We break this degeneracy by mapping the fundamental quantum decoherence of the horizon (the Danielson-Satishchandran-Wald mechanism) into a macroscopic effective reflectivity $\mathcal{R}$. Utilizing Kerr ray tracing, we show that a partially reflective boundary ($\mathcal{R}>0$) generates delayed electromagnetic echoes under both specular and diffuse (Lambertian) conditions. In the spatial domain, these echoes illuminate the inner shadow and alter low-frequency visibilities, while leaving metric-governed photon subrings unchanged. The signal strength scales with the membrane compactness $\epsilon$ as $\epsilon^{\Gamma}$, where $\Gamma=0$ for specular reflection and $\Gamma\to1$ for diffuse re-emission due to escape-cone collapse. This brings specular reflectivities down to $\mathcal{R}\simeq0.12$ (ngEHT) and $0.04$ (BHEX) within reach of static imaging. For Sagittarius A$^\ast$, we translate these echoes into a robust time-domain signature. Using an Autocorrelation Function (ACF) pipeline, we demonstrate that single-flare echoes can be cleanly extracted from severe accretion red noise, achieving a $3\sigma$ detection for amplitudes $\mathcal{A}\gtrsim0.3$ within 15 to 33 hours of continuous monitoring. This framework provides a directly deployable pathway to test black hole unitarity.

We formulate a generally covariant extension of London electrodynamics in four-dimensional curved spacetime and investigate the propagation of electromagnetic perturbations in a superconducting medium surrounding a black hole. The ordinary London relation is promoted to a gauge-invariant four-dimensional constitutive equation involving the electromagnetic four-potential and the phase of the superconducting condensate. When combined with the covariant Maxwell equations, the resulting system is equivalent, in the London (unitary) gauge, to a Proca theory with an effective photon mass set by the inverse London penetration depth. We derive the corresponding Schrödinger-like wave equations for electromagnetic perturbations in the axial and polar sectors of the Schwarzschild spacetime in the presence of the superconducting plasma. The axial sector is governed by a single Regge–Wheeler-type equation whose effective potential contains the London mass term, whereas the polar sector contains two coupled physical degrees of freedom. Quasinormal-mode boundary conditions are formulated for the Schwarzschild geometry. The London penetration depth shifts the oscillation frequencies, modifies the damping rates, and can generate long-lived quasibound configurations when the effective field mass is sufficiently large. This formalism provides a framework for studying electromagnetic relaxation in curved superconducting media, compact objects containing superconducting phases, and effective massive-vector fields around black holes.

Ocean wave forecasting is essential for maritime safety, offshore operations, and coastal resilience, yet remains challenging due to systematic biases in physics-based models. Physical models, while widely used, rely on approximations and parameterizations that limit their accuracy under complex ocean-atmosphere conditions. To enhance ocean wave forecasting, we propose BridgeCast, within a physics-AI hybrid framework for bias correction. BridgeCast is a probabilistic model based on conditional flow matching (CFM) that learns to transform physical model forecasts into reanalysis-like fields. It treats physical forecasts as corrupted observations and employs a continuous-time generative process to bridge their distribution toward that of reanalysis data. BridgeCast is parameterized by a Transformer-based architecture that enables spatiotemporal modeling, incorporation of exogenous atmospheric variables, and flexible inference via both ordinary and stochastic differential equation formulations. Extensive experiments on real-world datasets demonstrate that BridgeCast consistently outperforms state-of-the-art baselines across regions and forecast lead times.

A charge-$r$ coupling vortex can remain as one fused order-$r$ zero or split into $r$ nearby unit-charge zeros after weak symmetry breaking. The two configurations have the same total winding and the same number of dark states in the lowest-Landau-level projection, so neither the imposed orbital angular momentum nor the total winding number distinguishes their local geometry. We study this distinction in a two-component Haldane-sphere model coupled by a Raman field. For monopole flux $N$, the detuning $\tau_{\rm c}$ at which a defect branch crosses zero energy scales as $|\tau_{\rm c}|\sim N^{-(r+1)}$ for a fused zero and $N^{-2}$ for resolved unit zeros. A Feshbach reduction establishes these asymptotic laws for the full multiband Hamiltonian, and numerical calculations in a monopole-harmonic basis confirm the fused-vortex scaling for $r=1,2,3$. For a partially split cluster of diameter $d$, the scaling crosses over when $d$ is comparable to the magnetic length $\ell_B$, allowing $d$ to be inferred spectroscopically even below the spatial resolution of direct imaging.

We study the Ising spin glass with independent, identically distributed couplings on the diamond hierarchical lattice with $n$ branches, of effective dimension $1+\log_2 n$; $n=4$ is the Migdal-Kadanoff lattice of $\mathbb{Z}^3$. For $n\ge4$ and every coupling law with a bounded density we prove that at sufficiently low temperature $T>0$, uniformly in the level of the lattice, the poles are ordered, every spin has Edwards-Anderson parameter $1-O(T)$ when the poles are fixed, and the overlap of two free-boundary replicas has second moment $1-O(T)$. For standard Gaussian couplings, $n=3,4,5,7,8$ and every $T\le T^*(n)=4/15,\,6/7,\,6/5,\,7/4,\,2$ ($0.89$ to $0.98$ times numerical estimates of $T_c$), a computer-assisted proof gives pole order and, as the level tends to infinity, site-overlap order and the blue-cluster statements below; likewise for every larger $n$ at these temperatures. Previously, spin-glass order on these lattices with frustrated independent couplings had been proved only for more than $10^{18}$ branches (Collet and Eckmann, 1984). The key step is growth of the effective coupling under the exact renormalization map: for $n\ge4$, by a one-step contraction, via Rogozin's inequality, of a density bound on an event of high probability; near $T_c$, by interval-arithmetic bounds in the peakedness order. A transfer theorem following the ancestor-chain argument of Collet and Eckmann turns this growth into bulk statements. In the Chayes-Machta-Redner representation the same input gives a blue cluster that contains both poles with probability tending to one and whose expected density is bounded away from zero, while the largest other blue cluster has density tending to zero in probability and in $L^1$; hence blue-cluster density imbalance. To our knowledge this is the first proof of such an imbalance for a spin glass on a graph other than the complete graph.

In this work, we analyze a two-parameter $(\mu, b)$ asymmetric family of traversable wormhole solutions generated by a massless conformally coupled scalar field. We show that, for a suitable range of parameters, the spacetime is everywhere regular and has two asymptotically flat regions. We then define the wormhole throat and verify the flare-out condition, which leads to violations of the classical energy conditions in GR, thereby requiring exotic matter to hold the throat open. We further analyze the motion of photons governed by null geodesics through an effective potential. The resulting trajectories are computed numerically and visualized using embedding diagrams. Following this route, we investigate scalar perturbations governed by the massless Klein-Gordon equation and find the QNM spectrum semianalytically and numerically. Interestingly enough, we show that such perturbations are governed by only one parameter $\mu$. Therefore, in $D = 4$, we find an isospectrality between the wormhole and the BBMB/Extremal Reissner-Nordström black hole. In the spirit of the seminal work of Morris and Thorne, we derive the conditions for traversability and compute the proper time for a traveler to traverse the wormhole. Finally, we discuss possible extensions and future directions for our work.

We present an autonomous model to simulate the daytime variation of sub-ionospheric Very Low Frequency (VLF) signal amplitude, beginning with the computation of the D-region electron density by numerically solving the electron continuity equation (ECE). From the resulting altitude-dependent electron density profile (Ne), we extract Wait's ionospheric parameters (h' and beta) using a log-linear fitting method. The study focuses on two VLF propagation paths (one short and one medium in length) in India, originating from the VTX (18.2 kHz) transmitter. The model employs the Long Wave Propagation Capability (LWPC) framework to reproduce the daytime VLF signal amplitude profile. It accurately captures the daytime variations observed at the Bengaluru (BAN) station, where the ground-wave component is dominant, as well as at Khukurdaha, WB (KHK). A quantitative comparison between the simulated (Asim) and observed (Aobs) amplitudes shows good agreement, supporting the physical consistency and potential predictive capability of the proposed approach.

We study the monic recurrence coefficients of the generalized Charlier polynomials associated with the discrete weight \[ \rho_\mu(k) = \frac{\mu^k}{(k!)^2}, \qquad k\in\mathbb N_0, \qquad \mu>0. \] The coefficients $\beta_n$ and $\gamma_n$ in the recurrence relation \[ P_{n+1}(x) = (x-\beta_n)P_n(x)-\gamma_nP_{n-1}(x) \] are described through complementary moment, determinant, discrete dynamical, and continuous integrable formulations. We give a consistent normalization of the Markov function and its Jacobi continued fraction, and express the recurrence coefficients in terms of Hankel determinants, using a bordered determinant for the diagonal coefficient $\beta_n$. Starting from the original Laguerre–Freud equations, we derive the local recursive system used for computation and relate it to the Toda deformation. We also recall the known Painlevé~V representations associated with the two-parameter generalized Charlier family, in a normalization consistent with the present specialization. Moment/Hankelconstructions provide complementary moment-theoretic realizations of the recurrence coefficients, while the local Laguerre–Freud recursion provides an independent dynamical construction. Their comparison is used for numerical cross-validation. The numerical results are consistent with the leading large-degree behavior \[ \beta_n\sim n, \qquad \gamma_n\sim\mu. \]

The wave-particle decomposition of kinetic relaxation equations is extended to the full Boltzmann equation. An identity transformation writes the collision term as a relaxation toward the local Maxwellian plus a conservative remainder. Along characteristics, the equilibrium integral over a local kinetic horizon defines the wave, and its exact complement, the particle, carries the remainder. The moments of the wave and particle equations are extended Navier-Stokes equations, and the total conservation law and the particle equation form the wave-particle multiscale equations, a closed system, exact for every horizon, that spans a continuous spectrum from the Boltzmann equation to Navier-Stokes hydrodynamics, parametrized by the horizon-to-relaxation ratio. A coupled implicit wave-particle iteration solves this system, updating the conservative variables with the particle fixed and the particle with the predicted wave and an endpoint traction from the macroscopic prediction. Under discrete compatibility assumptions the iteration preserves the discrete Boltzmann solution as its fixed point, and its near-continuum convergence factor is bounded by a particle transport share decaying exponentially with this ratio. Tests on a normal shock, Couette and cavity flows, and hypersonic cylinder and Apollo flows agree with the conventional iterative scheme in rarefied and transition regimes and with Navier-Stokes solutions near the continuum limit. There the wave-particle iteration needs about three to more than four orders of magnitude fewer iterations than this scheme or, where it did not converge, its Shakhov version, and the Boltzmann solution costs one to four times the wall time of a Navier-Stokes solver on the same mesh.

Divergence-free vector fields are fundamental state variables in incompressible flows and many PDE systems. Redundant parameterizations, including Neural Conservation Law (NCL) potentials, map multiple auxiliary representations to the same physical field. Our experiments show that this redundancy can reduce static representation-fitting error by enlarging the set of equivalent solutions, but the resulting many-to-one mapping does not provide a unique state for operator learning. We introduce a minimal representation that encodes a real \(D\)-component divergence-free vector field on a \(D\)-dimensional domain as a real \((D-1)\)-component field on the same domain. Exploiting the transverse structure imposed by incompressibility in Fourier space, we use a Householder orthogonal transformation to construct the reduced coordinates directly. For periodic and closed impermeable fields, the transform is invertible, isometric, and angle-preserving. For open nonperiodic flows, Fourier extension constructs a compatible periodic field, and a minimum-energy rule selects a unique reduced representation. Neural operators then learn temporal evolution entirely in this reduced space. At inference, the predicted \((D-1)\)-component field is decoded directly into a physical divergence-free \(D\)-component field, without predicting an ambient field or applying post-hoc projection. Experiments on static fitting and temporal prediction reveal a task-dependent trade-off: redundancy facilitates static optimization, whereas unique invertible coordinates provide a well-defined state for temporal dynamics. By removing unconstrained longitudinal or null directions from the learned state space, the proposed formulation achieves lower prediction error and greater robustness while preserving divergence freedom by construction.

We demonstrate the generation of near-visible, broadband Kerr frequency combs using a tapered fibre Fabry-Pérot resonator. By incorporating micron-diameter tapered silica fibre into a pulsed-driven Fabry-Pérot configuration, we exploit geometric dispersion engineering to overcome the strong normal dispersion intrinsic to silica (and nearly all materials) at short wavelengths, achieving net anomalous dispersion in the near-visible regime. The strong mode confinement of the tapered fibre simultaneously enhances the Kerr nonlinearity by over an order of magnitude relative to standard fibre, substantially reducing the threshold drive power for nonlinear structure formation. Through precise control of the cavity fabrication, we experimentally demonstrate and numerically confirm a rich suite of coherent, phase-locked nonlinear structures, including conventional anomalous dispersion cavity solitons, zero dispersion solitons with spectral bandwidths exceeding 16 THz between 750 nm and 800 nm, as well as switching wave combs and broadband Raman solitons, the latter also reported here for the first time in the near-visible regime. Our results establish the tapered fibre Fabry-Pérot resonator as a versatile platform for near-visible and potentially visible coherent frequency comb generation.

In many turbulent flows, the quantities of interest are coarse-grained variables, either because resolving the fine scales is computationally prohibitive or because only coarse observations are available; in both cases, data-driven reduced-order models that evolve only these variables are required. Even when the governing equations are known, their projection onto the coarse variables is not closed, and the central difficulty lies in representing the feedback of the unresolved scales so that the reduced model reproduces the statistical and dynamical properties of the projected high-resolution system. We address this problem with a score-based framework, constructing a reduced-order model of quasi-geostrophic turbulence whose stationary distribution coincides by construction with the distribution learned from data and whose dynamics are calibrated to reproduce the finite-time correlations of the energies in individual wavenumber shells. The resulting model reproduces the stationary statistics of the resolved flow with high accuracy, and its calibration is computationally inexpensive because it requires no forward integration of the model.

Does the spatial organization of particle mobility in a glass predict future motion beyond what local structure knows? In leakage-free simulations of an aging Kob–Andersen liquid ($N=2028$; 200 trajectories; three temperatures), mobility-network topology raises the out-of-fold $R^2$ by $\dRtwo=0.0049$–$0.0122$, monotonically with quench depth, retaining $\ge 98\%$ atop softness-class baselines. Giant mobile components are dense hotspots whose members subsequently quiet down: exhaustion zones of cooperative motion — a spatial anticorrelation channel invisible to single-particle descriptors.