Papers

We extend the generalized anomalous diffusion framework established in Part 1 to the short-range forcing regime ($\beta>2/3$), where the multiscale-force dominated (MFD) subrange is intercalated after the inertial subrange, competing directly with the dissipation ranges. Focusing on electrokinetic (EK) turbulence as the prototypical example with $\beta=1$, we derive the relations for the velocity and scalar dissipation wavenumbers, $k_{\mathrm{MD}}$ and $k_{\mathrm{SD}}$, across all four subranges of the Quad-cascade process (inertial, constant-$\Pi_u$, constant-$\Pi_s$, and variable flux). By incorporating Golestanian's predicted anomalous diffusion regimes for electrolytes, we construct comprehensive phase diagrams showing how the relative magnitudes of $k_{\mathrm{MD}}$ and $k_{\mathrm{SD}}$ are governed by the scale-dependent anomalous Schmidt number $\mathrm{Sc}_Z$. We identify two new spectral subranges that emerge exclusively in this short-range forcing regime: (i) the convective-forcing-viscous subrange ($k_{\mathrm{MU}}\ll k\ll k_{\mathrm{CFVD}}$) for either $\mathrm{Sc}_Z\gg1$ or $\mathrm{Sc}_Z\ll1$ with $\gamma>\alpha$, where the scalar field drives viscous flow through electric body force; and (ii) the diffusive-forcing-convective subrange ($k_{\mathrm{MU}}\ll k\ll k_{\mathrm{DFCD}}$) for $\mathrm{Sc}_Z\ll1$ and $\gamma\le\alpha$, where the scalar structure dominated by diffusion determines electric body force, which in turn causes momentum convection. These results provide a complete analytical map of EK turbulence under anomalous diffusion, revealing how external parameters such as electric field strength and ionic diffusivity determine the cascade topology.

We present a theoretical model for momentum–scalar coupled turbulence in which both fields undergo anomalous diffusion, described by fractional biharmonic operators of orders $\gamma/4$ and $\alpha/4$, respectively. Focusing on the long-range external forcing or unforced turbulence, we derive analytical expressions for the kinetic energy spectrum $E_u(k)$, the scalar spectrum $E_s(k)$, and the characteristic wavenumbers $k_K = \left( \frac{\epsilon_u^{1/3}}{c_u} \right)^{1/(\gamma - 2/3)}$ (reciprocal of Kolmogorov scale) and $k_S = \left( \frac{\epsilon_u^{1/3}}{c_s} \right)^{1/(\alpha - 2/3)}$ (reciprocal of scalar dissipation scale) as functions of $\gamma$, $\alpha$, turbulent dissipation rate $\epsilon_u$, diffusivities of momentum ($c_u$) and scalar ($c_s$), respectively. An anomalous Schmidt number $Sc_Z = k_0^{\gamma - \alpha} \frac{c_u}{c_s}$ is defined to governs the cascade topology. It describes the ratio of diffusion times of scalar and momentum on the minimum wavenumber $k_0$. Superdiffusion ($\gamma<2$ or $\alpha<2$) is shown to counter-intuitively enlarge $k_K$ and $k_S$, broadening the inertial range. The theory unifies the classical Kolmogorov–Obukhov–Corrsin–Batchelor scalings as special cases when $\gamma=\alpha=2$, and provides a foundation for understanding non-Fickian transport in complex turbulent systems.

High-mass X-ray binaries (HMXBs) constitute a potential intermediate phase connecting massive stellar binaries to the formation of coalescing binary compact objects (BCOs). Yet, the specific circumstances that allow HMXBs to later develop into merging BCOs are still under debate. In this study, we focus on wind-fed HMXBs and investigate this link by generating synthetic catalogs with the population-synthesis code SEVN and assigning them to a sample of 66 Milky Way-like galaxies. Using stellar particles drawn from the TNG50 cosmological simulation, we assign HMXBs according to particle mass, age, and metallicity, and follow their subsequent evolution to BCOs. In this way, our approach provides a realistic framework for modelling HMXBs in the Milky Way by explicitly accounting for the varied metallicities and spatial distributions of binary systems. Our method recovers the spatial distribution inferred from the observed properties of Galactic HMXBs: their positions follow the spiral arms and agree with the measured radial profile. The age distribution aligns well with observations and shows that BH-HMXBs tend to be younger than NS-HMXBs. We find that the fraction of HMXBs that evolve into merging BCOs within a Hubble time for BH-HMXBs is ~0.2-3.2% (or ~0.3-5.4% when restricting to 10^35 <= L_X <= 10^40 erg s^-1), while for NS-HMXBs is ~3.6-23.4% (or ~3.5-26.0% with the same luminosity cut). We show that common envelope (CE) episodes and natal-kick magnitudes are the primary processes determining the number of merging systems. Successful BCO mergers are typically produced by systems that experienced significant orbital hardening (early CE), whereas stable mass transfer often yields wide, non-merging binaries unless extreme eccentricities are induced by kicks. Metallicity plays a secondary but important role by modulating compact-remnant masses and wind-driven orbital widening.

We study long-range correlated Wigner-type matrices built from row-independent stationary Gaussian sequences. For exponentially decaying (AR(1)) correlations, the bulk spectral density deforms from the semicircle law via an explicit combinatorial "hub" mechanism, yet we verify the flatness and decay hypotheses of the matrix-Dyson-equation framework (MDE), with numerical evidence supporting Tracy-Widom edge universality for every fixed $\rho<1$ of the exponential decay correlations; the degenerate limit $\rho\to1^-$ reduces to a symmetrized Volterra operator, connecting to the singular-value cascade identified in a companion BBP analysis. For power-law correlations $dt\sim t^{-\gamma}$, we identify $\gamma_c=1/2$ as the critical point for divergence of the bulk fourth-moment, while $\gamma=1$ marks the breakdown of the flatness condition governing the MDE edge analysis. We prove the fourth-moment transition exactly and find numerically that the self-consistent edge varies smoothly across $\gamma=1$, with no evidence of a kink or discontinuity.

Can a boundary determine the direction of circulation in a collectively moving active fluid? We study chiral self-propelled particles with nematic bulk alignment, confined by walls whose orientational coupling varies continuously from nematic to polar. For an isolated particle at a wall, we derive the exact parameter condition under which a stable orientation is tangent to the wall. With predominantly nematic wall coupling, however, the many-body circulation changes sign at a chirality that is nearly independent of the wall symmetry. This sign change follows a pronounced decrease in nematic order and disappears when bulk alignment is removed. As the polar wall coupling becomes dominant, opposite-handed circulation is suppressed and same-handed polar locking emerges. Thus local orientation at a wall and the direction of macroscopic circulation are selected by distinct physical processes: the wall determines the possible local orientations, whereas collective order determines whether those orientations control the global flow.

The position–momentum correspondence combines several mathematically distinct identifications that are often conflated. For the additive group $(\mathbb R,+)$, every continuous character has the form $x\mapsto \mathrm e^{ikx}$. After choosing a coordinate $p=\alpha k$ on the dual group, one obtains $\mathrm e^{ipx/\alpha}$, so Pontryagin duality alone does not identify a particular dual coordinate with physical momentum. For the corresponding unitary Fourier transform, multiplication in position space is transported to convolution in momentum space, while the diagonal distribution is transported to the specific composition with the addition map $(p,q)\mapsto p+q$; it is not transported to pointwise multiplication in momentum space. The family $\hat P_\alpha=-i\alpha\,d/dx$ has commutator $[\hat X,\hat P_\alpha]=i\alpha I$ on $\mathcal S(\mathbb R)$, and the standard quantum-mechanical normalization $[\hat X,\hat P]=i\hbar I$ therefore selects $\alpha=\hbar$ within this family. Equivalently, the standard normalization of the translation generator gives $\hat P=-i\hbar\,d/dx$. The resulting characters $\mathrm e^{ipx/\hbar}$ have spatial period $h/|p|$ for $p\neq0$. All distributional statements are formulated in the Schwartz rigging and no product or pullback of arbitrary tempered distributions is used.

Nitrogen-vacancy (NV) centers in diamond can serve as highly sensitive solid-state quantum sensors for high-sensitivity magnetometry. However, in the noisy intermediate-scale quantum (NISQ) era, extracting reliable information from noisy, finite-shot, and measurement-limited sensing data remains a considerable challenge. Whereas, quantum machine learning (QML) offers a potential path to improve parameter estimation by learning nonlinear relationships between quantum-sensing data and the underlying physical signal. In this work, we investigate the role of QML in magnetic-field estimation within an NV center-inspired magnetometry setting. We formulated magnetic field sensing as a supervised regression task. We compared the performance of several classical machine learning models trained on measurement-based classical data with that of quantum kernel-based models trained on pre-measurement coherent quantum states. Our objective is to isolate the impact of measurement-induced information loss and therefore provide a theoretical upper bound on the sensing performance. The upper bound is achievable only when coherent quantum information is directly available to the learning model. Our results show that QML-based sensing performance improves significantly with coherent quantum-state information, and not much with changes in model complexity or learning paradigm. This observation underscores the importance of learning pipelines that tightly integrate quantum sensors and QML models to enhance magnetic field sensing under realistic constraints.

We discuss a photogrammetry technique to measure the inter-module alignment in the Mu2e tracker. The tracker consists of 216 modules each with 96 straw tubes. The relative alignment of the straw tubes in a module was previously measured by an X-ray technique, which tied the straw tube measurements to three fiducials per module. The photogrammetry technique uses an array of 15 cameras to make precise position measurements of the module fiducials in a global tracker coordinate system. Measurements of the fiducial position and radius on the camera's CCD yield ~$25 \mu m$ resolution in the transverse directions and < $300 \mu m$ along the camera axis. In addition, we describe a procedure to combine the images with "local" mechanical measurements to yield $<100 \mu m$ precision along the camera axis. The technique offers a touch-less, rapid (~1 hour), and affordable metrology approach within the requirements of the tracker.

We study the approximation of the number of solutions of Laurent polynomials over finite fields. For a Laurent polynomial \[f(x)=\sum_{j=1}^{s}a_jx^{u_j}\in \mathbb{F}_q[x_1^{\pm1},\ldots,x_n^{\pm1}], \] let $U$ be its augmented support matrix whose columns are $(1,u_j)$ with rank $\rho$ and $N(f) := \# \{x\in (\mathbb{F}_q^\times)^n \mid f(x)=0\}$ be its torus point count. Our first main result is a quantum algorithm that outputs $\widehat{N}(f)$ satisfying \[ |\widehat{N}(f) - N(f)| \le \varepsilon q^{n+s/2-\rho} \] with success probability $1-\delta$. Provided that $\rho$ and $\|U\|_\infty$ are bounded, the algorithm runs in both classical bit and quantum gate complexity $\mathrm{poly}(n, s, \log q, 1/\varepsilon, \log(1/\delta))$. It provides finer resolution than relative-error approximations in general settings. To the best of our knowledge, in the explicit finite-field input model considered here, no previous algorithm achieves this additive accuracy with running time polynomial in $\log q$. Van Dam (arXiv:quant-ph/0405081) conjectured the existence of such an algorithm under the assumption of an oracle reflecting the algebraic properties of the polynomial. In contrast, by exploiting a point-counting formula derived from character sums over finite fields, we develop an alternative approach that efficiently approximates the number of points without assuming the existence of such an oracle. As a second main result, we prove that the same approximation problem becomes $\#$P-hard under randomized polynomial-time Turing reductions when the support matrix $U$ varies freely as part of the input. Thus, taken together, our results clarify how the effectiveness of the quantum approach depends on the tradeoff between the accuracy scale and the support parameters of the input polynomial.

The first analyses of the James Webb Space Telescope spectra of trans-Neptunian Objects (TNOs) revealed three discrete types of surfaces. This seems to contradict ground-based spectro-photometric datasets, which suggest a continuum of colors with only two surface types. Here we present linear spectral modelling that reconciles these two results. In our model, the sole parameter is the object's optical slope, and the reflectance spectrum at all wavelengths is linearly proportional to that color, with the slope of that function evaluated from the spectra themselves. When applied to small (H>5 for H2O-types and H>4 for the merged sample of organic-rich and CO2-types) and distant (q>18 au) objects, we find that this model does a reasonable job of reproducing the overall spectral behavior of both samples. Bootstrapping simulations show that if the optical slope were not a good predictor of an object's spectrum, then finding an explained variance of the model that is better than observed occurred in 2.3% of realizations for the H2O-types and 0% of realizations for the organics sample. In a chi^2 sense, the optical color is a better predictor of most spectra as compared to the mean spectrum of a class. The trends of optical color and spectra band-areas exhibited for many key compositional materials are well reproduced, and demonstrate that those materials govern the overall spectral shape within a class. Importantly, these results require that within a given class, the band-areas of those key materials are predictable given only its optical color and its surface type. Unsurprisingly, our simple one-parameter model does not account for the full spectral diversity of TNOs. We speculate that albedo encapsulates much of the remaining diversity.

Temperature-dependent electrical resistivity $\rho(T)$ in cuprate, iron-based, and nickelate superconductors represents one of unresolved problems in modern solid-state physics, because of the high absolute value of $\rho(T)$, which, in many cases, exceeds the Ioffe-Rigel criterion, and a large difference in the $\rho(T)$ shape for samples with different doping. Here I show that the nearest neighbors parallel resistivity model (arXiv: 2607.23484) can well describe the in-plane resistivity $\rho_{ab}(T)$ in iron-based superconductors (IBS) of type 11, 111, 122, 1111, 1144 and 42214 in which the spin density wave phase or nematic order is suppressed by doping. The model is based on the postulate that $\rho_{ab}(T)$ is a sum of two parallel conduction channels, where one channel is described by the Bloch-Grüneisen equation and the other by the Arrhenius hopping equation. Consequently, the variety of $\rho_{ab}(T)$ in the IBS is explained as a variation of the Debye temperature $\Theta_D$ and the hopping activation energy $E_a$. The derived Debye temperatures were used to estimate the electron-phonon coupling constant $\lambda_{e-ph}$in the studied IBS.

Nonlinear shear softening in soils and rocks is commonly described using empirical modulus-reduction laws. In this work, we investigate nonlinear softening within the Eringen–Mindlin micromorphic framework by interpreting its additional constitutive parameters in terms of coupling, internal relaxation, and micro-inertia. The micromorphic continuum is viewed as a dynamically enriched effective medium in which the macroscopic deformation interacts with an internal microstructural deformation field. This interaction naturally produces frequency-dependent effective elastic properties and provides a physical connection between macroscopic wave propagation and unresolved microstructural dynamics. We show that nonlinear shear softening can be described by a progressive reduction of the coupling between macroscopic and internal deformation. As this coupling weakens with increasing shear strain, the effective shear modulus decreases. In the low-frequency limit, the resulting constitutive relation takes a hyperbolic form closely related to the classical Hardin–Drnevich law. The model is validated against laboratory measurements of shear-modulus reduction in sand and reproduces the observed nonlinear behavior with only a small number of physically interpretable parameters. The proposed framework provides a new description of nonlinear softening and frequency-dependent behavior without requiring explicit knowledge of the underlying microstructural geometry. Classical empirical modulus-reduction curves emerge as a macroscopic consequence of the interaction between macroscopic and internal deformation.

Modeling frequency-dependent seismic wave propagation in porous media remains a major challenge because classical poroelastic theories generally require a large number of poorly constrained constitutive parameters. We investigate seismic wave propagation within a higher-order gradient constitutive framework as an effective dynamic homogenization model for poroelastic media. The proposed formulation extends classical strain-gradient elasticity by incorporating an additional curvature contribution associated with rotational deformation, allowing independent descriptions of longitudinal and transverse wave dispersion within a unified continuum framework. A general dispersion relation is derived together with its macroscopic and microscopic velocity limits, providing a direct physical interpretation of the characteristic inertial and elastic length scales introduced by the model. The framework is validated against laboratory measurements of frequency-dependent P- and S-wave velocities in tight sandstones under different confining pressures. The inversion demonstrates that a common inertial characteristic length and a common strain-gradient characteristic length govern both wave types, while an additional curvature characteristic length is required only for shear waves. Comparison with classical Biot theory shows that the proposed framework reproduces the observed laboratory dispersion using only a small number of effective constitutive parameters, providing a reduced constitutive description of poroelastic wave propagation. These results suggest that higher-order gradient elasticity offers a physically interpretable and computationally efficient alternative for modeling frequency-dependent seismic wave propagation, with potential applications to seismic imaging, inversion, and natural hydrogen reservoir characterization.

In this work we aim to present a new perspective for MOND theory, namely that MOND theory is not an answer for the missing matter at galactic scales, but it provides a phenomenological description of the dynamics that DM should produce at galactic scales. We also aim to point out that MOND dynamics at galactic scales is achieved by scale-dependent self-interacting dark matter, which can behave as collisionless and collisional, depending on the scales and the physical processes. To this end, we first aim to highlight the successes of the $\Lambda$-Cold-Dark-Matter model and how it overwhelms over the MOND paradigm. Using textbook physics, we present the successes of the $\Lambda$-Cold-Dark-Matter at cosmological and cluster scales, and how these phenomena cannot be described consistently by MOND theories. Thus, by excluding MOND as being a viable description of nature at all scales, we conclude that MOND may not be the answer behind missing matter in Newtonian galactic dynamics, but it is just showing how the dynamics of dark matter should behave at galactic scales.

A circularly polarized far field must be dark somewhere: its amplitude is a section of a twisted line bundle. We prove this exacts a joint coverage-rate cost that cannot vanish faster than the inverse fourth power of the mode order, and we construct an explicit family of fields attaining that exponent. At lowest order the global optimum is the spin-1 anticoherent state, independently known as optimal for rotations about an unknown axis. The same floor caps photon collection in single-helicity quantum links; the opposite helicity removes it at a cost set by the inverse mode count.

A quantum cascade laser based on a metal-insulator-metal structure is proposed, the heterostructure of which consists of diamond and metal films. The profile of the quantum potential in a quasi-periodic MIM heterostructure and the structure of metastable levels in quantum wells are investigated. A number of CCL configurations have been proposed. The possibility of generating radiation from the UV to THz range is theoretically shown.

FlowMLLab is an open-source framework that connects validated fluid-mechanics solvers to scientific machine-learning experiments under a reproducible contract. Its computational fluid dynamics (CFD) pathway generates cavity data, whereas its direct simulation Monte Carlo (DSMC) pathway supplies rarefied-flow evidence with sampling diagnostics. Case-wise partitions prevent leakage, and matched non-neural baselines determine whether learning offers a measurable advantage. Examples include a coordinate network and a proper orthogonal decomposition (POD) deep operator network (DeepONet), together with learned kinetic closures. Python components regenerate every figure, while sixteen tutorials use the same interfaces as the command-line tools. By retaining numerical provenance, blind-case protocols and physical validation targets, FlowMLLab emphasizes traceable evidence rather than black-box curve fitting.

Starting from the cyclic duality tensors introduced by Vernier, Miao, and Yamazaki (VMY), whose endpoint-traced matrix-product operators obey $\mathbb Z_N$ Tambara–Yamagami fusion and realize topological defect lines of the compactified-boson conformal field theory, we retain the virtual endpoint as an $N$-state dynamical degree of freedom and construct an exactly movable seam in the spin-$\tfrac12$ XXZ chain at $q=\mathrm e^{\mathrm i\pi M/N}$ with $\gcd(M,N)=1$. The local movement identity holds for any unitary $q$-Weyl pair; in the finite cyclic realization, all output phases are locally gauge equivalent and share the same four seam eigenvalues. On a ring, the output gauge becomes a directed twist on a single bond, while endpoint conjugacy reduces the $2N$ labels to two relative $\mathbb Z_2$ flux classes. An explicit antiunitary symmetry protects the class $\eta\equiv M-1\pmod 2$: for even $N$ it pairs distinct charge sectors isospectrally, whereas for odd $N$ it fixes one sector and squares to $-I$ there. Hence every many-body energy eigenspace in the protected class has even multiplicity. The source value $\eta_{\rm VMY}=1-M$ satisfies this condition for every coprime root, whereas the ungauged value $\eta=0$ does so only for odd $M$. Exact finite-size controls show that the opposite class can contain simple levels, so a global flux invisible to local gauge equivalence distinguishes the two classes spectrally.

We present AlchemQ v0.5, a proof-of-concept system that couples an untrusted beam-search optimizer with a machine-checkable per-result certification layer and a versioned certificate protocol (0.2.0), so that every optimized circuit ships with a verifiable artifact rather than a bare claim. The certifier proves equivalence up to global phase by ZX-calculus full reduction, with a numeric-tensor fallback based on the optimal Hilbert-Schmidt overlap. Certificates are self-contained and tamper-evident: canonical gate-canon-v1 hashes, measured residuals, tri-state verdicts (certified/rejected/inconclusive), and versioned phase-note schemas for cross-platform reproducibility. The agent aggregates three fuzzy t-norms, cannot return an uncertified circuit, and since v0.4 guarantees no componentwise regression against the original. On a benchmark of 100 circuits, all 400 optimizations terminate without error, every returned circuit is certified, every mutation is detected, and a 2998-test suite passes on two platforms. The PyZX baseline is strong (21.4% mean T-count reduction over 82 circuits) and the agent is strictly better on 9/100; the three t-norms return identical circuits on all 100 standard instances, diverging only on 4/38 of an adversarial suite. Two case studies are new: a false negative root-caused to a pivot-normalization bug in PyZX's compare_tensors (pivot 4.7e-9; the optimal-overlap residual is 7.4e-11), and eight certificates rejected on macOS due to BLAS-dependent floats in phase_note. Both were fixed; all artifact sets validate 400/400 on both platforms. A pilot run on IBM Heron r2 gives a certified circuit 78% shallower with 65% fewer two-qubit gates; output quality favors it on all three metrics but is not significant at 1024 shots. We release the certificate specification and a standalone reference verifier (Apache-2.0) with data and scripts; the engine is proprietary.

The Atlantic Meridional Overturning Circulation (AMOC) carries multi-decadal memory that ensemble-mean risk projections do not capture. We quantify this memory and its consequences for tail risk with a Volterra integral framework applied to ensemble-mean-subtracted variability in 14 CMIP6 models (1850-2100, three SSP scenarios), so that results reflect intrinsic thermohaline memory rather than the common anthropogenic forcing trend. Four results follow from leave-one-out cross-validation and an annealed-quenched tail decomposition. First, the ensemble-mean DFA1 Hurst exponent is H = 0.781 +/- 0.219, with 12 of 14 models showing long-range dependence (H > 0.5), consistent with thermohaline adjustment timescales near 33 yr. Second, a first-order Volterra model reduces out-of-sample RMSE by 16.8% over the best autoregressive baseline and by 12.3% over an unconstrained 20-lag distributed baseline, both robust to 200 circular-shift placebos (p < 0.05): the physically motivated kernel shape carries genuine predictive advantage. Third, the rolling 30-year lower-tail frequency rises 1.9-3.1x above the historical baseline depending on scenario, and the memory amplification index exceeds 1 in 8 of 14 models under SSP5-8.5 (median 1.15): persistence-driven clustering of weak-AMOC states amplifies tail frequency beyond forcing-only projections. Fourth, model-specific optimal memory horizons (15-52 yr) correlate with thermohaline regime (r = 0.74, p < 0.01), and the ensemble-mean Hurst exponent already exceeds a detection threshold H* = 0.70 in 9 of 14 models, with theoretical lead times to near-tipping conditions of 10-35 yr depending on scenario. These results support trajectory-specific, memory-aware AMOC risk assessment under moderate-to-high forcing and a physically grounded, scenario-conditional early-warning framework.

Recent observations by the Neutron Star Interior Composition Explorer (NICER) indicate that the massive pulsar PSR J0740+6620 ($2.08\,M_{\odot}$) has a radius comparable to those inferred for stars near $1.4\,M_{\odot}$, as shown by PSR J0030+0451 and updated analyses. Such near-vertical mass-radius behavior is difficult to obtain unless the high-density equation of state (EOS) stiffens strongly. We show that, for massive pulsars, the leading radial scale can be set by a relativistic, high-sound-velocity core beginning near twice the nuclear saturation scale, while the outer low-density layer, comprising the true crust and outer core, supplies only a subdominant correction. The key evidence comes from radius decomposition: replacing the low-density branch below the matching point with unified EOS models spanning a factor of two in transition pressure changes the $2.08\,M_{\odot}$ core radius by only $\sim160$ m, about half the variation of the total radius. This convergence is genuinely a high-mass phenomenon: at $1.4\,M_{\odot}$ the core radius remains more branch-sensitive, varying by about $0.5$ km. Fixed-fraction comparisons confirm that core dominance emerges systematically as the star grows more massive, where the traditional separation between “radius physics” and “maximum-mass physics” breaks down. We establish this picture by combining analytical Tolman VII profiles and thin-crust matching, numerical Tolman-Oppenheimer-Volkoff integration with a piecewise EOS, and direct-grid Bayesian inference using NICER and GW170817 constraints under causal and mass-support filters. Data modestly constrain the transition stiffness but leave the quadratic stiffening governed mainly by causality. A comparison with a constant-sound-speed core remains inconclusive: both descriptions produce comparable core-dominated radii, leaving a degeneracy that sub-kilometre radius measurements can break.

We present a robotic electrospinning platform and design method for depositing nanofiber membranes onto non-planar, three-dimensional conductive geometries. Conventional electrospinning relies on fixed emitters and planar grounded collectors, which restricts deposition to flat substrates: on concave geometries, field shielding prevents fibers from reaching recessed regions, and material bridges across elevated features instead. We address this with a custom end-effector integrated with a six-axis UR20 arm. The tool carries a localized stepper-driven syringe pump that maintains consistent polymer flow independent of orientation, and routes high-voltage DC (up to 25 kV) directly to a robot-mounted needle, turning the arm into a mobile emitter with full kinematic control over position, orientation, working distance, and traversal velocity. Toolpaths that continuously reorient the emitter along surface normals give access to concave topologies unreachable by fixed-axis systems. We characterize the resulting deposition behavior in two parts. A catalog of four bio-compatible polymer systems (PEO, PVA, keratin-PEO, silk-PEO) establishes the operating envelope, reporting deposition speed, jet stability, fiber size, alignment, and durability for each. A taxonomy of 3D-printed conductive scaffolds spanning geometric primitives, hybrid compositions, and square, triangular, and hexagonal lattices links collector geometry to fiber alignment, density, and cross-void bridging. We also demonstrate programmable grounding, in which selectively energized pins in an array steer deposition without changing physical geometry. Assembly instructions and toolpath-generation code are released as an open-source repository.

We study hard spherocylinders on a sphere with axes rigidly locked to a tangential director field at fixed angle $\tilt$ to the meridian, necessarily singular at the poles. Three lengths set the problem: the rod length $\Lrod$, the diameter $\Drod$, and the host radius $\Rsph$. Monte Carlo simulations across fifteen geometries and four coverages give two main results for the polar marginal, the azimuthal average of rod-center density. First, the tilt is a continuous handle on the width of the depleted region that packing induces around each singularity. Under meridian locking it is set principally by the rod length; turning the director toward the latitude contracts it substantially, the contraction being spent well before latitude locking. Second, how uniform the polar marginal can be made is limited by geometry, not tilt. The smallest variance on the sampled grid follows a power law in $\Lrod^{2}/(\Rsph\Drod)$, which measures how far a straight rod's ends stand off the curved surface in rod diameters, with an effective exponent between $1.1$ and $1.3$. Long rods on small hosts cannot be made uniform at any sampled tilt; the remedy is geometric, not orientational. The polar marginal is equator-heavy almost everywhere, inverting only at high coverage and tilt; meridian locking is the least uniform choice, and the variance-minimizing tilt usually lies in a sampled band from $31.7^{\circ}$ to $55^{\circ}$. The golden-ratio tilt $\arctan(1/\phigold)$ is one of those angles: a benchmark, not one the model selects. Both results describe the infinitely locked athermal ensemble.

We first consider lead isotopes with valence neutrons in the g9/2shell. We especially compare 211Pb (n=3), 213Pb (n=5) and 215Pb (n=7), 213Pb being at mid-shell. Motivated by the fact the J = 21/2+ and J =3/2+ states are pure seniority v=3 states for both n=3 and n=5, we compare the energy splitting E(J=21/2+)-E(J=3/2+) for various interactions. We then discuss the position of the lowest J=3/2+ state in both n=3 and n=5, although, this state has not been found experimentally. Calculations with configurations beyond g9/2 are also considered. We next address the fact that the J=21/2+ state is isomeric for both n=3 and n=5.

A simple regularization of the smooth quantum hydrodynamic model equations to prevent an unstable growing mode is proposed. The regularization involves replacing the spatial derivative of the electron density on the right-hand side of the momentum conservation equation by using the classical Boltzmann distribution for electron density. Time-dependent simulations of the resonant tunneling diode to steady state using this regularization are presented, which show realistic negative differential resistance (the experimental signal of quantum resonance) and hysteresis in the current-voltage curve. The simulations are in good agreement with fully quantum mechanical simulations of the resonant tunneling diode.

Denoising score matching trains diffusion models by regressing onto a conditional score, although generation ultimately requires the marginal score. The two objectives share the same population minimizer, but the conditional target remains random at fixed noisy state and introduces an irreducible excess in the training loss. We isolate this excess and show that, for a general corruption kernel under mild regularity assumptions, it is exactly the trace of the Fisher–Rao metric of the conditional endpoint family, integrated along the diffusion trajectory. This gives an exact conditional-variance decomposition of the denoising objective and identifies the information geometry observed in diffusion latent spaces as an intrinsic component of the training loss. We derive the result from a Schr"odinger bridge variational principle, in which the ideal objective arises as excess path-space relative entropy. For corruption diffusions, the Fisher term is proportional to the rate at which the noisy state loses mutual information about the clean data, separating the loss floor into an information flow determined by the data and a weight determined by the corruption schedule and objective. In the Gaussian case, this yields a closed form for the floor, recovers reparametrization invariance of the continuous-time objective, and relates its high-SNR divergence to the information dimension of the data. Finally, we show that raw losses obtained with different noise ranges or weightings need not rank models consistently because they contain different additive floors, and contrast the second-order geometry seen by training with the third-order conditional statistics entering numerical sampling error.

Recent JWST observations challenge the traditional 'cosmic shoreline' from both sides, revealing thick volatile atmospheres on the hottest close-in 'lava worlds,' where irradiation should drive the most extreme escape, and bare rocky surfaces on cooler terrestrial planets around M dwarfs, where atmospheres would be expected to survive. Using a coupled atmosphere-interior evolution model, we show that atmosphere retention is governed not by a single escape boundary but by two: a hot, outgassing-regulated 'cosmic sandbar' and a cooler, escape-regulated 'cosmic shoreline,' separated by an 'airless valley' that may mark a graveyard of stripped sub-Neptune cores. The sandbar arises because long-lived magma oceans, sustained further by tidal heating from secular eccentricity excitation in multi-planet systems, keep most volatiles dissolved and expose only a small atmospheric reservoir to escape, whereas cooler planets solidify, sequestering volatiles in the deep solid mantle while overexposing the rest to loss. This two-regime structure recasts the single cosmic shoreline as two boundaries set by distinct physics: outgassing and escape. We provide time-evolving fits for both boundaries across G, K, and M stellar types as a function of volatile inventory, planetary mass, age, and tidal heating. Lava worlds with thick atmospheres are unlikely around stars cooler than K-type unless sustained by extreme tidal and/or other interior heating. This framework links atmosphere survival from USP lava worlds to habitable zone planets, informing target selection and interpretation for TRAPPIST-1 and JWST DDT characterization.

The linearity of the Stokes equations organises the hydrodynamic response of a rigid particle into a hierarchy of resistance operators, coupling successive truncations of the ambient-flow jet to moments of the surface traction. Since the work of Kelvin and Larmor, it has been known that this response does not resolve particle geometry faithfully: bodies with discrete rotational symmetry may be indistinguishable from bodies of revolution (Brenner's helicoidal symmetry) and a chiral body may respond isotropically, as in Kelvin's isotropic helicoid. We regard the resistance operators as elements of finite-dimensional O(3)-representation spaces and use character formulae to determine, at every level of the hierarchy, which point-group symmetries are hydrodynamically distinguishable and the dimension of each invariant space. This yields an explicit nested sequence of hydrodynamic symmetry-group sets, from the translation-force level to the quadratic-flow level. The framework reveals hydrodynamic classes that no shape can realise geometrically, gives helicoidal symmetry a level-dependent definition, and shows that polyhedral symmetry becomes visible in a strict order: tetrahedral symmetry in shear, octahedral symmetry through the stresslet, and icosahedral symmetry in quadratic flow. Projecting the resistance operators onto force- and torque-free motion provides symmetry-based parameter counts and a constructive route to the corresponding dynamical normal forms. We thereby complete the Jeffery-Bretherton-Ishimoto classification, characterise all hydrodynamic classes producing Jeffery dynamics, and identify chiral tetrahedral and octahedral normal forms that can generate irregular full-attitude dynamics.

Motivated by the ubiquity of ramified fractal deposits in nature and engineered systems, we investigate the irreversible adsorption of diffusion-limited aggregation (DLA) clusters on a square lattice. We study the role of cluster shape diversity on jamming properties of the system by systematically controlling the number of distinct shapes used across and within realizations, encompassing both monodisperse and polydisperse model variants. Our large-scale simulations over a broad range of cluster sizes $2\leqslant k\leqslant4096$ show that the jamming density decreases with cluster size as a power-law $p_j(k)-p_j^\infty\sim k^{-\alpha}$. Both $\alpha$ and $p_j^\infty$ are found to depend on the degree of shape diversity, with $\alpha$ ranging from $0.374(2)$ to $0.417(1)$. It is observed that increasing shape polydispersity promotes denser packing. Importantly, the fluctuations of the jamming density exhibit distinct scaling behavior: $\sigma(L)\sim1/L$ for a fixed pool of cluster shape(s), but remain $L$-independent when the pool of shape(s) is refreshed across different realizations. Furthermore, our results demonstrate that the differences between the model variants systematically diminish with increasing $k$ and are expected to vanish as $k\to\infty$ due to the statistical self-similarity of the DLA clusters.

Reentrant transitions and temperature chaos are two unusual properties of spin glasses. We recently established a general logical relation between these two phenomena [Phys. Rev. E 112, 044140 (2025)]. In the present paper, we provide an explicit example of this logical relation in the fully connected Ising $p$-spin glass with a ferromagnetic bias. By expanding the free energy around the triple point, we show analytically that the ferromagnetic–spin glass boundary is reentrant in the vicinity of the triple point throughout the examined range of finite $p>2$. It then follows from the above logical relation that there exists at least one pair of distinct temperatures in the spin glass phase for which the overlap of spin configurations vanishes. This is a necessary condition for temperature chaos, but it would be quite unusual for the overlap to vanish only for selected temperature pairs but not for others within a single spin glass phase. These results therefore strongly suggest the existence of temperature chaos in the sense that the overlaps of spin configurations vanish for all temperature pairs throughout the spin glass phase. Independent evidence for this behavior is provided by a two-temperature replica calculation.