Yangyang Wang

Experimental measurements are commonly represented on a discrete grid, requiring a balance between granularity and statistical noise. Two strategies have traditionally been used to improve such representations: selecting an appropriate bin width to control discretization error and applying kernel-based smoothing to suppress fluctuations. Despite their shared goal, these approaches have largely developed independently, without a unified statistical description of how discretization and correlation jointly determine measurement precision. Here, we extend the discussion of optimal interval averaging to a correlation-aware setting by Gaussian process regression, which explicitly accounts for correlations among neighboring bins. Starting from first principles, we derive the mean-squared error of discretized measurements and obtain closed-form asymptotic expressions for the optimal bin width and correlation length. When recast in reduced variables, the theory reveals distinct universal scaling laws governing the error in the correlation-free and correlation-controlled regimes. Characterized by intrinsically smooth intensity profiles and counting-based statistics, neutron scattering measurements are well suited for demonstrating the enhanced error contraction enabled by inter-bin correlations. We show that such improvement is achievable over the experimentally accessible Q-range and across multiple instruments and material systems. These results show that explicitly accounting for correlations systematically reshapes the limits of precision in discretized, noise-limited measurements. More broadly, the framework provides a transferable statistical foundation for optimizing data representation, inference, and experimental design across the physical and data sciences.

Ultra-small-angle neutron scattering (USANS) measurements at the Spallation Neutron Source (SNS) at Oak Ridge require careful treatment of slit-geometry resolution effects and, in many cases, multiple scattering in complementary small-angle neutron scattering (SANS) data before meaningful structural interpretation can be made. We present a unified data-reduction framework that provides SNS USANS users with a systematic and reproducible workflow for obtaining intrinsic single-scattering intensities across the combined USANS–SANS Q range. The approach explicitly formulates the slit-geometry point-spread function for Bonse–Hart USANS, implements both analytical truncated Abel inversion and Bayesian Gaussian process regression for stable desmearing with uncertainty quantification, incorporates central-moment expansion for pinhole SANS resolution correction, and applies an orthonormal spectral method for probabilistic multiple-scattering removal. The ordered workflow ensures that instrumental resolution and multiple-scattering distortions are removed consistently prior to merging datasets, so that the resulting spectrum represents a physically meaningful resolution-free cross section. Experimental demonstrations on isotropic systems, uniaxially stretched materials and shear-induced anisotropic configurations illustrate both the applicability and the geometric limitations of anisotropic desmearing. This framework provides practical guidance for reliable SNS USANS data reduction and establishes a resolution-consistent foundation for quantitative structural analysis from nanometre to micrometre length scales.

Bonse–Hart ultra-small-angle neutron scattering (USANS) provides access to micrometre-scale structure, but useful measurements often require long counting times. In this work, we test whether the expected smoothness of the scattering profile can be exploited to improve data quality at lower counting statistics. We apply a Gaussian-process-based method to Bonse–Hart USANS data and evaluate its performance on pseudo-measurements generated from high-statistics experiments under Poisson statistics. This provides a stringent test of how well the underlying I ( Q ) profile can be reconstructed when the available counts are substantially reduced. We further show that, in the counting-limited regime, the reconstruction error follows a universal scaling behaviour that differs from the usual independent-counting expectation. At higher counts, the improvement crosses over to a resolution-limited regime set by analyser-angle discretization and rocking-curve width. These results clarify when correlation-aware inference is useful in USANS and provide a practical basis for improving measurement efficiency and beam-time usage.

Block copolymers with strong tendency for block demixing have attracted significant attention especially for applications in microelectronics and membranes. Enabling technological advances in these areas critically depends on access to well‐defined nanostructures with dimensions near or below 10 nm. Block copolymers bearing polyzwitterionic segments are a promising class of materials for phase separation due to their ion association‐induced phase segregation which bestow high‐ χ . In this work, the synthesis of parent poly(styrene)‐ block ‐poly(vinylpyridine) (PS‐ b ‐PVP) block copolymers that are subsequently modified to the targeted poly(styrene)‐ block ‐poly(vinylpyridine carboxybetaine) using a two‐step modification scheme is presented. We study the thermophysical and phase separation properties of the parent, polyelectrolyte intermediate and the final polyzwitterionic block copolymers. Ultra‐small, periodic nanostructures with half‐spacing as low as 5.3 nm are obtained from the polyzwitterionic copolymers. This work demonstrates a scalable synthetic methodology to access pH responsive polyzwitterions and establishes connectivity between polymer design attributes and phase separation behavior for neutral‐ block ‐polyzwitterionic copolymers.

A non-iterative analytical framework based on the truncated Abel inversion is developed for desmearing Bonse–Hart ultra-small-angle neutron scattering (USANS) data. The method directly inverts the slit-averaged intensity without empirical extrapolation or iterative regularization, establishing a closed-form relationship between the measured and intrinsic scattering profiles. Numerical benchmarks on representative models, including a rigid-line form factor, a Lorentzian function and a fractal structural model, demonstrate quantitative recovery of the ground-truth intensity across the full Q range. Application to a deuterated polystyrene/poly(2-vinylpyridine) blend further confirms that the approach yields smooth continuous profiles consistent with companion small-angle neutron scattering data. The truncated Abel inversion thus provides a stable, model-independent and physically transparent route for accurate desmearing of Bonse–Hart USANS measurements.

Ultra-small-angle neutron scattering (USANS) enables access to micrometer-scale structures but is intrinsically affected by strong, anisotropic resolution smearing arising from slit-geometry optics. As a result, recovery of the intrinsic scattering intensity constitutes an ill-posed inverse problem, and commonly used iterative desmearing methods lack rigorous uncertainty quantification. We present a Bayesian desmearing framework for slit-geometry USANS based on Gaussian process regression. In this approach, the scattering intensity is modeled as a smooth random function, and the instrumental point spread function is incorporated explicitly as a forward operator. The resulting formulation yields a closed-form maximum a posteriori solution with well-defined credibility intervals. Computational benchmarks and experimental validation using combined USANS and small-angle neutron scattering (SANS) measurements demonstrate that the framework enables stable desmearing, suppresses experimental noise, and preserves physically meaningful structural features under realistic conditions.

We point out that, under the incompressibility constraint, the two-time pressure-fluctuation correlator of polymeric liquids becomes an isotropic, symmetric, and pair-index-traceless fourth-rank tensor. As a consequence, the self- and cross correlations of normal pressure fluctuations are strictly proportional to the shear pressure correlation, with universal prefactors of 4/3 and −2/3, respectively, for equilibrium dynamics in the long-time limit. By contrast, this symmetry structure is violated in a broad class of polymer models, including the Rouse and slip-link models, which predict incorrect relative weights between normal pressure-fluctuation correlations and shear pressure correlation. This observation suggests that the pressure tensor generated by these models must be projected onto the traceless symmetric subspace to recover hydrodynamically consistent behavior.

Multiple scattering in small-angle neutron scattering (SANS) redistributes spectral weight and distorts structural interpretation, particularly for thick or strongly scattering samples. We develop a finite-dimensional spectral desmearing framework that corrects multiple scattering without resorting to integral transforms or model-dependent extrapolation. The primary intensity is expanded in an orthonormal basis adapted to the isotropic transverse-momentum measure, under which convolution reduces to a recursive tensor contraction, allowing the Poisson-weighted multiple-scattering series to be evaluated directly in a finite-dimensional basis representation. This formulation yields a stable forward–inverse mapping between apparent and primary spectra. Numerical tests demonstrate convergence under repeated convolution and accurate recovery of the single-scattering intensity. Application to SANS measurements collected at multiple neutron facilities, including the Spallation Neutron Source, the High Flux Isotope Reactor, and the Institut Laue-Langevin, shows the quantitative reconstruction of the underlying primary spectrum across a wide range of transmission conditions, including strongly attenuating samples. The method provides a stable, model-agnostic framework for multiple-scattering correction in SANS and enables consistent structural interpretation across instruments and scattering regimes.

Ultra-small-angle neutron scattering (USANS) using Bonse–Hart optics provides micrometer-scale structural insights but suffers from severe slit-geometry smearing. While well-established for isotropic systems, quantitative desmearing of anisotropic data remains a challenge because conventional corrections break down for non-radial scattering. We address this by developing a resolution-aware Bayesian framework that explicitly incorporates anisotropy via an affine deformation to the scattering pattern, guided by the principle of parsimony. This results in orientation-resolved point-spread functions that enable a self-consistent determination of both the resolution and deformation parameters. Using Gaussian process regression with uncertainty quantification and a probabilistic correction for multiple scattering, we demonstrate the framework’s effectiveness through numerical benchmarks and experimental studies of a stretched polymer melt. Our approach enables the seamless integration of SANS and USANS data, facilitating quantitative structural analysis of deformed materials at nanometer to micrometer scales.

Polyzwitterions, composed of repeating units with equal numbers of anionic and cationic groups, have drawn considerable interest for applications ranging from antimicrobial coatings and antifouling membranes to low-friction interfaces, energy storage media, and actuators. A characteristic feature of many polyzwitterions is the anti-polyelectrolyte effect─salt-induced chain expansion in aqueous solution─a phenomenon often implicated in their functional behavior. In this study, we investigated the conformational behavior of poly(2-vinylpyridine-N-oxide) (P2VPNO) using small-angle X-ray and neutron scattering (SAXS and SANS). Small-angle X-ray scattering (SAXS) revealed that, in salt-free aqueous solution, P2VPNO adopts an expanded wormlike conformation stabilized by hydration. With increasing concentration, the chains contract due to screening of intrachain excluded-volume interactions, qualitatively consistent with de Gennes’ scaling predictions for neutral polymers. Small-angle neutron scattering (SANS) further demonstrated that P2VPNO exhibits the characteristic anti-polyelectrolyte response to added salt, as observed in many other polyzwitterions. At elevated temperatures, chain flexibility increases, leading to a shorter Kuhn length and reduced radius of gyration. Notably, however, salt-induced chain expansion persists, indicating that the anti-polyelectrolyte effect remains operative under elevated thermal conditions. These findings provide the first experimental evidence of scaling behavior in polyzwitterions, as well as the first observation of their altered anti-polyelectrolyte response at elevated temperatures, offering new insights into the solution physics of this important class of polymers.