CATpie: A Python tool for quantifying membrane curvature, area, and geometrically faithful normal-line thickness from molecular dynamics simulations.

Ferroelectric ordering in polar liquids has been observed in numerical simulations and liquid-crystal experiments. Within the mean-field framework, this behavior remains associated with the sample-shape-dependent surface contribution to the free energy, which does not vanish in the thermodynamic limit due to the long-range nature of dipolar interactions. Yet, numerical simulations performed under conducting periodic boundary conditions, for which the surface contribution vanishes, still exhibit ferroelectric order, pointing to an intrinsic bulk origin of the transition. Moving beyond the mean-field approximation, Kirkwood's seminal study of the dielectric properties of polar liquids emphasized the role of hindered dipolar rotation in shaping the corresponding pair correlations. In Kirkwood's analysis, hindered rotation stems from the mean force between nearest-neighbor dipoles, placing the focus on local structure. Introducing a different perspective while retaining the central role of hindered rotation in the onset of ferroelectricity, the present study establishes, as an original finding, that annealed averaging of dipolar interactions over positional disorder generates hindered dipolar rotation that favors dipole alignment and can drive a bulk ferroelectric phase transition. As a result, unlike approaches centered on local structure, ferroelectricity emerges not in spite of the liquid nature, but because of it. Annealed averaging over positional disorder defines an effective dipolar interaction that is shorter-ranged than the bare potential. This is analogous to the Keesom interaction, where screening arises from annealed dipolar disorder. Derived within classical density functional theory, these findings are exact for dimensions d → ∞ and remain valid within the optimized cluster expansion for d ≥ 3.

In this paper, we concentrate on the superconvergence of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional nonlinear time-dependent fourth-order equations. The numerical flux for the nonlinear convection term is chosen as the generalized local Lax–Friedrichs flux, and the generalized alternating fluxes are employed for the fourth- and second-order terms, which are beneficial for long time simulations with a slower error growth due to the adjustable numerical viscosities. For nonlinear fourth-order equations with periodic boundary conditions, by using generalized Gauss–Radau projections, a modified projection and correction functions, we show a superconvergent bound for the interpolation errors. Then, by designing the numerical initial condition as an interpolation function of the third-order derivative, we derive supercloseness and thus superconvergence results, no matter whether the wind direction is fixed or not. Specifically, for polynomials of degree k, we obtain (2k+1)th order superconvergence for the numerical flux and cell averages, (k+2)th order superconvergence at generalized Radau points, and (k+1)th order for the error derivative at generalized Radau points, followed by a supercloseness result of order k+2 between the generalized Gauss–Radau projections and the numerical solutions. The superconvergence results are extended to the case with mixed boundary conditions when the wind direction is fixed. A series of numerical examples, including various boundary conditions and nonlinear terms, together with long time simulations, are provided to validate the theoretical results and demonstrate the effectiveness of the method.

This work examines conditionally convergent Coulomb lattice sums under periodic boundary conditions. The recently developed finite lattice sum cleanly decomposes the series into three distinct components: a periodic bulk term νpbc, a shape-dependent nonperiodic boundary term νb, and a finite-size correction term νcorr. This rigorous formulation explicitly parametrizes the geometry of a finite lattice by its exact shape and size and takes an effective pairwise form. We analyze it in detail and compare it with various derivations of lattice sums in the literature. Perspectives on future applications are discussed, including analytical developments for arbitrarily shaped crystals and numerical mesh-type algorithms for condensed matter simulations.

Predicting and controlling the optical response of dynamically evolving nanoarrays are crucial for advancing applications in sensing, photonics, and optoelectronics. Discrete dipole approximation (DDA) under periodic boundary conditions (PBCs) has been widely used, but it becomes prohibitively expensive for structurally evolving systems, as each structural or compositional change requires resolving a large electromagnetic problem. Recently, we introduced the rank-one decomposition DDA (RD-DDA) to accelerate the simulation for isolated nanostructures, and here, it is extended to periodic boundary conditions, establishing an efficient and accurate framework for modeling the optical behavior of nanoarrays with dynamically evolving lattice units. Using this RD-DDA-PBC framework, we continuously tracked the spectral evolution of plasmonic nanoarrays during etching and coating, capturing simulated intermediate configurations and associated transient spectral features that are difficult to sample efficiently with repeated full DDA-PBC calculations. By coupling RD-DDA-PBC with kinetic Monte Carlo (KMC) simulations, we investigated the etching kinetics of nanoarray structures under a localized electric field enhancement. Furthermore, integration with reinforcement learning (RL) enables inverse optical geometry design, allowing the autonomous generation of nanoarray structures with prescribed spectral features. Overall, this work establishes an efficient framework for updating periodic DDA calculations during lattice evolution and demonstrates its use in forward spectral tracking, coarse-grained field-biased KMC simulations, and the proof-of-concept inverse design of periodic nanoarrays.

Asphalt pavement is a critical component of transportation infrastructure, and the development of renewable bio-based modifiers offers a promising strategy for improving asphalt performance and sustainability. This research involved the synthesis of three asphalt modifiers (Oxa_1, Oxa_2, and Oxa_3) by regulating the molar ratio between epoxidized soybean oil (ESO) and methylenediphenyl diisocyanate (MDI). The relationship between the modifiers and asphalt properties was analyzed using molecular dynamics (MD) simulations and multi-scale experimental characterizations. The results indicate that the molecular structure of the modifiers significantly influences the performance of modified asphalt. The dual-arm Oxa_2 structure demonstrated the highest degree of physical entanglement and the lowest fractional free volume (FFV), attributable to its symmetrical comb-like configuration, which offers superior resistance to permanent deformation. In contrast, the three-arm star-shaped Oxa_3 enhanced cohesive energy density and complex modulus by introducing a higher density of polar oxazolidinone rings and MDI-derived groups, thereby promoting the formation of a stronger three-dimensional physical cross-linking network. Although Oxa_3 provided the most pronounced improvement in high-temperature stiffness, the single-arm Oxa_1 showed superior low-temperature stress relaxation owing to its higher FFV and greater chain flexibility. Finally, grey relational analysis (GRA) confirmed the close correlation between molecular descriptors and rheological indicators, demonstrating that the molecular architecture of ESO-MDI modifiers governs the multi-scale performance of modified asphalt. This study provides a theoretical basis for the molecular design of sustainable bio-based asphalt modifiers. METHODS: MD simulations were performed using Materials Studio with the COMPASS II force field. Van der Waals interactions were calculated using the atom-based method, while electrostatic interactions were treated using the Ewald summation method. Periodic boundary conditions were applied to eliminate boundary effects. Temperature and pressure were controlled using the Andersen thermostat and Berendsen barostat, respectively.

X-ray absorption near-edge structure (XANES) provides element-specific insights into local electronic and structural environments, but quantitative interpretation of molecular XANES under periodic boundary conditions (PBC) remains challenging due to finite-size effects and core-hole treatments. In this work, we systematically investigate how core-hole approximations and charge compensation schemes affect transition energies, energy alignment, and chemical-shift reproducibility in PBC-density functional theory-based molecular XANES calculations. Using ethane as a model system, we show that the full core-hole (FCH) approach exhibits a pronounced supercell-size dependence originating from interactions between background charge and charged molecules, with transition energies largely changed by leading-order finite-size terms. In contrast, the excited core-hole (XCH) method rapidly converges owing to its neutral final state. We further demonstrate that most finite-size effects in FCH can be removed by Makov-Payne corrections based on multipole expansion of the electrostatic energy of charged supercells under PBC. Furthermore, we propose a simple Fermi-level-based energy correction (EF/2) that provides comparable improvement using only a single supercell. Extending the analysis to an n-alkane series reveals that while intrinsic electronic-structure changes govern peak shifts for small molecules, systematic energy drifts persist in FCH for larger molecules, whereas XCH and FCH + EF/2 remain stable. Finally, for small molecules at the C and N K-edges, XCH and FCH + EF/2 accurately reproduce experimental chemical shifts, whereas uncorrected FCH fails. These results provide practical guidelines for reliable energy alignment and chemical-shift analysis in molecular XANES under PBC, supporting robust applications to molecular, adsorption, and interfacial systems.

Standard periodic boundary conditions (PBC) impose a toroidal topology on simulation domains. While geometrically flat, this topology allows for coherent reentrant self-interactions that preserve spurious long-range temporal correlations. We show that these topological artifacts manifest as strong, lattice-aligned anisotropy in collective dynamic observables, rendering scalar relaxation rates direction-dependent even at near-particle length scales, thereby violating the static-dynamic correspondence of isotropic liquids (de Gennes narrowing). To resolve this, we introduce Spherical Boundary Conditions (SBC), a topological framework that replaces the periodic torus with a mixing quotient space. SBC is defined by a radial folding map coupled to a boundary remapping driven by deterministic chaos. This construction effectively acts as a measure-preserving information filter: it preserves thermodynamic conservation laws, while suppressing the Lagrangian memory responsible for periodic artifacts. Using Brownian dynamics simulations, we demonstrate that SBC eliminates lattice-aligned anisotropy by construction, recovering isotropic static and dynamic correlations and effectively restoring the ergodicity and static-dynamic correspondence of the infinite bulk limit on a finite support.

Abstract For solids and structures composed of architected metamaterials, detailed micro-level numerical modeling becomes a critical bottleneck due to both memory and processor requirements. For periodic metamaterials, computational homogenisation provides an attractive alternative, whereas multi-scale continuum theories provide an appropriate framework for capturing size effects stemming from the metamaterial architecture. This article focuses on asymptotic computational homogenisation for three-dimensional strain-gradient elasticity (SGE) by assessing its numerical performance for periodic unit cells. After revisiting the variational formulation of SGE, the derivation of homogenised fourth- and sixth-order elasticity tensors is accomplished, leading to solving micro-level corrector problems with periodic boundary conditions. Regarding verification of the corresponding numerical implementation, two stabilisation strategies are assessed: a global-constraint formulation and a Tikhonov regularisation—the latter avoids additional Lagrange multipliers and turns out to be both efficient and stable. The workflow is implemented by combining the finite element software COMSOL with MATLAB LiveLink for obtaining the homogenised (meta)material tensors. As a virtual validation phase, the homogenised constitutive tensors are involved in three-dimensional SGE simulations to solve macroscopic boundary-value problems of lattice structures via isogeometric analysis. This phase is accomplished within the open-source GeoPDEs-software via user-defined subroutines developed for SGE to obtain conforming Galerkin approximations. Verification and validation for the homogenisation approach cover p - and h -convergence studies, mesh-type comparisons between hexahedral and tetrahedral elements, sensitivity to unit-cell volume fraction, and a comparison between the global-constraint formulation and the Tikhonov regularisation. Results show that higher-order basis functions essentially accelerate convergence, mesh type differences become negligible for sufficiently rich approximation spaces, and gradient moduli peak at an intermediate range of volume fractions. Simulations for cantilever lattice beams confirm that SGE predicts bending deflections more accurately than classical elasticity due to the size effect phenomenon present in bending and shear deformations.

Flat bands exhibit vanishing group velocity and marked sensitivity to lattice geometry, making them a useful setting for studying localization driven by destructive interference. In this work, electrical-circuit simulations are employed to investigate flat-band systems in one, two, and three dimensions. A one-dimensional two-band circuit is first considered, and its flat-band response is characterized through node-to-ground impedance spectra and steady-state voltage distributions. The analysis is then extended to two- and three-dimensional Lieb lattice circuits characterized by sublattice imbalance. In the two-dimensional Lieb circuit, the flat band touches the dispersive bands at a Dirac point, so hybridization with dispersive modes affects the observed localization. Under periodic boundary conditions, wave vector quantization also produces responses that depend on whether the number of unit cells is even or odd. By contrast, in the three-dimensional Lieb circuit, the flat band is spectrally isolated from the dispersive bands, allowing stronger spatial confinement and clearer sublattice selectivity. The one-dimensional, two-dimensional, and three-dimensional models therefore represent three different situations: a singular flat band, a flat band that touches dispersive bands, and a spectrally isolated flat band. Comparing these cases shows how different degeneracy conditions shape impedance responses and localization patterns in electrical circuit systems. At the flat band frequency, the localized voltage response can also be used to generate spatial patterns in both two-dimensional and three-dimensional circuits, pointing to a possible route for spatial mode control of compact localized states in electrical systems.

We develop a high-order space-time spectral method for nonlinear convection–diffusion equations with a Riemann–Liouville time-fractional derivative and a spectrally defined space-fractional Laplacian. The spatial discretization uses a Fourier spectral method that diagonalizes the fractional Laplacian under periodic boundary conditions. The temporal discretization employs a Petrov–Galerkin method based on generalized Jacobi functions which capture the initial singularity exactly. The nonlinear convection term is treated pseudo-spectrally, and the resulting algebraic system is solved with a damped Newton iteration. Rigorous error analysis proves exponential convergence in both space and time. Numerical experiments for various fractional orders confirm the spectral accuracy. Simulations of the fractional Burgers equation demonstrate that increasing the viscosity enhances diffusion and stabilizes the solution, while a nonlinear coefficient that significantly exceeds the viscosity leads to error growth over long time intervals. The method provides an efficient and accurate tool for simulating anomalous transport phenomena.

A graphene-integrated refractory metasurface absorber is proposed for broadband solar thermal energy conversion. Near-unity broadband absorptance across 300–2500 nm is achieved through three concurrent mechanisms: free-space impedance matching, ground-plane-mediated transmission suppression, and multimodal electromagnetic energy dissipation distributed across spectrally coupled plasmonic and dielectric resonant channels. Spectral tunability without structural reconfiguration is demonstrated through electrostatic modulation of the graphene Fermi level, which enables reversible control of the optical sheet conductivity. Alternative material configurations incorporating caesium, gallium arsenide, copper, and strontium are evaluated through full-wave COMSOL Multiphysics simulations under periodic boundary conditions, with assessment of spectral bandwidth, resonance behaviour, and thermal robustness at elevated temperatures. A dielectric substrate thickness of approximately 4.1 μm satisfies the quarter-wavelength Fabry-Perot cavity resonance condition, suppressing mid-infrared radiative emission and reducing parasitic thermal losses. A random forest regression surrogate model trained on 1,200 finite-element simulation samples, with five geometric and material input parameters and 500 estimators, maps the design space with R2 > 0.90 across most parameter configurations. Accuracy decreases to R2 approximately 0.63 near normal incidence, where overlapping resonances increase spectral complexity. The optimised configuration achieves a peak absorptance of 99.99% and a broadband solar-weighted average of 98.6%.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-026-51399-w.

We develop a quantitative framework to determine the minimal periodic supercell required for representative simulations of capillarity-screened Darcy flow in stationary random, polydisperse granular media. The microstructure is characterized by two-point statistics (covariance and spectral density) that govern finite-size fluctuations. Capillarity is modeled as a screened, modified-Helmholtz problem with phase-dependent transport under periodic boundary conditions; periodic homogenization yields an apparent conductivity, an apparent screening parameter, and a macroscopic capillary decay length. Because screening imparts a spatial low-pass response, we introduce a distribution-aware treatment of polydispersity consisting of a capillarity-weighted volume fraction and a screened analog of the integral range that preserves variance units and recovers classical descriptors in the appropriate limits. These descriptors lead to two sizing rules: (i) a length criterion on the shortest cell edge controlled by a microstructural correlation length, the macroscopic decay length, and a high quantile of grain size; and (ii) a volume criterion that links the target coefficient of variation to the screened integral range and the phase contrast. The framework couples statistical microstructure information to capillary response and yields reproducible, distribution-aware supercell selection for image-based finite-element or fast-Fourier-transform solvers. The resulting criteria are therefore intended for representativity of the coarse-grained screened response, rather than for isolated nonlinear pore-scale events.

The special quasirandom structure (SQS) method is widely used for modeling disordered materials under periodic boundary conditions, with the ATAT mcsqs module being one of the most established implementations. However, SQS generation with mcsqs typically relies on manual preparation of input files, ad hoc execution scripts, and post-processing steps, which introduces user-dependent errors and limits reproducibility. Here, we present SimplySQS ( https://simplysqs.com ), an automated and reproducible workflow for SQS generation that is delivered through an online, interactive interface. SimplySQS guides users through structure import, compositional and supercell definition, and cluster parameter selection, while automatically generating all required ATAT input files and a single all-in-one execution script that encapsulates the complete search process. By standardizing input preparation, execution, and output analysis, the framework minimizes errors associated with manual file handling and enables consistent reproducibility of SQS searches. The workflow is demonstrated on the Pb 1- x Sr x TiO 3 (PSTO, including PbTiO 3 (PTO) and SrTiO 3 (STO)) perovskite system. SQSs spanning the entire concentration range were generated using a single automated bash script produced by SimplySQS , after which all resulting structures were subjected to geometry optimization using a universal machine-learning interatomic potential (MACE MATPES-r²SCAN-0). This approach reliably reproduced the experimentally observed cubic-to-tetragonal transition near x ≈ 0.5, with lattice parameters deviating by less than 1% in the cubic region ( x > 0.5) and less than 4% in the tetragonal region ( x ≤ 0.5). Overall, SimplySQS transforms SQS generation with ATAT into an intuitive, reproducible, and systematic framework for modeling disordered materials.

Digital quantum matter-realized when discrete quantum gates approximate continuous time evolution-is susceptible to heating into chaotic, structureless states1. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics2-7 can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviours observed in equilibrium systems, ranging from the non-trivial microscopic origins of thermalization itself8 to the stabilization of effective models hosting exotic emergent properties. Here we use Quantinuum's H2 quantum computer9,10 to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics owing to approximate energy conservation and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration11-13. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of 99.94(1)%) and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.

• Novel pseudo-periodic boundary condition accounts for sintering shrinkage. • Surface artifacts are eliminated in phase-field simulations on a fixed grid. • Bulk behavior is reproduced with ∼300 particles, vs 7000 conventionally. • High-accuracy microstructure prediction is achieved at low computational cost. Numerical simulation of sintering is essential for predicting microstructures and defects. However, applying periodic boundary conditions remains a challenge because sintering involves volumetric shrinkage due to densification. As a result, conventional methods require large-scale simulations to mitigate surface effects and capture bulk behavior, posing significant challenges in terms of computational cost and accuracy. In this study, we propose a novel pseudo-periodic boundary condition (PPBC) that simultaneously accounts for shrinkage and eliminates surface artifacts in multi-phase-field sintering simulations. By applying this approach to particles regularly arranged in one- and three-dimensional arrays, we demonstrate that the PPBC successfully reproduces bulk behavior independent of the boundary constraints. Furthermore, simulations with varying domain sizes reveal that the PPBC is highly effective in reducing the computational cost required to predict key microstructural parameters. The proposed method is expected to significantly contribute to the accurate prediction and control of sintered microstructures.

The electron-phonon/vibration interaction is crucial for electronic structures of solids and molecules, such as governing superconductivity and modifying band structures. While the Allen-Heine-Cardona (AHC) theory is widely used for evaluating phonon-induced band renormalization in periodic systems, it has not been rigorously assessed for molecular systems. Previous AHC-based studies of molecular systems are predominantly based on plane-wave basis sets under periodic boundary conditions. In this work, we implement the AHC theory with different levels of approximation for molecular systems by employing a full-potential all-electron framework with an atomic orbital basis and explicitly including Pulay corrections in the electron-vibration matrix elements. Our results indicate that both adiabatic and non-adiabatic formulations of the AHC theory can become unreliable for molecular systems, suggesting that an accurate description of the vibronic renormalization requires the explicit evaluation of electron-vibration self-energy. We further introduce the G0W0 approximation to the electronic self-energy to incorporate the many-body electronic effects. The agreement between computed vibronic spectral functions and experimental photoemission spectroscopy supports the proposed methodology. This work applies and implements first-principles electron-vibration renormalization in molecules while offering insights into understanding the role of many-body effects in phonon-induced band renormalization for periodic systems.

Driven nonequilibrium lattice models have wide-ranging applications in contexts such as mass transport, traffic flow, and transport in biological systems. In this work, we investigate the steady-state properties of a one-dimensional lattice system that allows multiple particle occupancy on each site. The particles undergo stochastic nearest-neighbor jumps influenced by both a directional bias and on-site repulsive interactions of the Bose-Hubbard type. With periodic boundary conditions, we observe a nonmonotonic dependence of intersite correlation functions on the interaction strength. At large interaction strengths, the state consists of quiescent stacks of stationary particles along with an emergent asymmetric simple exclusion process, and the particle current exhibits a periodic dependence on density. In contrast, with open boundary conditions, the system displays steplike density profiles reminiscent of those in tilted Bose-Hubbard systems, and a regime with a macroscopic number of empty sites followed by a steep parameter-dependent increase in density. Our results highlight how the interplay between drive, interaction, and boundary conditions leads to distinctive signatures on the current and density profiles in the steady state in different regimes.

Hexamethyldisilane (HMDS) serves as a critical single-source precursor for the chemical vapor deposition (CVD) of silicon carbide (SiC), yet its atomic-level pyrolysis mechanism and the kinetics of radical generation remain unclear. This study investigates the thermal decomposition behavior of HMDS to provide theoretical guidance for optimizing SiC deposition processes. The results demonstrate that HMDS pyrolysis follows first-order kinetics with an apparent activation energy of 44.47 kcal/mol, a value significantly lower than the theoretical dissociation energy of the Si-Si bond. By combining this kinetic data with reaction pathway analysis, it is concluded that the decomposition is governed by a multistep cooperative mechanism rather than simple homolytic bond cleavage. The reaction proceeds through three distinct stages: initial precursor decomposition dominated by C-Si bond dissociation, secondary reactions of intermediates involving cascading demethylation, and small-molecule formation accompanied by radical recombination. Methyl radicals (CH3) are identified as the primary chain carriers, which are ultimately converted into thermodynamically stable methane (CH4) via hydrogen abstraction. Furthermore, temperature is found to critically regulate the generation and accumulation behavior of CH3 radicals. Density functional theory (DFT) calculations were carried out with Gaussian 16 at the unrestricted ωB97XD/6-311G(d,p) level to optimize geometries and train the force field. A broken-symmetry strategy with guess = (mix,always) and nosymm was adopted to reliably describe bond dissociation and radical behaviors. Using the high-quality DFT data, the ReaxFF force field was further optimized. Reactive molecular dynamics simulations were then performed in LAMMPS with the optimized potential under the NVT ensemble at 2500-4000K with a 0.1-fs time step. A cubic box with 100 HMDS molecules and periodic boundary conditions was adopted, and each condition was run three times for statistical reliability.

Aiming at the problems of cumbersome parameter tuning and low computational efficiency in traditional methods for the bandgap optimization of periodic thin-walled stiffened coupled structures, this paper integrates the null-space method with the Kirchhoff thin-plate theory to establish an efficient model for bandgap analysis. The proposed method realizes matrix-based construction of coupled and periodic boundary conditions, decouples boundary constraints from displacement shape functions, avoids the limitations of virtual spring stiffness, and requires no remeshing during parameter variation. Comparisons with the finite element method verify its convergence and accuracy: the average deviation of bandgap widths in the 0–250 Hz range is 0.37 Hz, and the computational efficiency is about 2.5 times that of FEM(Finite Element Method). This paper also systematically analyzes the effects of four key parameters, including thin-wall thickness, stiffener thickness, stiffener height and stiffener spacing, on the number and width of bandgaps and proposes targeted optimization strategies for different engineering scenarios. The results provide a new method for vibration and noise reduction design of such structures and lay a foundation for future bandgap modeling and optimization of advanced lightweight periodic structures.